ABSTRACT Title Of Disertation: THE USE OF VARIABLE CELESTIAL X-RAY SOURCES FOR SPACECRAFT NAVIGATION Suneel Ismail Sheikh Doctor of Philosophy, 2005 Disertation Directed By: Profesor Daryll J. Pines Department of Aerospace Engineering University of Maryland Acurate control and guidance of spacecraft require continuous high performance thre-dimensional navigation solutions. Celestial sources that produce fixed radiation have demonstrated benefits for determining location near Earth and vehicle atitude. Many interplanetary navigation solutions have also relied on Earth-based radio telescope observations and substantial ground procesing. This disertation investigates the use of variable celestial sources to compute an acurate navigation solution for autonomous spacecraft operation and presents new methodologies for determining time, atitude, position, and velocity. A catalogue of X- ray emiting variable sources has been compiled to identify those that exhibit characteristics conducive to navigation. Many of these sources emit periodic signals that are stable and predictable, and al are located at vast distances such that the signal visibility is available throughout the solar system and beyond. An important subset of these sources is pulsar stars. Pulsars are rapidly rotating neutron stars, which generate pulsed radiation throughout the electromagnetic spectrum with periods ranging from miliseconds to thousands of seconds. A detailed analysis of several X-ray pulsars is presented to quantify expected spacecraft range acuracy based upon the source properties, observation times, and X-ray photon detector parameters. High acuracy time transformation equations are developed, which include important general relativistic corrections. Using methods that compare measured and predicted pulse time of arival within an inertial frame, approaches are presented to determine absolute and relative position, as wel as corrections to estimated solutions. A recursive extended Kalman filter design is developed to incorporate the spacecraft dynamics and pulsar-based range measurements. Simulation results demonstrate that absolute position determination depends on the acuracy of the pulse phase measurements and initial solutions within several tens of kilometers are achievable. The delta-corection method can improve this position solution to within 100 m MRSE and velocity to within 10 m/s RMS using observations of 500 s and a 1-m 2 detector. Comparisons to recorded flight data obtained from Earth-orbiting X- ray astrophysics misions are also presented. Results indicate that the pulsed radiation from variable celestial X-ray sources presents a significant opportunity for developing a new clas of navigation system for autonomous spacecraft operation. THE USE OF VARIABLE CELESTIAL X-RAY SOURCES FOR SPACECRAFT NAVIGATION By Suneel Ismail Sheikh Disertation submited to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfilment of the requirements for the degre of Doctor of Philosophy 2005 Advisory Commite: Profesor Daryll J. Pines, Chair Asociate Profesor David L. Akin Dr. N. Glenn Creamer Dr. Robert A. Nelson Profesor John E. Osborn Asistant Profesor Benjamin Shapiro ? Copyright by Suneel Ismail Sheikh 2005 i Dedication I dedicate this disertation and its research to those who have gone on before me and had such a great influence on al that I have done. My Dad: Dr. Hyder Ismail Sheikh (FRCS) My Grandparents: Haji Ismail Ibrahim Sheikh (Bhaisaheb) James and Annie Duncan Mae and George Waler My Grandparents-In-Law: Ela Gahler Walace Thul My Grandparents-In-Friends: Robert and Loraine Rowe I also dedicate this disertation to the two women who have given me life and made it worth living. My Mum: Joan Mary Duncan Sheikh Bauder My Wife: Kristen Louise Thul Sheikh ii Acknowledgements ?If I have sen further than others, it is by standing upon the shoulders of giants.? ? Isac Newton 1675 For anyone as fortunate as I am to have reached this point in life, you realize it could only have been done by the support, love, and friendship of many people. Although everyone we met during our lives influences us in some manner, some do more than others. Some shape our lives, others enrich it. From some, we have so many great memories we could never forget them, while others, unfortunately, I could not forget if I tried. It is therefore with great respect and admiration (and yes, a litle bit of fun) I acknowledge the persons below who have contributed significantly to my life experience. Yes, the list is long, but for this I fel privileged. Many more could be added and to those I say, ?thank you?. To my Mom, Joan, who has provided me so much. Her biggest gifts were the fredom to explore and learn al that I could, and the encouragement to chase after my dreams. During al this, she has always been there to support me whenever I felt too low to cary on. Her own life lesons for me were always the most influential. Her love for my father and stories about him only make me wish we al could have known him longer. It is his succes and struggles through life that have delivered me to this point in my life. To my brothers and sisters, who gave me my fondest memories and inspirations: My big sister, Nena, you have been an incredible inspiration to me through al you have acomplished in your chalenging life. For those of you who have had the pleasure of iv arguing with an older sister, you know that you always lose. Brady Bunch vs. Star Trek, the batle continues? But I was ?alowed? to se enough of my shows that it kept me wanting more. Maybe this drove my interest in space, since I never knew when I would get a chance to se it. To my brother, Kiran, it was al those play times in our youth, and not so youth, that shaped me today. Launches in the rocket house, cutting lawns, fixing Karmann Ghias and Suzukis, al our adventures, they al taught me. A great brother to us al. To my younger sister, Tifani, I wil always remember that bright blonde hair chasing after ?squeels?, singing to the Muppets, and giggling. Your pasion to help others has impresed us al. To my youngest brother Courtney, the most mischievous one: throwing snowbals at cars when you couldn?t even se over the snow bank, climbing the camel hils, playing soccer, and watching the Packers. Your globetrotting has made us al envious, but very proud. To my newest brother, Scott, for al the enjoyable Mac OS and Packers talk and ideas. To my upcoming new sister, Heather, buckle up, you are in for one hel of a ride! To the new generation of our family: Tianna, it has been wonderful watching you grow into a beautiful young woman, literaly from the day you were born. I always enjoy hearing what you are up to next. To Seth and Zach, those two smiling bundles I met wearing matching baby tuxedo outfits, ?and the bal poppas loose?! To Chanel, originaly the quiet one, but now is the loudest with your pasion and goals for the future. Graham, who has astounded us al with his drawing skils and knowledge of cars and computers, I am looking forward to riding in one of your designs that Seth and Zach have built! And to Duncan, our newest, welcome to our family and I wil definitely have some secrets about your Mum when you are ready! v To my ?newer? family: Tom, Janet, and Amy Thul, and of course, Nanny (Ela Gahler) and Grandpa (Waly Thul). You welcomed me into your family with big open arms, and helped us so much while we were here. I am most thankful to you for leting me take your daughter and sister away for a while. Can?t wait for al the family RV trips. To my family in England: Eric, Pearl, Theresa, John, Yvonne, Mario, Alexandra, and Horatio. Thank you for al the great memories and potential dreams of another life. Of course, I must include Hazel and Myles Jackson as our extended family, for al the times they took care of us after our long journeys. To my family in India: Al my father?s sisters and their families, I wish we knew each other beter. Haider Noorani and family, a great friend of my father?s, who has always kept in touch. Also, Uncle Razak (Bom-Bom) for giving us a piece of my father?s history. To my friends at a young age across the globe: My Edmonton pals, including Ian Leonard, Scott McKerchar, Kate Rogers, and the Coulters. To my Reading pals, including Chris Hiester, Peter Cres, David Solinger, Gary Miler, Eddie Brown, the Taylor gang, and Anna Mae Adams. To al my Gren Bay pals on Rowe Lane (what a crew!). To Chris Schultz, who became a life long friend (wil you ever eat another popsicle?). Al your friendships and memories have supported me through this journey. Many of my early teachers were incredibly influential in my beginning years. To Mrs. Lines, Mrs. Grainger, and Mrs. Priebe, who helped me through some dificult times. To Mr. Bruce Gehret, whose gift of a globe of the Earth has always helped keep the world around me in perspective. Who could forget those pants that (Crazy) Ray Greisinger wore for physics and chemistry? He knew we were laughing, but surprisingly we were al stil paying atention. Or Jef Parish?s red eyes ? yeah, he was ?tired?. Or how about al the vi stories of bears by Peter Bonkowski? Never again was Calculus as interesting. My language teachers of Ginny Giguere and Mary Schwartz. I learned that writing could take you places you may never go but can stil imagine. My guidance counselor, Marlyn Gilbert, who also enjoyed woodworking and was always so encouraging. He was as depresed at losing those scholarships as I was. To Russ Holdiman, a realy great man who understood wood like no one else, and the antics of young boys in shop clas. When are we going parachuting? Thanks for al you taught me and for being a friend to us al. To my profesors at University of Minnesota, including Chester Miracle and George Brauer (red tongue and ?what is infinity like??). This is where I learned the most. To al my friends in my early college years, especialy Stuart Bale, Philip Price, Chris Sietz, Lary Leon, Sean McName, Neil Simons, Jay Larson, Jason Hinze, and the whole third floor ?Tower? and ?Reno? friends. My, those were formative years. To Joe Walerius, I shared lots of laughter and fun with his brothers and family. Thanks for al the rides to and from Gren Bay. You also taught me that its ok to go backwards for a while once you?ve reached your limit, and this is not such a bad thing, could be the smartest move you ever make! To John Siebenshuh, memories of listening to music late at night for Mechanical drawing, the long drive to CA, and lots of Mountain Dew. You taught me that I should enjoy life, and one can never have enough electronics (?I?ve got to have more wats!?). We met the night of freshman orientation, man those people dancing were hosers (Joe, we?re looking your way). To David Schnorenberg, watching you work you?re a** of and stil get up at 4 am, just so you could make your dreams come true. Always wondered how hard one could kick Pumpkinhead?s door without being expeled ? it helps being the teacher?s pet! Who wil move across the country next? vii To the Stanford ?B? Team: John Siebenshuh, Greg Augenstein, David Schleicher, Jery Yen, and Daryl Kabashigawa. You are al on my ?A? list ? 8). Also to my lab and homework partners, Mike Prior and Clark Cohen, couldn?t have done it without you. You al told me the PhD wasn?t worth it ? can?t say you are al wrong, but glad you convinced me not go back to our alma mater. To Dave Wahlstedt and al the woebegone members of ?Dave?s House for WE?, including Paul Felix (?1 st Ave. Man!?), Chris Okey, Craig, Carleton, and Vance. Robes were always at 8:00. Stil remains the longest time I ever spent in one house my whole life. Also to the Sunday morning footbal crew ? on those fields I learned one can never play enough sports, watch sports, or start fantasy games about sports. To my traveling partners and oh, so many wild nights: Michael Caroll, Misy Fisher, Lori Sorensen, Ada Farnel, and Jody Sorensen. Good times ? To Alex Case and Paul Samanant. Much wisdom imparted with large quantities of libation. The thre of us hit almost every Sexorama night there ever was. Too much fun. Glad Honeywel never found out we went out five nights a wek! To al my Honeywel co-workers, many who became good friends, Mario Ignagni (taught me so much about Kalman filters), Lary Valot (stil one of the brightest persons I know), Scott Snyder (hey, Tom Cruise? ? 8), Erik Lindquist (late night comrade), Tony Case (Tetris anyone?), Bil Volna (?Can I borrow your camera??), Alan Touchbery, Mahesh Jerage, Brian Schipper, Jennifer Sly, Rich Olson, Ron Quinn, Valerie McKay, Dave Lowry, and al the members of the Navigation section and those in MN, FL, AZ, and NM. To my friend Tricia Syke, who was always there to help me get through tough times by making me laugh at something crazy (moo!). vii A big thanks goes to Jef Dinsmore, the best flight instructor, and the Honeywel Flying Club. Learning to fly has only deepened my interest in engineering. To Holly Paige, thanks for keeping Kristen busy while I was always gone. Our house and lawn have always appreciated your care. To John Drake for helping us fix our house up. To our renters, thanks for helping us over the years. To our neighbors, Janet, Fred, Greg, Stephanie, Ed, Richard, and the Hernandez family (?the Christo-kids?), who made lots of many interesting memories. To the Space Systems Laboratory, including David Akin (thanks for the office and the advice!), Mary Bowden, Ela Atkins, and Rob Sanner (you taught me so much). I would not have made it here without the support and friendship of my peers in the lab: Craig Carignan, Sarah Hal, Dave Hart, Glen Henshaw, Mike Perna, Brian Roberts, Stephen Roderick, Brook Sullivan, and al the rest. Kejoo Le and al the felow students in the Manufacturing building made graduate life completely tolerable. My Teaching Asistant buddies: Joe Schultz (Go Packers! Beat the Vikings!), Ryan Le (who went through hel during our time together, but came out the other side a beter man), Igor Alonso-Portilo (who could ever forget this smiling character?), and Marc Gervais (I stil hear Igor weping). To my study partner, Jim Simpson, who got me through a lot of long homeworks. Thanks for al the friendship you have shown over these years, making Kristen and I fel at home. To Ken Walace, who inspired us al with his flights at Top Gun ? you are our Ace, and I wish we could have done more research together. To Yannick Pennecot, Sylvan (Woody), Maria Ribera, and Ramon. Igor and Yannick never ceased to keep me from laughing at their antics (if Ela only knew ?). ix To my footbal buddies at Maryland: Falcon Rankins, Ashish Purekar, Karthikeyan Duraisamy (?Super Safety?), Sean Guera, Michel Santos, Michael Brigley, and al the rest. Was a great break from the research routine. Glad we did it for Swami. Also to the Engineering Graduate Student Council: it has been an honor and a privilege to work with al of you. Kep up the great work! Special thanks go to al in the Aerospace Engineering Department, who have helped me along in many simple and a few dificult situations, including Bryan Hil (always full of good advice ? at least ?full? of something ?), Patricia Baker (who is realy kind to Kristen and I and always interested about our personal lives here in Maryland ? a great ?mother? figure to al us displaced students), Becky Sarni, Debora Chandler, and al. I owe a lot of my succes here at Maryland to Dr. Wiliam Fourney, our Department Chairman. He has been a friend, mentor, and sage my entire time here. I am grateful for al he has done for me, which is quite a lot. Thanks for encouraging me al along the way. To my friends and colleagues at the Naval Research Laboratory, who collaborated in much of this research, Kent Wood, Paul Ray, Michael Wolf, Michael Lovelete, Zachary (Wiz) Fewtrel, Jon Determan, Daryl Yentis, and Lev Titarchuk. I realy owe a large debt of gratitude to Kent Wood for giving us the opportunity to investigate pulsars and navigation with his USA experiment data. Paul taught me everything I know about X-ray pulsars, and I never could have done it without his help. I must also thank Liam Healy for al his orbit determination help, Glenn Creamer for his helpful filtering discussions, and Robert Nelson for his enlightening insights on relativity. Much of this research would never have been acomplished without the astronomers and astrophysicists who tirelesly observed these sources and discovered their unique x characteristics. I realy appreciate the helpful discussions from David Nice, Saul Rappaport, Christopher Reynolds, Cole Miler, Charles Misner, and Depto Chakrabarty during my studies. Yong Kim?s early work catapulted my cataloguing eforts. We were able to survive through this research with the significant contributions of the Metropolitan Washington DC Chapter of the ARCS Foundation. We enjoyed meting al the members and their curious nature, on science and our lives. My work succeded through the wonderful contributions of Dr. Edna Hokenson. She has turned her sacrifice into something realy special. It has been an honor to be awarded the grant in Gus? name. We wil al mis her lovely smile, laugh, and thoughts on life. To my advisor, Daryll Pines, who took a chance on a lonely, frustrated soul. Tremendous amounts of encouragement, support, and friendship don?t even begin to describe al that you have given me. My future wil always be bright after al you taught me. Realy enjoyed al the late evening discussions, surprisingly litle about our research. Don?t ever let your ?creative energy? become extinguished. And of course most importantly, to my beautiful wife, Kristen. Thank you for everything only starts to expres what you have provided. I could not have ever made it without you here to share the joys and frustrations. The experience was worth it al, especialy having my best friend beside me. Looking forward to a wonderful long future together ? where are we of to next? And lastly, to al those slogging at their research late at night while al their buddies are out drinking. Kep it up, and take a break when you have to. Remember the journey itself is the reward. xi Table of Contents Dedication...............................................................................i Acknowledgements.......................................................................ii Table of Contents........................................................................xi List of Tables............................................................................xv List of Figures.........................................................................xvi List of Abreviations....................................................................xix Chapter 1 Introduction..................................................................1 1.1 MOTIVATION......................................................................1 1.1.1 Navigation on Earth............................................................2 1.1.2 Navigation in Space............................................................5 1.1.3 Future Space Navigation Architectures...........................................15 1.2 PREVIOUS RESEARCH..............................................................18 1.2.1 Variable Celestial Sources......................................................18 1.2.2 History of Pulsar-Based Navigation..............................................20 1.3 OVERVIEW OF CONTRIBUTIONS......................................................24 1.4 DISSERTATION OVERVIEW..........................................................26 Chapter 2 Variable Celestial Sources.....................................................30 2.1 VARIABLE INTENSITY SOURCES......................................................30 2.1.1 Variation Physics.............................................................32 2.1.2 Source Types Conducive to Navigation............................................34 2.1.3 Variable Source Radiation......................................................35 2.1.4 Radio and Visible Sources......................................................38 2.2 VARIABLE CELESTIAL X-RAY SOURCES................................................41 2.2.1 X-ray Source Types............................................................41 2.2.2 X-ray Pulsars................................................................45 2.2.3 Navigation Chalenges with X-ray Sources........................................51 2.3 X-RAY SOURCE CATALOGUE........................................................54 2.3.1 X-ray Source Survey Misions...................................................5 2.3.2 Selection of Sources...........................................................5 2.3.3 X-ray Catalogue Parameters....................................................59 2.3.4 X-ray Catalogue Data Characteristics............................................65 Chapter 3 Pulse Identification, Characterization, and Modeling.............................86 3.1 PULSE PROFILE...................................................................87 3.1.1 Photon Detection and Timing...................................................87 3.1.2 Profile Creation..............................................................89 3.1.3 Pulse Arival Time Measurement................................................91 3.2 PULSE TIMING MODELS.............................................................95 3.2.1 Frequency and Period Forms of Models...........................................96 3.2.2 Pulsar Timing Stability.........................................................98 3.3 PULSE ARRIVAL TIME MEASUREMENT ACCURACY......................................101 3.3.1 Pulse Profile Fourier Transform Analysis........................................102 3.3.2 SNR From Source Characteristics Analysis.......................................103 3.3.3 X-ray Source Figure of Merit...................................................17 3.3.4 Source Selection Criteria......................................................19 3.4 ARRIVAL TIME COMPARISON.......................................................121 xii 3.4.1 TOA Comparison Discusion...................................................124 Chapter 4 Time Transformation and Time of Arival Analysis.............................129 4.1 INERTIAL CORDINATE REFERENCE SYSTEMS.........................................130 4.1.1 Parameterized Post-Newtonian Frame...........................................130 4.1.2 Solar System Barycenter Frame................................................130 4.1.3 Terestrial Time Standards....................................................131 4.2 PROPER TIME TO CORDINATE TIME.................................................132 4.2.1 Spacetime Interval...........................................................13 4.2.2 Near-Earth Mision Aplications...............................................136 4.2.3 Interplanetary Mision Aplications.............................................137 4.3 TIME TRANSFER TO SOLAR SYSTEM BARYCENTER......................................138 4.3.1 First Order Time Transfer.....................................................139 4.3.2 Higher Order Time Transfer...................................................142 4.3.3 Pulse Arival Time Comparison Sumary........................................153 4.4 PULSAR TIMING ANALYSIS EQUATIONS...............................................154 Chapter 5 Variable Celestial Source-Based Navigation.....................................159 5.1 NAVIGATION....................................................................159 5.2 TIME DETERMINATION............................................................161 5.3 ATITUDE DETERMINATION........................................................163 5.4 VELOCITY DETERMINATION........................................................165 5.5 POSITION DETERMINATION.........................................................167 5.5.1 Source Ocultation Method....................................................168 5.5.2 Source Elevation Method......................................................170 5.5.3 Absolute Position Determination................................................172 5.5.4 Relative Position Determination................................................173 5.5.5 Delta-Corection To Position Solution...........................................174 5.6 VARIABLE CELESTIAL SOURCE-BASED NAVIGATION SYSTEM DESCRIPTION.................175 Chapter 6 Absolute and Relative Position Determination...................................180 6.1 DESCRIPTION....................................................................180 6.2 OBSERVABLES AND ERRORS........................................................186 6.2.1 Range Measurement..........................................................186 6.2.2 Phase Measurement..........................................................190 6.2.3 Pulse Arival Time Determination...............................................192 6.3 MEASUREMENT DIFFERENCES......................................................19 6.3.1 Single Diference.............................................................202 6.3.2 Double Diference............................................................210 6.3.3 Triple Diference.............................................................217 6.3.4 Velocity Measurement........................................................219 6.4 SEARCH SPACE AND CYCLE AMBIGUITY RESOLUTION...................................20 6.4.1 Search Space................................................................22 6.4.2 Cycle Candidates............................................................26 6.4.3 Cycle Ambiguity Resolution....................................................28 6.5 RELATIVE POSITION...............................................................238 6.5.1 Vehicle Atitude Determination.................................................240 6.6 SOLUTION ACCURACY.............................................................242 6.6.1 Position Covariance..........................................................242 6.6.2 Geometric Dilution of Precision................................................246 6.7 NUMERICAL SIMULATION..........................................................249 6.7.1 Simulation Description........................................................249 6.7.2 Simulation Results............................................................253 Chapter 7 Delta-Corection of Position Estimate..........................................259 7.1 CONCEPT DESCRIPTION............................................................259 xii 7.1.1 Estimated Position...........................................................259 7.1.2 Algorithms..................................................................261 7.2 EXPERIMENTAL VALIDATION OF METHOD.............................................275 7.2.1 USA Experiment Description...................................................275 7.2.2 USA Detector Crab Pulsar Observations.........................................276 7.2.3 Delta-Position Truth Comparisons..............................................278 Chapter 8 Recursive Estimation of Position and Velocity...................................281 8.1 KALMAN FILTER DYNAMICS........................................................282 8.1.1 Spacecraft Orbit Navigation States..............................................282 8.1.2 Orbit State Transition Matrix...................................................291 8.1.3 Covariance Matrix Dynamics..................................................29 8.2 KALMAN FILTER EASUREMENT MODELS............................................30 8.2.1 Pulsar Range Measurement....................................................302 8.2.2 Pulsar Phase Measurement....................................................308 8.3 SPACECRAFT CLOCK ERRORS AND MEASUREMENT.....................................308 8.3.1 Clock State Dynamics.........................................................309 8.3.2 Clock Measurement..........................................................310 8.4 VISIBILITY OBSTRUCTION BY CELESTIAL BODY........................................31 8.5 SIMULATION AND RESULTS........................................................317 8.5.1 Simulation Description........................................................317 8.5.2 Simulation Results............................................................324 Chapter 9 Conclusions.................................................................342 9.1 RESULTS........................................................................342 9.1.1 Navigation System Comparison.................................................346 9.2 SUMARY OF CONTRIBUTIONS......................................................348 9.3 FUTURE RESEARCH RECOMENDATIONS.............................................351 9.3.1 Higher Fidelity Simulation.....................................................351 9.3.2 Photon-Level Simulation......................................................352 9.3.3 Source Observation Scheduling.................................................352 9.3.4 Dopler Velocity Measurement.................................................353 9.3.5 Kalman Filter Models.........................................................353 9.3.6 Pulsar Observation Models....................................................354 9.3.7 Pulsar Range Measurement Sensitivity...........................................35 9.3.8 Multiple Detector Systems.....................................................35 9.3.9 Previous Celestial Source Navigation Methods....................................35 9.3.10 Mision Analysis............................................................356 9.3.1 Aditional Aplications......................................................357 9.4 FINAL SUMARY.................................................................359 Apendices............................................................................360 Apendix A Suplementary Mater.....................................................360 A.1 CONSTANTS AND UNITS...........................................................360 A.1.1 Aditional Notes.............................................................361 A.2 TIME STANDARDS AND CORDINATES...............................................362 A.2.1 Terestrial Time Standards....................................................362 A.2.2 Cordinate Time Standards....................................................362 A.3 CORDINATE REFERENCE SYSTEMS.................................................363 A.3.1 Terestrial Cordinate Reference Systems........................................363 A.3.2 Interplanetary Cordinate Reference Systems.....................................364 A.4 X-RAY FLUX CONVERSION.........................................................365 A.4.1 X-ray Spectrum..............................................................365 A.4.2 Energy.....................................................................365 A.4.3 Flux.......................................................................36 xiv A.4.4 Luminosity..................................................................367 A.4.5 Other Conversions...........................................................368 A.4.6 Experiment Conversion Factors................................................368 Apendix B X-ray Navigation Source Catalogue..........................................370 B.1 DESCRIPTION....................................................................370 B.2 PARAMETERS WITHIN CATALOGUE LISTS.............................................371 B.2.1 Simple List Parameters.......................................................371 B.2.2 Detailed List Parameters......................................................372 B.2.3 2?10 keV Energy List Parameters...............................................374 B.3 CATALOGUE DATA LISTS..........................................................375 B.3.1 Simple List..................................................................375 B.3.2 Detailed List................................................................403 B.3.3 2?10 keV Energy List.........................................................519 B.4 CATALOGUE SPECIFIC REFERENCES.................................................537 Apendix C TOA Observations and Spacecraft Orbit Data.................................540 C.1 ARGOS BARYCENTERED AND NON-BARYCENTERED TOAS.............................540 C.2 SPACECRAFT ORBIT DATA.........................................................54 Apendix D State Dynamics and Kalman Filter Equations.................................546 D.1 STATE DYNAMICS AND OBSERVATIONS..............................................546 D.1.1 Linear System Equations......................................................546 D.1.2 Non-Linear System Equations..................................................50 D.1.3 Dynamics Sumary..........................................................56 D.2 KALMAN FILTER EQUATIONS.......................................................57 D.2.1 Random Variables and Statistics...............................................57 D.2.2 Covariance Matrix...........................................................560 D.2.3 Discrete Kalman Filter Equations..............................................561 D.2.4 Continuous Kalman Filter Equations............................................568 D.2.5 Measurement Testing.........................................................569 D.2.6 Kalman Filter Algorithm Sumary.............................................571 D.2.7 Eror Measures.............................................................573 Apendix E X-ray Detectors............................................................575 E.1 DETECTOR TYPES................................................................575 E.2 CONCEPTUAL DETECTOR SYSTEM DESIGNS...........................................583 Bibliography...........................................................................586 xv List of Tables Table 1-1. Spacecraft Time Determination Methods and Comparisons [48, 49, 21]...................14 Table 1-2. Spacecraft Atitude Determination ethods and Comparisons [107, 21]..................14 Table 1-3. Spacecraft Position Determination Methods and Comparisons [107, 21]..................15 Table 1-4. Contributions to Pulsar Astronomy and Timing Research...............................24 Table 1-5. Contributions to Pulsar Navigation Research..........................................24 Table 2-1. Description of Various X-ray Source Types [145, 27].................................43 Table 2-2. X-ray Source Survey and Discovery Misions [75].....................................57 Table 2-3. Major Contributors to the XNAVSC.................................................58 Table 2-4. Radio Pulsar Catalogues..........................................................58 Table 2-5. Sources Within the XNAVSC Database..............................................6 Table 2-6. LMXB Sources Within the XNAVSC Database.......................................67 Table 2-7. HXB Sources ithin the XNAVSC Database.......................................67 Table 2-8. CV Sources Within the XNAVSC Database..........................................67 Table 2-9. NS Sources ithin the XNAVSC Database...........................................68 Table 2-10. AGN Sources Within the XNAVSC Database........................................68 Table 2-1. Other Sources ithin the XNAVSC Database.......................................68 Table 2-12. Milisecond Period Sources in XNAVSC Database....................................83 Table 3-1. List of Rotation-Powered Pulsar Position and References..............................109 Table 3-2. List of Rotation-Powered Pulsar Periodicity and Pulse Atributes........................10 Table 3-3. List of X-ray Binary Source Position and References..................................11 Table 3-4. List of X-ray Binary Source Periodicity and Pulse Atributes............................12 Table 3-5. RPSR Range Measurement Acuracy Values (1-m 2 Detector)...........................16 Table 3-6. XB Range easurement Acuracy Values (1-m 2 Detector).............................16 Table 3-7. RPSR FOM Rankings (1-m 2 Detector)..............................................19 Table 3-8. XB FO Rankings (1-m 2 Detector)................................................19 Table 3-9. Ofset of X-ray and Optical Data from Radio Data for Crab Pulsar.......................124 Table 4-1. Time Transfer Algorithm Acuracy Comparison......................................153 Table 4-2. Simplified Time Transfer Algorithm Component Contributions.........................153 Table 4-3. Pulse Time Transfer and Comparison Proces........................................154 Table 6-1. TOA Calculations and Diferences for Crab Pulsar Observation.........................198 Table 6-2. Sources Used By Absolute Position Simulation.......................................251 Table 6-3. Simulated Orbit Search Space And Threshold Data...................................254 Table 6-4. Example Simulation Results For ARGOS pacecraft..................................25 Table 6-5. Example Simulation Results For GPS Spacecraft.....................................256 Table 6-6. Example Simulation Results For DirecTV 2 Spacecraft................................256 Table 7-1. Delta-Corection Method Performance Within Solar System............................274 Table 7-2. USA Experiment Parameters [72, 16, 232].........................................276 Table 7-3. Crab Pulsar (PSR B0531+21) Ephemeris Data [15]..................................27 Table 7-4. Computed Position Ofsets from Crab Pulsar Observations.............................278 Table 8-1. Spacecraft Orbit Information......................................................318 Table 8-2. Spacecraft Simulation Information.................................................323 Table 8-3. ARGOS imulation Performance Values............................................37 Table 8-4. LAGEOS-1 Simulation Performance Values.........................................38 Table 8-5. GPS Block IA-16 PRN-01 Simulation Performance Values............................39 Table 8-6. DirecTV 2 Simulation Performance Values..........................................340 Table 8-7. LRO Simulation Performance Values...............................................341 Table 9-1. Navigation System Comparison [8, 156, 17].......................................348 Table A-1. Fundamental Constants [16, 183]..................................................360 Table A-2. Astronomical Constants [16, 183].................................................360 Table A-3. Unit Conversions [183]..........................................................361 Table B-1. CV Sources Within the XNAVSC Database.........................................371 xvi Table B-2. Parameters for Simple List in XNAVSC............................................371 Table B-3. Parameters for Detailed List in XNAVSC...........................................372 Table B-4. Parameters for 2-10 keV Energy List in XNAVSC....................................374 Table B-5. XNAVSC References...........................................................537 Table C-1. Crab Pulsar Observations by USA on ARGOS.......................................541 Table C-2. Geocenter-Based TOAs and ARGOS-Based TOAs....................................541 Table C-3. Corected TOAs and Integer Cycles................................................543 Table C-4. Comparison of Measured and Actual Phase Diferences...............................543 Table E-1. Characteristics Of Detector Types (Part A)..........................................582 Table E-2. Characteristics Of Detector Types (Part B)..........................................582 Table E-3. Characteristics Of Detector Types (Part C)..........................................583 xvii List of Figures Figure 2-1. Variable celestial source clasifications.............................................36 Figure 2-2. Electromagnetic spectrum........................................................36 Figure 2-3. Crab Nebula and Pulsar acros electromagnetic spectrum...............................37 Figure 2-4. Pulse profiles from various sources acros electromagnetic spectrum.....................37 Figure 2-5. X-ray source type clasifications...................................................4 Figure 2-6. Diagram of pulsar with distinct rotation and magnetic axes.............................48 Figure 2-7. Vela Pulsar (PSR B083?45) X-ray image taken by Chandra observatory.................48 Figure 2-8. High-mas X-ray binary system....................................................50 Figure 2-9. Low-mas X-ray binary system....................................................50 Figure 2-10. Pulse profile and widths.........................................................64 Figure 2-1. Plot of X-ray sources from XNAVSC in Galactic longitude and latitude..................69 Figure 2-12. Plot of X-ray sources from XNAVSC in Right Ascension and Declination................69 Figure 2-13. Plot of X-ray sources along globe viewed from 45? RA and 45? Dec....................70 Figure 2-14. Plot of X-ray sources along globe viewed from -45? RA and 25? Dec...................70 Figure 2-15. Plot of neutron star sources in Galactic longitude and latitude..........................71 Figure 2-16. Plot of neutron star sources in Right Ascension and Declination........................71 Figure 2-17. Plot of LMXB sources in Galactic longitude and latitude..............................72 Figure 2-18. Plot of LXB sources in Right Ascension and Declination............................72 Figure 2-19. Plot of HMXB sources in Galactic longitude and latitude..............................73 Figure 2-20. Plot of HXB sources in Right Ascension and Declination............................73 Figure 2-21. Plot of CV sources in Galactic longitude and latitude.................................74 Figure 2-2. Plot of CV sources in Right Ascension and Declination...............................74 Figure 2-23. Plot of AGN and other types of sources in Galactic longitude and latitude................75 Figure 2-24. Plot of AGN and other source types in Right Ascension and Declination.................75 Figure 2-25. First period derivative versus period for sources in the XNAVSC.......................78 Figure 2-26. Second period derivative versus period for sources in the XNAVSC.....................78 Figure 2-27. Characteristic age versus period for sources in the XNAVSC...........................79 Figure 2-28. Magnetic field versus period for sources in the XNAVSC.............................79 Figure 2-29. X-ray flux versus period for sources in the XNAVSC.................................80 Figure 2-30. X-ray flux versus magnetic field for sources in the XNAVSC..........................80 Figure 2-31. Pulsed fraction versus period for sources in the XNAVSC.............................81 Figure 2-32. Pulse width (FMHW) versus period for sources in the XNAVSC.......................81 Figure 2-3. Milisecond period sources from the XNAVSC......................................84 Figure 2-34. First period derivative versus period for milisecond period sources.....................84 Figure 2-35. X-ray flux versus period for milisecond sources.....................................85 Figure 3-1. Crab Pulsar standard pulse template. Period is about 3.5 miliseconds (epoch 51527.0 MJD).92 Figure 3-2. Crab Pulsar observation profile....................................................92 Figure 3-3. PSR 1509-58 pulsar standard pulse template. Period is about 150.23 miliseconds (epoch 4835.0 MJD).......................................................................93 Figure 3-4. Stability of several atomic clocks (Courtesy of Matsakis, Taylor, and Eubanks [127])......10 Figure 3-5. Stability of two pulsars (Courtesy of Kaspi, Taylor, and Ryba [96]).....................10 Figure 3-6. Stability of atomic clocks and pulsars (Courtesy of Lomen [12]).....................101 Figure 3-7. Range measurement acuracies using RPSRs versus observation time [Area = 1 m 2 , X-ray background = 0.05 ph/cm 2 /s (2?10 keV)]...............................................13 Figure 3-8. Range measurement acuracies using RPSRs versus observation time [Area = 5 m 2 , X-ray background = 0.05 ph/cm 2 /s (2?10 keV)]...............................................13 Figure 3-9. Range measurement acuracies using XBs versus observation time [Area = 1 m 2 , X-ray background = 0.05 ph/cm 2 /s (2?10 keV)]...............................................14 Figure 3-10. Range measurement acuracies using XBs versus observation time [Area = 5 m 2 , X-ray background = 0.05 ph/cm 2 /s (2?10 keV)]...............................................14 Figure 3-1. Range measurement acuracies using RPSRs, with SNR limited to 100 [Area = 1 m 2 , X-ray background = 0.05 ph/cm 2 /s (2?10 keV)]...............................................15 xvii Figure 3-12. Range measurement acuracies using XBs, with SNR limited to 100 [Area = 1 m 2 , X-ray background = 0.05 ph/cm 2 /s (2?10 keV)]...............................................15 Figure 3-13. Radio, X-ray, and optical Crab Pulsar TOA residual comparisons......................125 Figure 3-14. Comparison plot with ofsets in TOA residuals removed.............................125 Figure 4-1. Position of spacecraft upon pulse arival within solar system...........................141 Figure 4-2. The unit direction to a pulsar and the position of a spacecraft [50].......................141 Figure 4-3. Spacecraft position ofset distance in direction of pulsar signal.........................142 Figure 4-4. Light ray path ariving from distant pulsar to spacecraft within solar system..............14 Figure 4-5. Spacecraft position relative to Sun and SB origin...................................147 Figure 5-1. Phase-locked lop for clock adjustment [72]........................................162 Figure 5-2. Ocultation of pulsar due to Earth's disc and atmosphere..............................170 Figure 5-3. Spacecraft position with respect to Earth and elevation of pulsar........................172 Figure 5-4. Pulsar-based navigation system data procesing flowchart.............................178 Figure 5-5. Navigation system schematic.....................................................179 Figure 6-1. Range and phase measurement along a train of pulse cycles............................191 Figure 6-2. High signal-to-noise profile template of two pulses from Crab Pulsar....................196 Figure 6-3. Crab Pulsar profile with photon arival times transfered from ARGOS position to SB.....196 Figure 6-4. Crab Pulsar profile with photon arival times transfered from geocenter to SB...........197 Figure 6-5. Crab Pulsar profile with no time transfer on photon arival times........................197 Figure 6-6. Second Crab Pulsar profile with no time transfer on photon arival times. Profile is distorted due to Dopler efect on pulses ariving at vehicle........................................19 Figure 6-7. Pulse arivals from individual pulsars at spacecraft location............................20 Figure 6-8. Range vectors from single pulsar to Earth and spacecraft locations......................204 Figure 6-9. Phase diference for individual pulses ariving at the spacecraft and Earth................208 Figure 6-10. Pulse plane arivals within solar system from two separate sources.....................21 Figure 6-1. Phase diference at the spacecraft and Earth from two sources.........................214 Figure 6-12. Phase cycle candidate search space, centered about Earth.............................24 Figure 6-13. Phase cycle search space, containing candidate cycle sets, centered about Earth..........27 Figure 6-14. Position of remote spacecraft relative to base station spacecraft........................240 Figure 6-15. Orientation of two detectors on spacecraft relative to pulsar...........................241 Figure 7-1. Estimated position eror relative to the signal received from two pulsars.................263 Figure 7-2. One-dimensional position estimate eror example....................................267 Figure 7-3. NRL's USA experiment onboard ARGOS spacecraft [Courtesy of NRL]..................276 Figure 8-1. Multiple pulsars viewed by Earth-orbiting spacecraft.................................303 Figure 8-2. Pulsar-based measurement and radar-range measurement comparison...................306 Figure 8-3. Shadow cast by Earth on spacecraft orbit...........................................314 Figure 8-4. Geometry of body shadow ith respect to spacecraft orbit.............................314 Figure 8-5. Visibility of Crab Pulsar in ARGOS orbits about Earth................................315 Figure 8-6. Visibility of two pulsars in ARGOS orbits about Earth................................315 Figure 8-7. Visibility of thre pulsars due to shadows from Earth, Sun, and Mon in ARGOS orbit......316 Figure 8-8. Visibility of thre pulsars due to shadows from Earth, Sun, and on in GPS orbit........316 Figure 8-9. Analytical and numerical orbit propagation position diferences........................319 Figure 8-10. Analytical and numerical orbit propagation velocity diferences.......................320 Figure 8-1. Position standard deviation and eror for ARGOS orbit...............................34 Figure 8-12. Velocity standard deviation and eror for ARGOS orbit...............................34 Figure 8-13. Position standard deviation and eror for GPS orbit..................................35 Figure 8-14. Velocity standard deviation and eror for GPS orbit.................................35 Figure 8-15. Uncorected and NKF position eror magnitude for ARGOS orbit......................36 Figure 8-16. Uncorected and NKF position eror for GPS orbit..................................36 Figure E-1. Gas proportional counter X-ray detector diagram....................................576 Figure E-2. Microchanel plate X-ray detector diagram [59].....................................57 Figure E-3. Scintilator X-ray detector diagram [59]............................................578 Figure E-4. Calorimeter X-ray detector diagram...............................................579 Figure E-5. CD semiconductor X-ray detector diagram........................................580 Figure E-6. Solid state semiconductor X-ray detector diagram....................................581 Figure E-7. Side, top, and botom views of conceptual multiple X-ray detector system................585 xix List of Abbreviations AGN ? Active Galactic Nuclei APSR ? Acretion-Powered Pulsar ARGOS ? Advanced Research and Global Observation Satelite ATNF ? Australian Telescope National Facility AXP ? Anomalous X-ray Pulsar BCRS ? Barycentric Celestial Reference System BH ? Black Hole BHC ? Black Hole Candidate BV ? Binary Variable star CD ? Charge-Coupled Device CS ? Coronal Star CV ? Cataclysmic Variable star CXC ? Chandra X-ray Center DBS ? Direct Broadcast Satelite Dec ? Declination DSN ? Dep Space Network DXB ? Difuse X-ray Background ECI ? Earth Centered Inertial ESA ? European Space Agency (European Union) ET ? Ephemeris Time FK5 ? Fifth Fundamental Catalogue FOV ? Field Of View xx FW10 ? Full-Width 10% Maximum FWHM ? Full-Width Half Maximum GC ? Globular Cluster GCVS ? General Catalogue of Variable Stars GDOP ? Geometric Dilution Of Precision GEO ? Earth (related) GEO ? Geosynchronous Earth Orbit GLONAS ? Global Navigation Satelite System GPS ? Global Positioning System GRE ? Galactic Ridge Emision GSFC ? Goddard Space Flight Center GXC ? Galaxy Cluster HEAO ? High Energy Astronomy Observatory HEASARC ? High Energy Astrophysics Science Archive Research Center HMXB ? High-Mas X-ray Binary ICRF ? International Celestial Reference Frame INS ? Isolated Neutron Star ITRF ? International Terestrial Reference Frame J2000 ? Epoch year 2000, JD 2451545.0 TDB JAXA ? Japan Aerospace Exploration Agency JD ? Julian Date LAGEOS ? Laser Geodynamics Satelite LEO ? Low Earth Orbit xxi LHS ? Left Hand Side LMC ? Large Magelanic Cloud LMXB ? Low-Mas X-ray Binary LORAN ? Long-range Radio Navigation LRO ? Lunar Reconnaisance Orbiter MEO ? Medium Earth Orbit MJD ? Modified Julian Day MPSR ? Milisecond Period Pulsar MRSE ? Mean Radial Spherical Eror NASA ? National Aeronautics and Space Administration (USA) NDB ? Non-Directional Beacon NKF ? Navigation Kalman Filter NORAD ? North American Aerospace Defense Command NRAO ? National Radio Astronomy Observatory NRL ? Naval Research Laboratory NS ? Neutron Star NSF ? National Science Foundation OMEGA ? Optimized Method for Estimating Guidance Acuracy PDOP ? Position Dilution Of Precision PNT ? Post-Newtonian Time PN ? Parameterized Post-Newtonian PT3 ? Position and Partials as functions of Time Version 3 PRN ? Pseudorandom Noise xxii PSPC ? Position Sensitive Proportional Counter PSR ? Pulsar RA ? Right Ascension RAC ? Radial, Along-Track, and Cross-Track RHS ? Right Hand Side RMS ? Root Mean Square ROSAT ? R?ntgen Satelite RPSR ? Rotation-Powered Pulsar RS CVn ? RS Canum Venaticorum type star SAO ? Smithsonian Astrophysical Observatory SAO ? Special Astrophysical Observatory (Russia) SC ? Spacecraft SDP4 ? Simplified Dep Space Perturbations Number 4 SGP4 ? Simplified General Perturbations Number 4 SGR ? Soft Gama Repeater SMC ? Smal Magelanic Cloud SNR ? Signal-to-Noise Ratio SNR ? Supernova Remnant SB ? Solar System Barycenter SPS ? Solar System Positioning System TAI ? International Atomic Time TCB ? Barycentric Coordinate Time TCG ? Geocentric Coordinate Time xxii TDB ? Barycentric Dynamical Time TDOA ? Time Diference Of Arival TDOP ? Time Dilution Of Precision TDT ? Terestrial Dynamical Time TLE ? Two-Line Element TOA ? Time-Of-Arival T ? Terestrial Time URA ? User Range Acuracy USA ? Unconventional Stelar Aspect experiment USA ? United States of America (also U.S.) UT ? Universal Time UTC ? Coordinated Universal Time VLBI ? Very Long Baseline Interferometer VOR ? VHF Omni-directional Radio Range WD ? White Dwarf star XB ? X-ray Binary XNAVSC ? X-ray Navigation Source Catalogue XPSR ? X-ray Pulsar XTE ? Rossi X-ray Timing Explorer 1 Chapter 1 Introduction ?I must go down to the seas again, to the lonely sea and the sky, And all I ask is a tall ship and a star to ster her by ?? ? Sea-Fever, John Masefield 1902 1.1 Motivation This quote from Masefield?s early 20 th Century poem reflects the perspective of a traveler?s ambition to plot a course over Earth?s oceans and ster one?s vesel towards its destination. This yearning of humankind to explore their surroundings has always been directly related to their ability to determine a path to follow along their journey, with the eventual goal of returning home. As their skil to precisely determine dependable paths has developed, the evolution of human?s capability to safely traverse their environment has progresed. Although unique discoveries are often unveiled through deviations off an intended path, whether planned or unplanned, reliable routes and methods to maintain one?s location and speed along these routes have promoted humankind?s expansion over its livable globe. The esence of exploration has thre components: navigation, guidance, and control. Navigation is the art of determining one?s location and orientation relative to the intended 2 destination. Guidance is the art of determining the optimal path to follow to arive at a destination based upon one?s current location. Control is the art of directing one?s vehicle to follow the optimal path. Since navigation is the crucial first step in the proces of beginning any journey, and is the method of verifying the location along an intended path, substantial capabilities have been created for this proces while on Earth. As humans continue their reach about and beyond their tiny planet into the space environment where there are yet many unknowns, methods of advancing the capability of navigation must continue. Therefore, investigating new methods to improve the ability to navigate while in space aids current day exploration, and may eventualy advance this capability in al environments. 1.1.1 Navigation on Earth The development of navigation methods and tools has been continual since humans first ventured out of sight and safety of their local refuge. Land-based navigation over Earth has been acomplished with aceptable acuracy for thousands of years. Humans are wel adapted to identifying landmarks to maintain a reference to their location. Methods of triangulation with respect to multiple landmarks alow refined location estimation. As these landmarks were recorded, the creation of maps asisted travel over foreign lands. Methods to determine speed over the terain were eventualy developed, as wel as determining the orientation of a vesel with respect to known fixed objects or the planet?s magnetic poles. Map reading and proceses of dead reckoning asisted many succesful journeys. However, when humans ventured to travel over the seas and oceans, many of these fixed visual cues were no longer available once land slipped past the visible horizon. 3 New methods of navigating needed to be devised. Although some cultures adapted quicker than others, many sought the use of celestial objects as points of reference for navigating the featureles oceans. As observed from Earth?s surface, the motions of the Sun, Moon, planets, and stars initialy provided the concept of time, as their periodic motions formed the concept of a celestial clock. As long as one could look up and recognize a celestial object above the horizon, a reference to time, and eventualy to location, could be computed. Early Polynesians traveled thousands of miles across open oceans using only the knowledge of the motion of stars, the existence of sea swels, and the appearance of certain birds and sea creatures. This information was handed down oraly from one generation to the next, often simply in the form of a song [92]. The great distances these seafarers traveled with regular repeatability proved that these simple objects and their reported characteristics could provide sufficient navigation information. Al celestial objects, including the Sun, Moon, planets, and stars, came to be widely used for many centuries as sources for positional reference markers. Using catalogued celestial almanac data the observation of visible stars provided navigators on Earth a means to determine location information relative to observation stations fixed on Earth. The chief drawback of celestial-based navigation, however, was the restricted viewing times and the limited visibility of these objects due to inclement weather. However, as methods of utilizing these objects have matured over time, in addition to the development of instrumented time clocks, or chronometers, the performance of navigation methods has improved. Determining latitude over Earth via inclination of celestial objects above the horizon proved simpler than computing longitude. Acurate, al-weather methods of navigation 4 across vast ocean longitudes was not acomplished with sufficient acuracy and repeatability until chronometers improved in acuracy within the 1800s [197]. The use of the chronometer alowed navigators to compare the local observed time to the time at a known fixed location in order to determine the change in longitude with respect to the known location. The use of these instruments eventualy replaced many proposed schemes that utilized celestial-based clocks. The time comparison method required knowledge of time at a known reference location, which typicaly meant transporting multiple timepieces, one for local time and one for reference time. If instead this information could be broadcast to a user, the complexity of the user?s equipment would be reduced. In addition to chronometers, local navigation beacons were created to asist navigation relative to a specific location. Optical lighthouses were established, which produced periodic flashes of light, to warn mariners of potential dangerous shorelines, as wel as provide an estimate of distance to the fixed lighthouse location. Radio-based navigation beacons, such as LORAN, NDB, OMEGA, and VOR, were developed once radio communication was invented. These systems provide distance and direction information to both sea craft and aircraft for improved navigation acuracy, although the data communicated by these navigation beacons to vehicles has limited range and many beacons are necesary to cover a large geographical area. Recognizing the need for al-weather, systematic time comparisons and range determination, during 1960-1980 the United States military developed a timing system which has grown into what is known today as the Global Position System (GPS) [156, 157]. A constelation of satelites orbiting Earth broadcast time and data information for 5 users to receive and proces in order to compute time, position, velocity, and atitude over Earth. These human-made celestial objects achieve similar, but greatly improved, reference information that the Sun, Moon, planets, and visible stars provided to early history navigators. GPS has developed into a useful utility for Earth-bound users. In addition to the U.S. GPS system, the existing Russian Global Navigation Satelite System (GLONAS) [177] and the future European Union planned Galileo system provide worldwide time and navigation information to users on or near Earth. The term navigation has advanced to signify the proces of determining position, velocity, atitude, and atitude-rate of a vehicle specified at a certain time or times. Navigation systems that provide this data for a vehicle include components that measure internal characteristics of the vehicle?s motion as wel as sensors that derive information from external sources to maintain acurate computed motion. 1.1.2 Navigation in Space Human?s ability to travel has progresed to the point of alowing exploration outside Earth?s atmosphere into the outer space environment. With this new seting in which to explore, new methods for determining navigation information for vesels in space have been devised. Several descriptive terms have developed that distinguish betwen the various types of navigation used for spacecraft misions: ? Orbit Determination: Proces of determining the orbit of vehicle or object through repeated and/or succesive observations of the vehicle or object from Earth ground stations. Observational measurements are combined to produce the best estimate of orbit state dynamics of vehicles. 6 ? Orbit Propagation: Proces of propagating the state dynamics of a vehicle or object in orbit using models of force acting upon the vehicle or object. The state dynamics are numericaly or analyticaly integrated to produce the best estimate of position and velocity. ? Orbit Navigation: Proces of determining the vehicle or object state data by utilizing external sensors to measure the vehicle?s navigation state, including time, position, velocity, aceleration, atitude, and atitude rate. Includes the blending of external sensor data with internal sensor data to produce high acuracy navigation solutions for a vehicle. The navigation solution is generated autonomously by the vehicle and its sensors, and may be verified using a ground-based orbit determination solution. Navigation of vehicles above and beyond Earth?s surface has gained significantly from knowledge of the navigation methods developed on Earth. For example, many satelites orbiting Earth and spacecraft traveling through the solar system have relied on celestial sources to sucesfully complete their misions. Additionaly, celestial source navigation systems have been augmented with human-made systems to further increase spacecraft navigation performance. To date, many methods have been used to compute the navigation information of spacecraft that have traveled around Earth, through the solar system, and beyond the solar system?s outer planets, as far as the heliopause. Exploration betwen Earth, its Moon, and other solar system planets has ben largely succesful. Most misions have encountered their target object with relatively good acuracy, sufficient enough to cary out their mision. Navigating and controlling vehicles within Earth-orbits or towards their planetary destinations is stil a chalenge 7 however, requiring acurate ground-based tracking of a vehicle to correct any solution discrepancies. Since spacecraft in orbit about a central mas follow a predictable, often stable, path that can be estimated using the propagation of the vehicle?s dynamics, an analytical solution of a spacecraft trajectory can be studied prior to launch. However, unmodeled or unforesen disturbances may perturb the vehicle from the orbit path and eventualy an orbit propagator?s position eror grows to an unaceptable level for vehicle guidance or control. Orbit determination methods using observations of the spacecraft from Earth ground stations can detect these deviations of the vehicle from the predicted path and can update the estimation of the orbital elements. Alternatively, vehicles can perform the navigation function with onboard sensors in order to detect these disturbances and correct its own solution. Whether the navigation solution is produced via ground station observations or onboard systems, various types of sensors have been developed to support the navigation function. Knowledge of time onboard a spacecraft is important for various operations, such as proces timing for payload functions, communications, and for determining locations of local bodies using ephemeris data. Time has been determined using a clock on-board the spacecraft, or through periodic computer updates from ground control stations. Therefore, an acurate clock has become a fundamental component of most spacecraft navigation systems. For example, in order to track radio signals from Earth at acuracies of a few tenths of a meter, a clock with nanosecond acuracy over several hours is needed [128]. This tracking acuracy requires the clock to be stable within one part in 10 13 . Just as early chronometers helped improve navigation over Earth?s ocean, more acurate chronometers asist navigation through the solar system. Atomic clocks available for spacecraft 8 applications provide high acuracy references and are typicaly acurate to within one part in 10 9 -10 15 over a day. Atitude determination of spacecraft is necesary in order to properly orient payloads with respect to their intended targets. Onboard gyroscopes can sense the spacecraft?s rotation rate relative to an inertial frame and once initialized can provide atitude and atitude rate information to the vehicle. Sensors that measure Earth?s magnetic field, magnetometers, and Earth horizon sensors can also be used to orient Earth-orbiting satelites relative to an Earth frame. Celestial objects including the Sun and stars are also used for atitude determination. Sun sensors, star cameras, and star trackers are often used for many spacecraft misions due to their high acuracy from these distant stelar objects. The extremely large distances to the stars in the Milky Way galaxy and other galaxies esentialy create the ilusion that the stars are stationary with respect to a coordinate frame fixed to Earth. Therefore, the rotation and/or translation of a spacecraft with respect to the apparently fixed background of stars alows the measurement of atitude, atitude rate, and to some extent, position. However, just as the solar system rotates, so does the Milky Way rotate and the Galaxy translates with respect to neighboring galaxies. Hence, although these distant objects sem stationary, they are speeding away or towards the solar system continualy at al times. Fortunately, the motion of the stars is very slow compared to many other measurements of time such that for the vast majority of applications this motion can be considered negligible. Similar to methods developed on Earth to triangulate a position relative to identifiable landmarks, it is conceivable to use persistent starlight as markers for triangulating spacecraft position [17]. The large distances to these objects, however, does not produce 9 large changes in line-of-sight angles even with significant position changes of spacecraft within the solar system. Typicaly only unit directions to these objects and their relative directions to other solar system objects are utilized. In addition to smal angular changes due to the extreme distances to these objects, there is no method of determining when the visible light was sent from these stars, thus determining range information from an individual star to triangulate a spacecraft?s position is problematic. During the instance of occultation, or when a known celestial body pases in front of a selected star, the relative position information to a known object can be deduced directly from starlight [17]. If the atmosphere of a local body is in view, measurements of spacecraft range from the body can be produced by the refraction of starlight as a stelar object pases behind the body?s atmosphere [68]. Both of these methods require a local body to be in view, acurate models of the body?s atmosphere to be available, and the spacecraft must be near to the body such that multiple measurements can be produced. Although there are substantial benefits of celestial-based navigation, most space vehicle operations have relied heavily on Earth-based navigation solutions to complete their task [89, 128, 221]. Radar range and optical tracking methods have been the predominant system for tracking and maintaining continuous orbit determination of spacecraft [16, 219, 221]. In order to compute the position of a spacecraft, radar range systems compute the range, range-rate, and/or the angular orientation angles to the spacecraft relative to the radial direction from a radar tracking station. This is achieved primarily through the reflection of signals transmited from an Earth observing station by the space vehicle structure and measurement of the transmited signal round-trip time. Acuracies on the order of a few meters or les in range and fractions of m/s in range- 10 rate are possible, although the remaining two axes of position typicaly have much larger eror [89]. Early demonstrations using these tracking systems on the Vikings spacecraft misions to Mars showed positional acuracies to within 50 km, and projected acuracies of hundreds of kilometers at the outer planets [128]. Although a ground-based tracking system requires no active hardware on the spacecraft itself, it does require extensive ground operations and careful analysis of the measured data against an electromagneticaly noisy background environment. By procesing multiple radar measurements over time, the vehicle?s orbit parameters can be computed. The position of the vehicle can be propagated ahead in time using standard orbital mechanics that includes known models of solar system object?s gravitational potential field and any known disturbance or perturbations efects, such as object body atmospheric drag. This propagated orbit determination solution is then compared to subsequent radar measurements and the orbit solution is corrected for any computed erors. This proces continues until a satisfactory orbit solution converges to within the expedition?s required parameters. However, vehicle maneuvers or any unanticipated disturbances wil afect the trajectory of the vehicle. Without exact knowledge of these maneuver dynamics or disturbance efects, it is necesary for the propagation and radar measurement comparison to continue throughout the flight. As a spacecraft moves further away from Earth observation stations, the eror increases in radar-ranging solutions of spacecraft orbit data. To achieve the necesary range determination, the radar system requires knowledge of the observation station?s position on Earth to great acuracy, which necesitates sophisticated surveys of each ground antenna [89]. An additional limitation is the acuracy of known positional 11 information of the solar system objects [89]. This solar system ephemeris data has continualy improved with new observations and spacecraft flybys. However, even with this precise station and ephemeris knowledge, the vehicle position measurement can only be acurate to a finite angular acuracy. The transmited radar beam, along with the reflected signal, travels in a cone of uncertainty. This uncertainty degrades the position knowledge in the transverse direction of the vehicle as a linear function of distance. As the vehicle gets more distant, any fixed angular uncertainty reduces the knowledge of vehicle position, especialy in the two transverse axes relative to the range direction. These axes are along-track of the vehicle?s velocity and cross-track, or perpendicular, to the vehicle?s velocity and radial direction. Alternatively, many spacecraft, including those traveling into deep space or on interplanetary misions, have employed active transmiters to be used for orbit determination purposes [89]. The radial velocity is measured at a receiving station by measuring the Doppler shift in the frequency of the transmited signal. The spacecraft esentialy receives a ping from an observation station on Earth and re-transmits the signal back to Earth. Although improvements in the radial direction range and range-rate measurements are made utilizing such system, transverse axes erors stil exist, and this method has erors that also grow with distance. The Dep Space Network (DSN) asists navigation of vehicles far from Earth by determining range and range-rate along the line- of-sight from the ground radar station to the vehicle [88]. Thre locations, located roughly 120? apart, at Goldstone (California, USA), Madrid (Spain), and Canbera (Australia) can provide continuous observation of vehicle misions. Although acurate radial position can be determined, DSN requires extensive ground operations and 12 scheduling to coordinate the observations. Even utilizing interferometry, by using the diference betwen multiple signals compared at two ranging stations, the angular uncertainty can grow significantly for distant spacecraft. Total position acuracies on the order of 1 to 10 km per AU of distance from Earth are achievable using interferometric measurements of the Very Long Baseline Interferometer (VLBI) through the DSN [89]. Optical tracking measurements for spacecraft position and orbit determination are completed in a similar fashion as radar tracking [16]. Optical tracking uses the visible light reflected off a vehicle to determine its location. Some optical measurements require a photograph to be taken and the vehicle?s position is calculated after analysis of the photograph and comparison to a fixed star background. Real-time measurements using such systems are typicaly not easily achieved. Additionaly, optical measurements are limited by favorable weather and environmental conditions. Since many misions have concentrated on planetary observation, augmentation to the ranging navigation system can be made within the vicinity of the investigated planet. By taking video images of the planet and comparing to known planetary parameters (such as diameter and position with respect to other objects), the video images can determine position of the spacecraft relative to the planet [17]. Often the objective is to orbit the planet, thus only relative positioning is primarily required for the final phase of the flight. Based upon solar system dynamics, it is possible to predict a planetary object?s location within the solar system?s coordinate frame to high acuracy over time. Using the determined relative position information and the objects inertial location, a spacecraft can consequently determine its absolute position. 13 Typicaly, combinations of Earth-based radar ranging and on-vehicle planet imaging are required to produce acurate navigation solutions for deep space misions to another planet. This method of navigation stil requires human interaction and interpretation of data. Additionaly, as radar-ranging system erors grow as the distance from Earth increases, acurate orbit determination to the outer planets becomes progresively more complex due to the required finer pointing acuracy of ground antennas. Vehicles that proces planetary images to improve radar-ranging solutions have complicated vehicle subsystems and increased cost. This imaging proces also requires planets to be sufficiently close along the vehicle?s trajectory in order to be photographed. For vehicles operating in space near Earth, the current Global Positioning System (GPS) ? and similar human-developed systems ? can provide a complete navigation solution comprised of referenced time, position, velocity, atitude, and atitude rate [156, 157]. The GPS system produces signals from multiple transmiting satelites that alow a receiver to determine its position from the ranges to each transmiting satelites. However, these satelite systems have limited scope for operation of vehicles relatively far from Earth. Unpredictably, these systems may have their service interupted through malfunction or unforesen circumstances. Table 1-1 through Table 1-3 provide a summary of sensors and methods used to determine spacecraft time, atitude, and position. Estimates of performance for each system are provided. 14 Table 1-1. Spacecraft Time Determination Methods and Comparisons [48, 49, 221]. Method Advantages Disadvantages Performance Computer-Counters (ex. Crystal Oscilators) - Measures intervals - No absolute time - Stable to 1 part in 10 10 per orbit - About 10 ?s within GMT Ground-based Time Taging - Timing handled by ground operations - Extensive ground tracking and comunication - 2.5 - 25 ?s Atomic Clocks - High acuracy - Expensive - Weight - Stable to 1 part in 10 14 per year GPS - High acuracy - Visibility - Requires system maintenance - ? 40 ns (95%) (SPS) Table 1-2. Spacecraft Atitude Determination Methods and Comparisons [107, 221]. Method Advantages Disadvantages Operating Range Performance Horizon Sensor - Scaner - Fixed Head - Infrared sensing of Earth limb - Low operating range LEO <0.1? to 0.25? Magnetometer - Simple, reliable, lightweight - Uses Earth magnetic field - Requires separation from payload LEO 0.5? to 3? GPS - High acuracy - Ful nav solution - Requires GPS system maintenance - Signal multipath LEO (< GPS orbit) 0.3? to 0.5? (requires antena separation) Sun Sensor - Can use data from observing payload - Requires unobstructed view of Sun LEO to Interplanetary 0.05? to 3? Inertial Measurement Unit (gyros and acelerometers) - Angular rate data and aceleration - Requires external aiding LEO to Interplanetary Gyro drift rate: 0.03?/hr to 1?/hr Acel linearity: 1 to 5 ?10 -6 g/g 2 Star Sensor - Camera - Tracker/Maper - High acuracy - Moderate to High Cost LEO to Interplanetary 0.003? to 0.01? 15 Table 1-3. Spacecraft Position Determination Methods and Comparisons [107, 221]. Method Advantages Disadvantages Operating Range Performance Landmark or Ground Object Tracking - Can use data from observing payload - Landmark detection may be dificult - May have geometry singularities LEO 5 km Stelar Refraction (Horizon Crosings) - Could be autonomous for atitude and position - Uses atitude-sensing hardware - Fairly new concept LEO 150 m - 1 km TDRS Tracking System - NASA spacecraft - High acuracy - Same hardware for tracking & data - Not autonomous - Mostly NASA misions LEO 50 m Satelite Croslinks - Can use satelite croslink hardware - Unique to each satelite constelation - Only relative position (no absolute) - Potential problems with system deployment and S/C failures LEO 50 m (in theory) GPS - High acuracy - Ful nav solution: time, atitude, position and velocity - Requires GPS system maintenance LEO to MEO (< GPS) 15 m-10 m (in LEO) Star/Mon Sextant - Could be autonomous for atitude and position - Fairly new concept - Heavy and high power LEO to GEO 250 m Sun, Earth & Mon Observer - Could be autonomous for atitude and position - Uses atitude-sensing hardware - Flight tested - Initialization and convergence depend on geometry LEO to GEO 10 m-40 m (in LEO) Ground-based Tracking Systems - Traditional aproach - Method wel established - Acuracy depends on station coverage - Not autonomous, operation intensive LEO to Interplanetary 1 - 10 km 1.1.3 Future Space Navigation Architectures As exploration of the solar system continues, methods of increasing the navigation performance while reducing the system complexity are atractive to many expeditions. With the benefits of a complete navigation solution provided by the GPS system for near- Earth applications navigation and the acuracy provided by range measurements from radar system for deep space misions by DSN, it is necesary to investigate methods that 16 could provide a complete, acurate navigation solution throughout the solar system, and perhaps even interstelar and eventualy intergalactic regimes. On a larger scale, conceiving a GPS-like human developed and controlled system that encompases the entire solar system it not unimaginable. For example, a solar system positioning system (SPS) could be created. This would require transmiting spacecraft to be deployed throughout the solar system in orbits either inclined to the ecliptic plane of the solar system, perhaps outside the orbit of Jupiter or Pluto, or in halo orbits above or below the ecliptic plane in order to provide sufficient coverage for operations to al planets. However, it can be quickly realized that the cost in development and operation of such a system would be tremendous. This type of system could only be justified once travel betwen Earth and other planets becomes commonplace. Alternatively, local system constelations could be deployed, such as a GPS-like system about the Moon, the Earth-Moon system, or Mars and its moons. These types of local systems would alow communication as wel as navigation to be performed by the orbiting spacecraft. Even though only a few satelites would be necesary in these local system constelations, the deployment and operations cost would stil be significant. Since the ground control segment of the GPS system provides a significant role in maintaining the acuracy of that system, similar control segments would be required for these GPS-like systems, which would utilize extensive resources back on Earth. With the newly proposed misions for humans to explore the Moon and Mars [5], these types of local system constelations would support navigation in orbits about these bodies and on their surfaces. However, unles these beacons can produce powerful, omni- directional signals, the interplanetary trajectory phase of these misions would stil 17 require radar-tracking based navigation from Earth. A single system that could support both phases of these mision would be much more atractive. A les complex method than local satelite constelations about each body may be to place several navigation beacons on planetary or moon surfaces throughout the solar system, efectively creating a ranging system spread across the system with adequate visibility. The remotely operated beacons could aid spacecraft along their journeys to diferent planets. Unfortunately, the cost of even operating these remote beacons is stil prohibitive, and the need for such beacons would have to grow substantialy to be considered. 1.1.3.1 Autonomous Operation As the cost of vehicle operations continues to increase, spacecraft navigation is evolving away from Earth-based solutions towards increasingly autonomous methods [58, 68]. Autonomous operations of spacecraft require the determination of a complete navigation solution in order to control itself towards its destination, without the interaction or asistance of human operations. Using onboard and external sensors, the vehicle?s navigation system internaly computes its own navigation and guidance information. Any deviations from its planned path would be detected, reported, and corrected without input from the ground mision control. Although not necesarily fully independent operation, using absolutely no oversight from mision control, this autonomous operation would reduce the control segment?s labor-intensive operations for vehicle control, especialy for constelations of multiple spacecraft or formations of spacecraft. 18 For near-Earth operations, using GPS can aid autonomous navigation for spacecraft that can receive sufficient signals from these satelites. Until a SPS system is realized, the question remains whether there are any other possible methods for near-Earth and interplanetary navigation that can be used in a similar manner as GPS is used today. Celestial-based systems, which use sources at great distance from Earth, remain atractive for complementing existing systems and for developing future navigation systems that could operate in an autonomous mode. 1.2 Previous Research 1.2.1 Variable Celestial Sources Celestial sources have proven to be significant aids for navigation throughout history, although the majority of sources used have been the fixed, persistent visible radiation stars. Those sources that produce variable, or modulated, intensity of radiation, refered to as variable celestial sources, have also been discovered and observed for the past few centuries [61]. Astronomical observations have revealed several clases of variable celestial objects that produce signals that vary in intensity throughout the electromagnetic spectrum, including those that emit in the high energy bands of X-ray and gama-rays [2, 38]. Of the diferent variable source types, individual stars that have a uniquely identifiable signal and whose signals are periodic and predictable, can be utilized in a diferent manner for navigation purposes than the persistent sources. Chapter 2 provides additional detail on the discovery of these variable sources, as wel as the various types. It 19 wil be shown that those sources that emit X-ray radiation are atractive for spacecraft navigation applications. A particularly unique clas of variable celestial sources is pulsars. It is theorized that pulsars are rotating neutron stars [13, 14, 155]. Neutron stars are formed when a clas of stars collapse, and from conservation of angular momentum, as the stars become smaler, or more compact, they rotate faster. For certain types of pulsars, the rotation can be extremely stable. No two neutron stars have been formed in exactly the same manner, thus their periodic signatures are unique. Because many pulsars provide signals that are unique, periodic, and extremely stable, they can asist navigation by providing a method to triangulate position from their signals. Pulsars were first discovered in the radio band by Bel and Hewish in 1967 [80]. Pulsars have been observed in the radio, visible, X-ray, and gama-ray bands of the electromagnetic spectrum. Most variable celestial sources, including pulsars, are extremely distant from the solar system, which provides good visibility of their signal near Earth as wel as throughout the solar system. However, unlike the transmiting satelites within the GPS or GLONAS systems, the distances of the celestial sources cannot be measured such that direct range measurements from each source can be determined. Rather, indirect range measurement along the line-of-sight to a pulsar from a reference location to a spacecraft can be computed. Thus, precise direction information to each source at a selected time epoch as wel as any motion of the source over time is esential for acurate navigation. Existing catalogues of these variable celestial objects exist, which can asist the identification of sources that would support the navigation endeavor. However, improvements or additional acuracy of the recorded data wil most likely be required for future use. 20 1.2.2 History of Pulsar-Based Navigation Since their discovery by Bel and Hewish, early observers of the stable, periodic signals from pulsars recognized the potential of these stars to provide a high quality celestial clock. In 1971, Reichley, Downs, and Morris proposed using pulsar signals as a clock for Earth-based systems [167]. Pulse timing resolution of fractions of a milisecond from pulsars was achievable during that early research [168]. The stability of these sources were shown to be quite stable once long term observations were produced [167]. In 1980, details of methods to determine pulse time of arivals from pulsar signals were provided by Downs and Reichley based upon decade-long observations made using NASA?s DSN [51]. Presentations by Alan, Matsakis, Taylor, and others in the 1980s and 1990s, demonstrated that several pulsars match the quality of atomic clocks [7, 127]. Indeed, due to their measured stabilities, pulsars have been considered as celestial time standards. As discussed above, some form of time synchronization is typicaly utilized for acurate navigation, and improved performance can be achieved by using higher quality clocks. Thus it was soon conjectured that pulsars could also be used as clocks for navigation. In 1974, Downs presented a method of navigation for orbiting spacecraft based upon radio signals from a pulsar [50]. This method proposed developing omni directional antennae to be placed on a spacecraft to record pulsar signal phase and create a thre- dimensional position fix. Thre to nine antennas of pyramidal shape that are 2 m on a side would be required for full sky coverage. Based on the 27 proposed radio pulsars for navigation and their achievable signal quality over integration time of 24 hours, position acuracy on the order of 150 km was projected to be atainable. The method asumed that 21 no ambiguities in the phase cycles would exist if existing navigation schemes were employed in paralel with the pulsar position determination method. No relativistic efects of the pulse time transfer betwen a spacecraft and the inertial origin were considered. Although today?s acuracy of existing navigation methods has surpased the acuracy of the method proposed by Downs, this introductory paper on pulsar navigation provided the original basis for succeding research. Both the radio and optical signatures from pulsars have limitations that may reduce their efectivenes for spacecraft navigation. Walace, in 1988, discussed the isues related to using celestial sources that produce radio emision, including pulsars, for navigation applications on Earth [218]. He states that neighboring celestial objects including the Sun, Moon, Jupiter, and close stars, as wel as distance objects such as radio galaxies, quasars, and the galactic difuse emisions, are broadband radio sources that could obscure weak pulsar signals. It is expected that radio-based systems would require large antennas to detect sources, which would be impractical for most spacecraft. Furthermore, the low signal intensity from radio pulsars would require long signal integration times for an aceptable signal-to-noise ratio as demonstrated by Downs and others [50, 51]. The smal population of pulsars with detected optical pulsations (only five isolated pulsars [185]) severely limits an optical pulsar-based navigation system. Since optical pulsars are also dim sources, large aperture telescopes are required to collect sufficient photons. Any nearby bright visible sources would require precise pointing and significant procesing to detect these pulsars. During the 1970s, astronomical observations within the X-ray band of 1?20 keV (2.5?10 17 ?4.8?10 18 Hz) yielded pulsars with X-ray signatures. In 1981, Chester and 22 Butman proposed using pulsars emiting in the X-ray band as an improved option for Earth satelite navigation [40]. They listed 17 known X-ray pulsars that could provide good signal coverage. Although lacking supporting analysis, sensors on the order of 0.1 m 2 were proposed, which would be significantly smaler than the antennas or telescopes required for radio or optical observations. Their proposed navigation method compares the pulse time of arivals from pulsars betwen a distant spacecraft and a satelite in orbit about Earth. Using this diference in arival times, they projected that positional acuracy on the order of 150 km after one full day of measurements could be computed. Although their analysis did not produce imediate motivation for implementing such a pulsar- based system, X-ray emiting sources present a significant benefit to spacecraft applications, primarily through their utilization of smaler sized detectors. Also, there are fewer X-ray sources to contend with and many are unique signatures, which do not get obscured by closer celestial objects. In 1993, Wood proposed studying a comprehensive approach to X-ray navigation covering atitude, position, and time, as part of the NRL-801 experiment for the Advanced Research and Global Observation Satelite (ARGOS) [229]. This study included utilizing X-ray sources other than pulsars. Atitude was proposed to be determined in a similar manner as existing visible star cameras. Position of a vehicle was to be determined using the occultation of a source behind Earth?s or the Moon?s limb, and acuracy on the order of tens of meters was forecast. Timekeeping was also presented as a potential from X-ray sources, and acuracy approaching 30 ?s over diferent timescales was promoted. As part of the Naval Research Laboratory?s (NRL) development efort for this experiment, Hanson produced a thesis in 1996 on the subject of X-ray navigation 23 [72]. This work included a detailed description of spacecraft atitude determination based upon the two-axis gimbaled detector. Comparison studies to data collected by the HEAO- 1 spacecraft [233] showed atitude acuracies on order of 0.1-0.01 degres using either a single or dual detector. Hanson?s thesis also presented autonomous timekeeping using X- ray sources, including the implementation of a phase-locked loop to maintain acurate time aboard a spacecraft. From 1999?2000, NRL?s Unconventional Stelar Aspect (USA) experiment onboard the ARGOS satelite provided a platform for pulsar-based spacecraft navigation experimentation [166, 231, 232, 234, 235]. The X-ray data from this experiment was initialy used to demonstrate the concept of atitude determination [232]. The proportional counter detector portion of this experiment ended prematurely due to the loss of gas within the detector chambers, the leak was theorized to be created by a micrometeorite strike. Research eforts, including this disertation, are continuing to demonstrate position determination and timekeeping using the recorded data from this flight experiment. A summary, in chronological order, of significant contributions to the theoretical prediction, discovery, and observations of pulsars is provided in Table 1-4. Elaboration of these contributions, as wel as other relevant references, is continued throughout the following chapters of this disertation. Table 1-5 summarizes, in chronological order, contributions into the investigation of using pulsars as acurate, periodic beacons in space for vehicle navigation. Since the discovery of pulsars, a significant amount of research has been done with respect to navigation in general. However as sen in these tables, only recent limited introductory analysis on solving the thre-dimensional position solution for spacecraft using pulsars has been atempted. 24 Table 1-4. Contributions to Pulsar Astronomy and Timing Research. Year Name Description Refs. 1916 1930s 1930s 1967 197 1980 1983 1986 1987 192 197 198 Einstein Various Chandrasekhar Bel, Hewish, et al. Manchester & Taylor Downs & Reichley Muray Helings Alan Taylor Matsakis, Taylor & Eubanks Lyne & Graham-Smith The general theory of relativity Theoretical predictions of neutron stars Theories on stelar structure and atmospheres Discovery of radio pulsars Detailed overview of pulsars Techniques for measuring pulse arival times Pulsar astrometry and timing Relativistic efects in pulsar timing Showed comparison of pulsars & atomic clocks Pulsar timing and relativistic gravity New statistic for pulsar & clock stabilities Overview of pulsar astronomy [53] [13, 14, 15] [37] [80] [18] [51] [140] [15, 79] [7] [204] [127] [14] Table 1-5. Contributions to Pulsar Navigation Research. Year Name Description Refs. 1974 1981 198 193 196 199 Downs Chester & Butman Walace od Hanson USA Experiment Proposed using radio pulsars for spacecraft navigation Sugested X-ray pulsars for interplanetary navigation Investigated ?radio stars? for al-weather Earth navigation Proposed X-ray pulsars for near Earth orbit navigation Doctoral thesis on X-ray navigation: atitude and time Earth orbit atitude determination using X-ray sources [50] [40] [218] [29] [72] [16, 231, 232] 1.3 Overview of Contributions This disertation research pursued an in depth analysis of the use of pulsars, specificaly those emiting X-ray radiation, for navigation of spacecraft. The original contribution of this disertation research consists of the first comprehensive study of al aspects of spacecraft navigation using variable celestial sources. This includes reviewing previously proposed methods of navigation using these types of sources; investigating the types and number of sources that can support high acuracy navigation; determining the acuracy of pulse measurements of individual and groups of sources; developing new methods of computing time, atitude, position, and velocity; and demonstrating the expected performance of these methods using recorded and simulated data. An X-ray celestial source catalogue has been created to support this research. Via thorough research of existing catalogues and individual source papers, this new catalogue 25 identifies candidate sources for navigation. A quality figure of merit is derived to rank individual sources that benefit time and position determination. To support the pulse timing analysis, a study of the comparison of pulse arival times at the visible, radio, and X-ray energy ranges for the Crab Pulsar was produced. This work demonstrated that each energy range has a unique arival time, and identified several isues with absolute timing of photon arivals for X-ray astronomy misions. A detailed derivation of the time transfer equations betwen an orbiting spacecraft and the solar system barycenter has ben developed. These equations are used to transfer the arival time of a pulse on a spacecraft to the inertial origin or pulse model definition location. This derivation has identified a potential discrepancy with existing pulsar timing equations. Numerous original algorithms and analysis were generated during this research efort. The time of arival acuracy is identified using a method based upon the signal-to-noise ratio of an observation of an individual source and its characteristics as identified in the source catalogue. Range acuracy based upon this time of arival acuracy and the geometric dilution of precision of a set of sources is determined. Algorithms used to determine the absolute or relative position to a known location have been produced. These algorithms provide a method to resolve the phase cycle ambiguities due to the unknown location of the vehicle, whereas most previous methods have asumed external information to determine the ambiguous number of phase cycles betwen a detector and the pulse model location. These algorithms esentialy solve the lost-in-space problem for spacecraft, without requiring any external asistance. Algorithms to recursively corect estimated position and velocity based upon sequential pulsar range measurements have 26 been developed. This approach compares the measured to the predicted arival time of a pulse signal, and diferences are converted to range corrections. Simulated results of the operation of these algorithms have been presented, and empirical validation of the concept has ben presented based upon recorded data. These new algorithms also provide a scheme to correct vehicle clock time. Methods to determine vehicle atitude have also been produced, as extensions to the presented methods of position and time determination. 1.4 Disertation Overview This disertation is separated into four major sections. The first section, Chapter 2, introduces variable celestial sources, including the diferent types, their emision mechanisms, and radiation at diferent wavelengths. The second section, Chapters 3 and 4, describes modeling and timing of pulses from variable celestial sources. The third section, Chapters 5 through 9, provides a detailed description of the various methods of navigation using variable celestial sources developed during this research. The fourth section is the Appendices that provide the source catalogue and supporting material for the descriptions within the various Chapters. Chapter 2 presents an overview of the variable celestial sources. It presents the physics and mechanisms for the variable intensity radiation produced by the objects. A discussion is provided on which of the sources are most conducive for navigation, including the selection of X-ray emiting sources as opposed to those that produce radio or visible radiation. A detailed discusion is provided on pulsars, including the diferent pulsar types. Chalenges for navigation due to the characteristics of these variable sources 27 are identified. A catalogue of X-ray sources is provided to asist in the selection of source candidates for navigation. Important properties of sources within the catalogue are graphed in plots. An important subset of these sources, those with periods on the order of miliseconds, is analyzed in further detail. Chapter 3 discuses the identification and modeling of pulses from variable celestial sources. Methods to produce profiles of pulses are provided, as wel as the development of models used to predict the time of arival of individual pulses. The measured stability of pulses from several objects is provided in order to demonstrate their predictability. A detailed method is presented for determining pulse time of arival acuracy based upon the acquired signal relative to its projected noise. This method is used to provide the determination of acuracy of range measurements computed betwen a pulse detector and the identified location of the pulse model. During the investigation of this research, a preliminary analysis of the pulse arival times at diferent wavelengths was pursued, and this analysis is presented at the end of this Chapter. Chapter 4 discuses the methods of time transformation betwen spacecraft clock measured time and inertial time standards. The various time standards used within the framework of navigation using these celestial sources are presented. Conversion from spacecraft clock proper time to coordinate time is discussed for near-Earth and interplanetary applications. The time transfer equation betwen the location of the spacecraft and the solar system barycenter is presented in detail. This transfer is the primary measurement equation used within many of the navigation schemes presented. A discussion is provided of how this transfer equation is related to existing pulsar-timing equations. 28 Chapter 5 gives a broad overview introduction into the methods of navigation using variable celestial sources. These include methods of time, atitude, velocity, and position determination. A description of a navigation system using these sources is provided. Chapter 6 provides the methods and algorithms for determining absolute position based upon measurements from variable celestial sources. The observable values and their erors, as wel as diferences of these values that can be computed, are presented in detail. Methods to compute solution acuracy based upon an observed set of sources are supplied. A simulation of the absolute position algorithms is described, and their performance is demonstrated for several orbit scenarios. Chapter 7 discuses the details of the scheme to correct an estimate of position and velocity. The necesary algorithms and acurate measurement equations are developed. An experimental validation of this method is provided using actual measured data from the NRL USA experiment. Chapter 8 presents the methods and algorithms necesary to implement sequential measurements of pulse observations with the dynamics of an orbiting spacecraft. The Kalman filter measurement models for both first-order and higher-order implementations are discussed. Results from simulations of these algorithms and discussions about the filter?s performance are provided. Chapter 9 concludes the disertation, identifying future work to be continued in the pursuit of the navigation goals using these celestial sources. There are several appendices that support the content within this disertation. Appendix A lists necesary supplementary data for use in various analyses throughout the text. Appendix B provides details on the X-ray catalogue created to support this navigation efort. Appendix C lists time of arival observations data used by the analysis in Chapter 7 and orbital elements of the investigated spacecraft. Appendix D provides an 29 overview of the Kalman filter related equations to support the discussion of Chapter 8. Appendix E identifies several known types of X-ray source detectors that could be utilized for spacecraft applications, including known advantages and disadvantages of each type. 30 Chapter 2 Variable Celestial Sources ?Twinkle, twinkle, litle star. How I wonder what you are ?? ? Jane Taylor 1806 The celestial sources that are utilized in this investigated method of spacecraft navigation are variable in their output intensity. A detailed description of these types of sources is provided below, including the physical mechanisms that produce the variable signal and the diferent types of electromagnetic radiation emited by these sources. It wil be shown that sources within the X-ray band of the electromagnetic spectrum posses perhaps the most advantageous characteristics for navigation. The diferent types of X-ray sources are presented, along with details of a newly created catalogue of the objects, which can be used to select candidate variable sources for navigation. 2.1 Variable Intensity Sources The known Universe is filed with numerous celestial objects that emit copious amounts of radiation. During the daytime, the solar system?s Sun is the singular bright, intense visible object in the sky. In contrast, as sen in the night sky, multitudes of objects emit, or reflect, radiation within the solar system, across the Galaxy, and beyond. 31 A momentary flicker, or twinkle, of these objects may occasionaly be sen. This is due to the light from these sources being atenuated in Earth?s atmosphere or pasing too close to a nearby object. However, mostly the light from these sources appears to be relatively constant. Although it appears that al sources produce fixed amounts of radiation, celestial objects exist whose intensity of their emisions vary over time. The variation in brightnes of many of these objects is quite regular, or periodic. Hence these objects are refered to as variable objects, or variable stars. It is these objects that hold promise in creating a new navigation system for spacecraft. Bright, fixed stars, with their continuous, steady, or persistent emision of radiation have been excelent navigation aides for travels across Earth?s globe, as wel as for some spacecraft traveling in the solar system. Existing star cameras and star trackers use persistent celestial sources to determine the atitude of the vehicle within an inertial frame to high acuracy. These sensors have also been occasionaly used to determine position of a spacecraft relative to a planetary body. These systems rely on the nature of these sources that their signal is constant, or invariable, such that database searches can identify viewed objects through their visible magnitude and relative position to nearby sources. Once the characteristic parameters of these persistent objects are entered into a database, it is expected that only minor updates in position would ever be required. However, variable celestial objects posses very diferent characteristics when compared to persistent sources. At a given instance, the intensity of the variable object fluctuates with respect to its observation at a later time. Many of the variable sources exhibit highly regular variations in intensity, although there are some variable sources that have iregular or inconsistent outbursts of energy. The variability of these sources 32 provides a periodic signal that asists in the prompt identification of each specific source, since most of these signatures are of unique period and strength. There are far fewer variable sources that have been detected and catalogued than the visible persistent stars. Approximately 38,500 visible variable sources have been catalogued versus the many milions of persistent sources [179]. The discovery of these types of sources was made only in recent history. The first variable source discovered was the super nova (stela nova, or new star) within the constelation Casiopeia by Tycho Brahe and W. Schuler in 1572 [62]. Shortly thereafter in 1596, the variable red giant star Mira (Omicron Ceti) in the constelation Cetus was discovered by David Fabricius; however, its periodicity was not established until 1638 by Holwarda [82, 175]. With their natural periodic signals, these variable sources posses similar navigation qualities of navigation beacons, or lighthouses, used by ocean-going vesels. Once a lighthouse upon the shore is identified, by using the known rotation frequency and color of the signal beacon one can determine the coarse range and heading estimates from the ship to the lighthouse. With the varying signal intensity due to the rotation, it is possible to ensure the detection of a lighthouse near the horizon, as opposed to a fixed signal that may be interupted or obscured, such as by waves on the surface of the ocean, shoreline obstructions, or atmospheric efects. The use of the variable celestial sources for spacecraft utilizes these same concepts as lighthouses on Earth for thre-dimensional navigation through space. 2.1.1 Variation Physics The variation of the signal intensity from these sources is due to either an intrinsic or extrinsic physical mechanism [179]. Intrinsic forms of producing this variability are due 33 to the object itself and its internal characteristics. Extrinsic methods are due to the external environment acting upon the source, which therefore varies the output of the source?s radiation. Intrinsic mechanisms include the two major clasifications of pulsating and eruptive types [2, 179]. Pulsating variable sources show variability due to their expanding and contracting surfaces, which can be detected during observation. This shape-change can either be in a radial or non-radial manner. Eruptive variable stars fluctuate due to violent thermonuclear outbursts within their coronae or chromospheres. These sources typicaly have iregular outbursts and flaring characteristics. Extrinsic mechanisms include the thre major clasifications of rotating stars, eclipsing binaries, and cataclysmic variables [2, 179]. Rotating stars produce variable radiations due to the rotation about their axes with respect to an observer. Hot, bright spots on their surfaces can become visible once per rotation. Alternatively, charged particles from the surrounding region about the star can be acelerated outward along the star?s magnetic axis, which sweps around the rotation axis and becomes visible once per rotation. Eclipsing binaries are sources that are eclipsed by their binary companions along the line-of-sight to an observer. As sources are eclipsed, their intensity diminishes until the eclipse is completed. Cataclysmic variables are explosive sources [44]. Their variation is produced by thermonuclear efects in their surface layers (novae), within their cores (super novae), or from proceses that emulate nova outbursts (nova-like). Many of these types of cataclysmic sources are within binary systems. There exist many sub-clasifications of these variable star types discussed above [179]. Primarily, these sub-types depend upon a specific star?s evolutionary proces and 34 unique characteristics of mas, rotation rate, and surrounding environment. Figure 2-1 provides a clasification hierarchy of variable celestial sources. 2.1.2 Source Types Conducive to Navigation The variable celestial sources, presented in the previous sections and Figure 2-1, are unique objects that posses interesting capabilities for spacecraft navigation. Some of the types are more conducive to diferent aspects of navigation. As with any system, however, there are advantages and disadvantages of selecting a specific source type for each navigation aspect. It wil be shown in the following chapters that in order to determine or update time, position, and/or velocity of a spacecraft it is beneficial to utilize sources that are intense, or bright, sources, such that detectors need not be too large; are stable, periodic signatures, such that models can be developed to predict their behavior; and have narow, sharp pulse profiles, such that the ariving pulses are quickly and easily identified. Of the various types of variable celestial sources, the eruptive and cataclysmic types do not clearly match these criteria since although their outbursts may be intense, they are typicaly hard to predict because of their unstable or iregular nature. The pulsating variable type sources do not produce sufficient signal variation to create narow pulse profiles, and few are intense sources. The most advantageous sources for these methods of navigation are the rotating and eclipsing binary types, since typicaly these source?s signatures are periodic and many are stable. These types are not bright sources, so some compensation must be made in detector design. Of the rotating source types, pulsar stars, those generating pulsed emision through the rotation of their magnetospheres or by the acretion of mater from a companion, are 35 exceptional variable celestial sources for navigation. Many of these objects have stable periodic signatures, and enough signal intensity so that practical systems can be developed to use pulsars for spacecraft time, position, and velocity determination. For navigation systems that utilize variable celestial sources for spacecraft atitude determination, any of the source types can be considered candidates as long as their radiation is sufficiently bright and produces a recognizable image on the system?s detector. Some of the sources that are not appropriate for position or time may be suitable candidates for atitude determination. 2.1.3 Variable Source Radiation The variation in intensity that is observed from these sources is due to the varying amount of electromagnetic radiation that arives at an observer?s location. The diferent sources types can emit radiation throughout the electromagnetic spectrum. A majority of the variable celestial sources emit in the visible, or optical, band of the spectrum [179]. However, many of the sources have been shown to emit one or more of the radio, infrared, visible (optical), ultraviolet, X-ray, and gama-ray bands of the spectrum. Figure 2-2 provides a simple representation of the electromagnetic spectrum, along with the wavelength, frequency, and energy per photon asociated with each band [18, 108]. Figure 2-3 provides images of the Crab Nebula and its pulsar in multiple spectrum wavelengths. This specific source produces variable radiation across the electromagnetic spectrum. Many variable sources produce radiation in multiple bands; however, the intensity and pulse shape of the radiation is typicaly not the same in each band. Figure 2-4 shows the pulse profiles observed from several sources across the electromagnetic spectrum. The diference in pulse shapes betwen sources across the spectrum is evident. 36 Figure 2-1. Variable celestial source classifications. Figure 2-2. Electromagnetic spectrum. 37 Figure 2-3. Crab Nebula and Pulsar across electromagnetic spectrum. (Courtesy of identified observatories [147]). Figure 2-4. Pulse profiles from various sources across electromagnetic spectrum. (Courtesy of D.J. Thompson (NASA/GSFC) [211]). NASA/CXC/SAOVLA/NRAO2MASS/UMass/ IPAC- Caltech/ NASA/NSF Palomar Obs. RadioInfraredVisibleX-ray 38 As the wavelength of each band within the spectrum changes, diferent methods of detecting these signals are required for observation. Radio and infrared wavelengths would typicaly utilize a type of antenna, whereas the visible band could use a standard telescope. The X-ray and gama-ray bands would require specialized detectors to capture and record the high-energy photons within these bands. Appendix E provides descriptions of several X-ray detector types. 2.1.4 Radio and Visible Sources By far the most studied variable sources are those that emit radiation within the radio and visible bands. This is primarily due to the ability of these longer wavelengths of the electromagnetic spectrum to penetrate Earth?s atmosphere, thus alowing early observers to make measurements at their observatories. Although variable sources have been found to emit in shorter wavelengths (implying higher frequency and higher photon energy), these discoveries were not made until instruments were taken above Earth?s signal absorbing atmosphere. There are numerous radio celestial sources that have been detected [77]. Many of these sources produce variable radiation in the radio band. Radio sources can be detected via large dish-type antennas on the order of tens to hundreds of meters in diameter. Examples of these include the National Radio Astronomy Observatory?s (NRAO) Telescope 85-3 at 26 m diameter or the Robert C. Byrd Gren Bank Telescope at 100 m diameter [154], the National Astronomy and Ionosphere Center?s (NAIC) Arecibo Observatory?s Radio telescope at 305 m diameter [142], or the Russian Academy of Science?s Special Astrophysical Observatory (SAO) Radio Astronomical Telescope Academy Nauk (RATAN-600) at 576 m diameter [181]. The Australia Telescope 39 National Facility (ATNF) has recently completed the most comprehensive radio pulsar study to date in their Parkes Multibeam Pulsar Survey. This survey has increased the number of known radio pulsars from 558 [208] to over 1400 [81, 119]. The General Catalogue of Variable Stars (GCVS) presents a detailed clasification of sources known and measured to produce variable radiation [178, 179]. These list al opticaly visible sources, with a total of 38,525 sources currently catalogued. Many are faint sources and require powerful optical telescopes to view them. Examples of these are NASA?s orbiting Hubble Space Telescope at 2.4 m in diameter [143], the California Institute of Technology?s Palomar Observatory Hale Telescope at 5 m in diameter [30], and the SAO Big Telescope Alt-azimuthal (BTA) telescope at 6 m in diameter [180]. 2.1.4.1 Navigation Isues with Radio and Visible Sources Selecting a wavelength to observe variable sources and utilize their information within a navigation system can be a chalenge due to al the options described above. Idealy, one would choose to select the best source candidates for high navigation performance. However, since these candidates may only be ideal in diferent wavelengths, a navigation system would be required to have sensors that could detect across multiple wavelengths. Multiple detector types are typicaly impractical for spacecraft systems due to their extra power and weight requirements. Selecting one type of detector is more advantageous for spacecraft operations. Variable sources that emit in the radio band are certainly one consideration for a navigation system. There are numerous radio sources, as wel as a significant number of radio emiting rotating stars [12, 77]. However, at the radio frequencies that these variable sources emit (~100 MHz to few GHz) and with their faint emisions, radio-based 40 systems would require antennas 20 m in diameter or larger to detect sources. For most spacecraft this size of an appendage would severely impact design, operation, and cost [69, 107]. Some celestial objects are broadband radio sources that could obscure weak pulsar signals at a spacecraft?s detector [218]. With these neighboring radio sources and the low signal intensity from radio pulsars, a navigation system based upon radio may require significantly long signal integration times to produce an aceptable signal-to- noise ratio from each source. Similarly, limitations exist with the optical variable sources. Given the number of variable sources presented by the GCVS catalog suggests there should be an ample number of candidates for navigation. However, this large number of sources can also be a hindrance, since many sources increases the complexity of the identification proces. If bright persistent visible stars exist nearby a variable source, precise telescope pointing and significant signal procesing would be required to detect the source?s signal variation in order to not be overwhelmed by the nearby source. As is shown in the visible band of the Crab Nebula in Figure 2-3 many sources are visible within a close proximity of the Crab Pulsar. Observing dim, visible variable sources requires a large aperture optical telescope to collect sufficient photons. Smaler spacecraft could not aford the extra mas of these observatories. However, perhaps the most detrimental aspect of creating a navigation system based upon optical variable sources is the very smal population of pulsars with detected optical pulsations. To date, there are only five faint, isolated pulsars observed in the visible band [185]. Therefore, even with the advantages of numerous, studied sources, the radio and visible bands appear not to be the proper choice for selecting variable source candidates. 41 2.2 Variable Celestial X-ray Sources Although the sources that emit in the radio and visible bands suffer from significant disadvantages when applied to spacecraft navigation, these disadvantages diminish for the sources that emit in the X-ray band. The primary advantage for spacecraft navigation using X-ray types of variable sources is that smaler sized detectors can be utilized. This offers significant savings in power and mas for spacecraft development and operations. It wil be shown in Chapter 3 that detectors on the order of one to several square-meters can be efectively utilized to perform the navigation function. Other important advantages of X-ray sources include being unique and widely distributed. This makes the identification of these sources les complex. The image of the Crab Nebula and its pulsar in Figure 2-3 shows that the pulsar can be much more easily identified as the unique source in the image without al the clutter of extra sources as can be sen in the infrared and visible band images. Because of the potential smaler detector size and their unique identification, variable celestial X-ray emiting sources were chosen as the primary source candidates for this research in spacecraft navigation. This section describes the types of X-ray sources, specificaly the X-ray pulsars that are wel suited for navigation purposes. Due to the characteristics of these sources, some potential chalenges of using these sources for navigation are also presented. 2.2.1 X-ray Source Types In order to utilize these types of sources for navigation, it is important to understand the characteristics and quantity of al X-ray sources. The X-ray sky contains several types of celestial objects that can be used for various aspects of spacecraft navigation. 42 Variable X-ray objects employ an aray of energy sources for their X-ray emisions. Table 2-1 presents a brief description of the various types of X-ray sources. Although al variable emision sources are excelent candidates for time, position, and/or velocity determination, those objects that produce persistent, non-pulsating X-ray flux may be good candidates for atitude determination. Figure 2-5 presents a hierarchy of X-ray source clasification. The many diferent X- ray source types can be categorized as either a simple, often solitary, object; a compound set of objects; an extended object, generaly a large, complex object; and an extragalactic object, which includes much of the X-ray background. The compact objects of white dwarf stars, neutron stars, and black holes are sources of significant mas but relatively smal radius when compared to most other stars. Although the maximum value may be defined higher (as shown in Appendix A), X- ray sources esentialy emit within the 0.1?200 keV energy band of the electromagnetic spectrum. The wavelengths and frequencies of such sources are 1.24?10 -8 ?6.20?10 -12 m and 2.4?10 16 ?4.8?10 18 Hz, respectively. A soft range of X-rays can be considered within the range of 0.1?10 keV, and a hard range of 10?200 keV. However, there is often great flexibility in the definition of these soft and hard ranges. The primary measurement from these X-ray sources is the high energy photons emited by the source. The rate of arival of these photons can be measured in terms of flux of radiation, or number of photons per unit area per unit time. Given the energy range of photons being observed, the total number of photons can be converted to energy, such that the received energy flux is in terms of energy per unit area per unit time. Typical units for these measurements of flux are photons/cm 2 /s or ergs/cm 2 /s. 43 Table 2-1. Description of Various X-ray Source Types [145, 227]. Source Acronym Description Active Galactic Nuclei AGN Acretion onto central black hole produces X-ray emisions. Algol -- Triple variable star system (named after first in clas, Algol). Atol Sources -- Quasi-periodic sources, neutron stars with weak magnetic field. Binary Variable BV Binary variable star system. Black Hole Candidates BHC Sources with indication of a black hole. Cataclysmic Variables CV White dwarf stars acreting material from a binary companion. Coronal Stars CS X-ray emision generated in the coronae of active stars. Difuse X-ray Background DXB Background X-ray radiation. Galactic Ridge Emision GRE Difuse X-ray emision extending along the Galactic plane. Galaxy Clusters GXC X-ray emision from hot intracluster gas traped near center. Globular Cluster GC Vast colection of stars with X-ray emision from within cluster. Neutron Star NS Compact star, either isolated or in binary system. Pulsar PSR Neutron star emiting pulsed radiation. RS CVn -- Binary variable star, no mas transfer (first: Canes Venaticorum). Soft Gama Repeaters SGR Highly magnetized neutron stars, ocasional burst of gama rays. Supernova Remnant SNR X-ray emisions of heated remnant material of supernova explosion. White Dwarfs WD Cores of stars after exhausted al their elements. Z Sources -- Quasi-periodic sources, neutron stars with strong magnetic field. 2.2.1.1 X-ray Background The difuse X-ray background is an appreciably strong signal that is observed when viewing the X-ray sky. The X-ray background is largely composed of two components, soft and hard [38]. The soft component is for energies les that 1.0 keV, and is produced by the glow of stars and clouds of hot gases within approximately 100 parsecs of the Sun. It is refered to as the galactic X-ray background. This galactic component of the X-ray background has a detectable spatial structure, and is based upon the strong sources within the Milky Way galaxy. The hard component of the X-ray background is for energies greater than 1.0 keV. This component is produced by the many sources outside the Milky Way galaxy, and is largely isotropic in structure. Measures of the X-ray background radiation must be considered when observing a source. Variable X-ray sources must emit more radiation than this background signal in order for it to be detectable. This background signal can be considered noise within the 44 detected X-ray flux from a source. Aceptable signal-to-noise (SNR) ratios of these source signals are esentialy the magnitude of the received X-ray flux above the expected X-ray background level for a certain location in the sky. Figure 2-5. X-ray source type classifications. 45 2.2.2 X-ray Pulsars This section provides detailed discussions on the pulsar stars; including their evolution, discovery, and details on the various types of these variable sources. 2.2.2.1 Neutron Stars Theories of general relativity and stelar structure project the evolution of a star as it progreses through its life cycle [37, 53]. These theories predict that upon their collapse, stars with insufficient mas to create a black hole, objects with such imense gravitational fields that even light cannot escape, produce several types of ultra-dense, compact objects. Two such proposed objects are white dwarf (WD) stars and neutron stars (NS) [13, 14, 155]. These objects are the result of a masive star that has exhausted its nuclear fuel and undergone a core-collapse resulting in a supernova explosion. For those with remaining material after the supernova of near 1.4 solar mases, the stelar remnant collapses onto itself to form a neutron star. The resulting neutron star is a smal, extremely dense object that is roughly 10 km in radius. This smal, compact object is an equilibrium configuration in which its nuclear efects provide support against the strong gravity. To reach this alowed equilibrium configuration the stelar constituents must be adjusted by reactions that force fre electrons together with protons to form neutrons, hence the name neutron stars. It is postulated that a neutron star is composed of a solid outer crust of neutron-rich nuclei a few tenths of kilometer thick surrounding a superfluid core. Conservation of angular momentum during the colapse phase of the stelar remnant greatly increases the rotation rate of the neutron star. Young, newly born neutron stars typicaly rotate with periods on the order of tens of miliseconds, while energy disipation 46 eventualy slows down older neutron stars to periods on the order of several seconds. Unique aspects of this rotation are that it can be extremely stable and predictable. 2.2.2.1.1 Pulsar Discovery In 1967, Cambridge University graduate student Jocelyn Bel and her supervisor Profesor Anthony Hewish discovered radio pulsations during a survey of scintilation phenomena due to interplanetary plasma in the radio frequency of 81.5 MHz [80]. Among the expected random noise emerged a signal having a period of 1.337 seconds and constant to beter than one part in 10 7 . Because of the extreme stability in the periodic signature, it was first conjectured that it could not be a natural signal (thus the original term of LGM, for litle gren men, was phrased for these objects). However, once the discovery confered with stelar theory, it was soon realized that these objects were rotating neutron stars, pulsars, pulsating at radio frequencies. Since their discovery, pulsars have been found to emit throughout the radio, infrared, visible, ultraviolet, X-ray, and gama-ray energies of the electromagnetic spectrum. With their periodic radiation and wide distribution, pulsars appear to act as natural beacons, or celestial lighthouses, on an intergalactic scale. 2.2.2.2 Rotation-Powered Pulsars Many X-ray pulsars are rotation-powered pulsars (RPSR). The energy source of these neutron stars is the stored rotational kinetic energy of the star itself. The X-ray pulsations occur due to two types of mechanisms, either magnetospheric or thermal emisions [38]. Some neutron stars can emit using both types of mechanisms. Neutron stars harbor imense magnetic fields [25]. Under the influence of these strong fields, charged particles are acelerated along the field lines to very high energies. 47 As these charged particles move in the star?s strong magnetic field, powerful beams of electromagnetic waves are radiated out from the magnetic poles. X-rays, as wel as other forms of radiation, can be produced within this magnetospheric emision. If the neutron star?s spin axis is not aligned with its magnetic field axis, then an observer wil sense a pulse of electromagnetic radiation as the magnetic pole sweps across the observer?s line- of-sight to the star. Alternatively, pulsed X-ray radiation can be sensed as hot spots on the rotating neutron stars cross the line-of-sight to the observer. After their formation following a supernova explosion, neutron stars are extremely hot. As they age, local areas on the surface of these stars cool at diferent rates, leaving some locations hotter than others. The thermal energy in these hot areas causes electrons to acelerate, collide with other particles, and radiate electromagnetic energy. Since no two neutron stars are formed in exactly the same manner or have the same geometric orientation relative to Earth, the pulse frequency and shape produce a unique, identifying signature for each pulsar. Figure 2-6 provides a diagram of a neutron star with its distinct spin and magnetic axes. These objects may exist either as an isolated neutron star (ISN), with no local companion objects, or as a component of a multiple star system [215]. Figure 2-3 shows an X-ray image of the Crab Nebula and Pulsar (PSR B0531+21) taken by NASA?s Chandra X-ray Observatory. The pulsar can be sen as a distinct object within the Nebula. Figure 2-7 provides an X-ray image from Chandra of the Vela rotation-powered pulsar (PSR B0833?45). 48 Figure 2-6. Diagram of pulsar with distinct rotation and magnetic axes. Figure 2-7. Vela Pulsar (PSR B0833?45) X-ray image taken by Chandra observatory. (NASA/PSU/G.Pavlov et al. [146]) 49 2.2.2.3 Acretion-Powered Pulsars Acretion-powered pulsars (APSR) are neutron stars in binary systems where material is being transfered from the companion star onto the neutron star. This flow of material is channeled by the magnetic field of the neutron star onto the poles of the star, which creates hot spots on the star?s surface. The pulsations are a result of the changing viewing angle of these hot spots as the neutron star rotates. These types of pulsars are subdivided into those with a companion of certain mas. A pulsar that produces X-ray radiation and orbits a high-mas companion exists in what is refered to as a High-Mas X-ray Binary (HMXB) system. The companion object is typicaly 10?30 solar mases in size. These objects are imense in comparison to the smal neutron star. A portion of the strong stelar wind produced by the companion star is absorbed, or acreted, by the neutron star. X-ray radiation is produced by the pulsar as it travels through the stelar wind in its orbit about its companion star [38]. Figure 2-8 provides a conceptual diagram of a HMXB system. Alternatively, neutron stars can inhabit systems with companion objects of much lower mas, perhaps of size les than one solar mas. These systems are refered to as Low-Mas X-ray Binary (LMXB) systems. The stelar wind of these lower mas companions is much smaler. However, the gravitational potential of the neutron star is sufficient to atract mater from the companion object. The proces of acretion transfers mas from the companion onto the neutron star producing a large accretion disk surrounding the neutron star [100]. X-rays are created as mater from the acretion disk is transfer onto the neutron star [38]. Figure 2-9 shows a conceptual diagram of a LMXB system. 50 Figure 2-8. High-mass X-ray binary system. Figure 2-9. Low-mass X-ray binary system. Although pulsars within binary systems can produce significant amounts of X-ray flux, the pulsations of these types of pulsars are more complex. This is due to the combined efects of both the rotating neutron star and the orbit of the star about its 51 companion. Also, along the line-of-sight to an observer, the companion can eclipse the neutron star and its signal. These eclipsing binary systems introduce additional signal complexity. 2.2.2.4 Anomalous X-ray Pulsars A smaler population of X-ray pulsars is those sources that are powered by the decay of their imense magnetic fields. The magnetic field strength of these sources is approximately 10 13 ?10 15 Gauss [210]. For comparison, the magnetic field strength of the Sun is approximately 50 Gauss [221]. These anomalous X-ray pulsars (AXP) have similarities to the soft gama repeater (SGR) sources. Magnetars, neutron stars with incredibly imense magnetic fields (> 10 14 Gauss) are asumed to be part of this pulsar type [52, 210]. 2.2.3 Navigation Challenges with X-ray Sources Al celestial sources that emit sufficient detectable X-ray photons can be implemented in some manner within the spacecraft navigation scheme. Of the various X-ray sources that exist, X-ray pulsars, including rotation-powered and acretion-powered types that produce predictable pulsations, posses the most desirable characteristics for determining time and position. However, several isues complicate their utilization for navigation solutions. Pulsars that emit in multiple electromagnetic wavelengths do not necesarily have the same temporal signature in al observable bands. Studies have compared pulsars at visible, radio, and X-ray bands, and show that the pulse arival times are disimilar across diferent bands, as is evident from Figure 2-4. While a vast majority of pulsars are 52 detectable at radio wavelengths, only a subset are sen at the visible, X-ray, and gama- ray wavelengths. As X-ray and gama rays are dificult to detect on the ground due to the absorption of these wavelengths by Earth?s atmosphere, observations in these bands must be made above the atmosphere. The highly energetic photons emited by the source must be detected by pointing the X-ray detector at the source, or by waiting until the source enters the field of view (FOV) of the detector. In addition, many X-ray sources are faint and require sensitive instruments to be detected. The Crab Pulsar (PSR B0531+21) is the brightest rotation-powered pulsar in the X-ray band, yielding ~9.9?10 -9 ergs/cm 2 /s of X-ray energy flux in the 2?10 keV band. The next brightest rotation-powered pulsars are over an order of magnitude fainter than the Crab Pulsar (ex. PSR B1509-58 and SAX J1846-0258) [158]. Due to the faintnes of these sources, long observation times are required to produce aceptable SNR values. Multiple detectors may be necesary if many independent measurements are required within a given procesing time span. Most bright X-ray sources, although located within the Galaxy, are stil very far from the solar system. The distances to X-ray sources cannot be determined to an acuracy that would alow absolute range determination betwen the source and a detector. However, the angular position in the sky can be determined with high precision, and this direction knowledge can be used in determining a navigation solution. These sources are not truly fixed in the celestial sky, as they have proper?motion, or radial and transverse motion relative to the solar system. However, the source?s displacement from this proper?motion is very smal compared to typical source observation durations. Many sources are clustered along the Milky Way galactic plane; hence there are a limited number of bright 53 sources that could provide off-plane triangulation for thre-dimensional position determination. Although pulsars are uniquely recognizable due to their diferent pulse shapes, a single pulse from a specific pulsar is not directly identifiable. Thus, a navigation system that updates position using the fraction of the phase cycle within a pulse must either have an a priori estimate of position to approximately align phase within a pulse, or must use additional methods to correctly identify which specific pulse is detected. The stability of pulse arival must also be considered when creating models to predict pulse arival times. Sources with large period derivatives must have their models updated if a long time has elapsed since the last model definition. Models that are efective for sufficiently long durations, thus requiring infrequent updates, are desirable from stable sources. Databases that contain precise models should be maintained and distributed frequently to alow users to create acurate measurements. Though nearly al rotation-powered pulsars are constant in intensity, many acreting pulsars and most other X-ray source clases often exhibit highly aperiodic variability in intensity that may compromise their usefulnes for precise time and position determination [214]. Those in binary systems introduce more complex signal procesing and pulse arival time determination than isolated sources. Many acreting sources are unsteady, or transient, sources. This phenomenon of reduced X-ray emision for some duration is due primarily to stelar physics [223]. The recurrence times of transient sources are often unpredictable. Sources that exhibit transient characteristics cannot be used as continuously detectable navigation source candidates. High intensity signals lasting for short periods, X-ray flares and X-ray bursts, are ocasionaly detected from 54 some sources [109]. Since neutron stars are believed to contain a solid crust and a superfluid interior, exchanges of angular momentum betwen the two materials can cause unpredictable star-quakes. These events can significantly alter the spin rates of these stars, and create timing glitches in the periodicity of the source. The difuse X-ray background would be present in al observations, and this would add to any noise present in the detector system. A navigation system that utilizes pulsed emisions from pulsars would have to addres the faintnes, phase cycle, transient, flaring, bursting, and glitching aspects of these sources, in addition to the presence of the noise from the X-ray background, in order to succesfully produce solutions. 2.3 X-ray Source Catalogue To support the use of these types of objects for spacecraft navigation, a catalogue of variable celestial X-ray sources has been asembled. Gathering al the data for these sources into one collective set alows the analysis of each source for its potential as a candidate for navigation purposes. This section describes the asembled X-ray Navigation Source Catalogue (XNAVSC) in further detail. A brief discussion is provided on the types of X-ray astronomy misions pursued to discover new objects. Many of these misions produced lists of their observed sources and characteristics, which can be merged together with other mision?s data. A description of how and where the sources for the catalogue were collected is presented. The types of parameters recorded for each source is discussed. Information and overal 55 statistics about the catalogue are also provided. Additionaly, Appendix B of this document provides a detailed listing of the XNAVSC. 2.3.1 X-ray Source Survey Missions The isues raised in the previous sections require careful analysis of X-ray sources in order to develop a working spacecraft navigation system with sufficient performance. To acomplish this analysis, the identification of X-ray sources that have been discovered and characterized is required. The first non-solar cosmic X-ray source, Scorpius X-1 (B1617-155), was detected in June 1962 using Geiger counters onboard a rocket at a 230 km altitude [45, 66, 67]. Since this discovery, numerous baloon, rocket, and satelite borne instruments have surveyed the sky. Diferent X-ray misions have observed the X-ray sky in various energy ranges, depending on instrument characteristics or mision goals. Table 2-2 provides a list of misions designed for X-ray source discovery and survey. During its mision in the late 1970s, HEAO-1 detected 842 sources within the 0.2?10 keV range [233]. The German X-ray observatory ROSAT in 2000 completed the latest comprehensive al-sky survey of the X-ray sky [216, 217]. This mision detected 18,806 bright sources (above 0.05 X-ray photon counts/s in the 0.1?2.4 keV range), and a significant number of sources, 105,924 objects, in its faint al-sky X-ray survey. 2.3.2 Selection of Sources The sources within the XNAVSC were collected from many diferent existing catalogues and individual source description papers, as wel as existing Internet web sites that provide databases on X-ray sources. The complete listing of the catalogue?s 56 references is provided in Appendix B. At the beginning of this research, no single definitive existing catalogue could provide al the information for these sources. Either the databases or articles concentrated on a specific type of X-ray source, they were too general in format with insufficient parameter detail, or they listed only detailed information on a smal subset of sources. Thus, it was necesary to collect al the source information into one database such that it could be acesed for source evaluation and selection. There are several major contributors to this catalogue, which either asisted the beginning formulation of this collection or provided additional detail on a large number of sources. Table 2-3 provides a summary of these major contributors, listed in order of the number of sources in their catalogues. Of these, the NASA High Energy Astrophysics Science Archive Research Center (HEASARC) X-ray Master Catalog [78] and the ROSAT Catalogs [216, 217] contain the most numerous sources. Special acknowledgement is made to the X-ray source tables generated by Dr. Yong Kim [99]. This major contribution was significant for the beginning development of the XNAVSC. Since the X-ray pulsars are of significant interest for navigation, the listing of radio emiting pulsars is important to study since radio pulsars are often later observed to also emit X-ray radiation. Table 2-4 provides a list of the primary radio pulsar catalogues refered to while asembling the XNAVSC. 57 Table 2-2. X-ray Source Survey and Discovery Misions [75]. Mision Name Mision Operation Energy Range (keV) ORS 3 July 1965 ? Sep 1965 0.8 ? 12 OSO 3 Mar 1967 ? Nov 1969 7.7 ? 210 Vela 5B ay 1969 ? June 1979 3 ? 750 Vela 6A Apr 1970 ? Mar 1972 3 ? 12 Vela 6B Apr 1970 ? Jan 1972 3 ? 12 UHURU Dec 1970 ? Mar 1973 2 ? 20 OSO-7 Sep 1971 ? July 1974 1 ? 10,00 Copernicus Aug 1972 ? Feb 1981 0.5 ? 10 Skylab May 1973 ? July 1979 0.1 ? 0.3 ANS Aug 1974 ? June 197 0.1 ? 30 Ariel V Oct 1974 ? Mar 1980 0.3 ? 40 Salyut-4 Jan 1975 ? Feb 197 0.2 ? 9.6 SAS-3 May 1975 ? Apr 1979 0.1 ? 60 OSO-8 June 1975 ? Sep 1978 0.15 ? 1,00 Apolo-Soyuz July 1975 0.6 ? 10 HEAO-1 Aug 197 ? Jan 1979 0.2 ? 10,00 Einstein Nov 1978 ? Apr 1981 0.2 ? 20 Hakucho Feb 1979 ? Apr 1985 0.1 ? 10 P78-1 Feb 1979 ?Sep 1985 3 ? 10 Tenma Feb 1983 ? Nov 1985 0.1 ? 60 Astron Apr 1983 ? June 1989 2 ? 25 EXOSAT May 1983 ? Apr 1986 0.05 ? 20 Spacelab 1 Nov 1983 ? Dec 1983 2 ? 30 Spartan 1 June 1985 1 ? 12 Spacelab 2 July 1985 ? Aug 1985 2.5 ? 25 Ginga Feb 1987 ? Nov 191 1 ? 50 Kvant Apr 1987 ? Oct 1989 2 ? 20 Granat Dec 1989 ? Nov 198 2 ? 10,00 BXRT Dec 190 0.3 ? 12 ROSAT June 190 ? Feb 199 0.1 ? 2.5 EURECA Aug 192 ? July 193 6 ? 150 DXS Jan 193 0.15 ? 0.28 ASCA Feb 193 ? Mar 201 0.4 ? 10 Rosi XTE Dec 195 ? Present 2 ? 250 IRS-P3 May 196 ? June 200 2 ? 18 BepoSAX Apr 196 ? Apr 202 0.1 ? 30 USA May 199 ? Nov 200 1 ? 15 Chandra July 199 ? Present 0.1 ? 10 XM-Newton Dec 199 ? Present 0.1 ? 15 HETE-2 Oct 200 ? Present 0.5 ? 40 Swift Nov 204 ? Present 0.2 ? 150 58 Table 2-3. Major Contributors to the XNAVSC. Authors Reference X-ray Source Types Number of Listed Sources NASA HEASARC X-ray Catalog [78] Al > 10,00 ROSAT (Voges et al.) [216] Faint Sources 105,924 ROSAT (Voges et al.) [217] Bright Sources 18,806 Yong Kim Tables [9] Al 81 HEAO A-1 (Wod et al.) [23] Al 842 Riter & Kolb [174] CV, LMXB, & Related 414 Meliani [129] Al 26 Liu, van Paradijs, & van den Heuvel [11] LMXB & AXP 158 Astronomical Almanac [1] Al 135 Liu, van Paradijs, & van den Heuvel [10] HMXB 130 NRL USA [230] Al 90 Singh, Drake, & White [196] RS CVn & Algol 8 XTE (ASM) & BATSE [139] APSR & AXP 8 Corbet et al. [43] XPSR in SMC 47 Majid, Lamb, & Macomb [16] XPSR in SC 46 Posenti et al. [158] RPSR 41 Meregheti [131] APSR & AXP 34 Becker & Tr?mper [19] RPSR 27 Freire et al. [60] XPSR in 47 Tucanae 20 Grindlay et al. [70] XPSR in 47 Tucanae 17 Becker & Tr?mper [20] MPSR 10 White & Zhang [22] PSR 10 Kuiper & Hermsen [105] MPSR 3 Table 2-4. Radio Pulsar Catalogues. Authors Reference Number of Radio Pulsars ATNF Pulsar Catalogue [12] 1412 Lyne & Graham-Smith [14] 73 Princeton University Pulsar Catalog [159] 706 Taylor, Manchester, & Lyne [208] 58 Manchester & Taylor [18] 149 2.3.2.1 Source Selection Criteria Sources were selected from the catalogues of Table 2-3 as wel as the individual source papers listed in Appendix B. Duplicate source listings from diferent catalogs were not repeated in the XNAVSC. The number of available X-ray sources is significantly larger than the number of sources listed in the XNAVSC. This is due to the selection criteria for the sources in the XNAVSC. 59 Firstly, in order for a source to be selected to the XNAVSC, it must have a wel- determined position. Position knowledge on the order of fractions of arcseconds in RA and Dec wil be shown to be important in Chapters 3 and 4, thus only sources with good position knowledge were added to the catalogue. Secondly, only sources with measured X-ray radiation flux were retained. Sources with unmeasured flux either identify a faint source (too faint to be adequately computed by a mision) or are not wel defined. The amount of flux produced by a source is critical for its evaluation as a navigation candidate. Thirdly, if a source had a measured pulse frequency, or orbital period in a binary system, determined within the X-ray band, these sources were retained. As mentioned previously, pulsars, either rotation-powered or acretion-powered, are the predominant sources for time and position determination. Thus, to be considered as candidates, sources should have measured X-ray flux, and preferably pulsed flux. 2.3.3 X-ray Catalogue Parameters The XNAVSC is separated into thre main lists, the Simple List, the Detailed List, and the 2?10 keV Energy List. The data parameters of each of these lists are discused below. 2.3.3.1 Catalogue Simple List The first list, refered to as the Simple List, provides a simplified listing of al the sources in the database. Many objects that have been discovered by a mision and then rediscovered by subsequent misions have multiple names asociated with them. This can be incredibly confusing when trying to determine which source is presented. The XNAVSC retains a source based upon its measured position, and not its name. For a 60 source that has multiple names, the common ones from various misions are collected in this Simple List. The Simbad Astronomical Database was refered to for both additional names and position verification [35]. Many individual sources are named by their measured position in the format of Right Ascension?Declination. If a source has a measured position asociated with the B1950 inertial frame, then the position name is typicaly pre-appended by a ?B? (B-name); for those measured in the J2000 inertial frame, they are pre-appended by a ?J? (J-name). Many sources, but not al, are pre-appended by either their type, such as PSR for Pulsar or SNR for Super Nova Remnant, or by their discoverer mision experiment name, such as SAX for BeppoSAX or XTE for Rossi X-ray Timing Explorer. The Right Ascension (RA) is typicaly broken into two numeral of hours and two numerals of minutes; however seconds are sometimes included by using fractions of minutes. For Declination (Dec) two numeral of degres and two numerals of arcminutes are used; although arcseconds can be included by using fractions of arcminutes. For example, the Crab Nebula pulsar is RA (B1950) = 05hr 3min and Dec (B1950) = +21? 58min, thus its name is often presented as PSR B0531+21. The naming convention for these sources follows the International Astronomical Unions Recommendations for Nomenclature of celestial objects [86]. To simplify source nomenclature, and to provide a specific source reference within the database, the XNAVSC creates a name of Jhhm?ddmm for al of its sources, based upon the J2000 inertial position of RA and Dec. In many cases, this name matches the common name of the source, but for those sources whose refined position location does not match the original discoverer?s position and name, the XNAVSC name may deviate 61 slightly from the common name. Caution should be taken, as these XNAVSC names are not intended to rename sources, rather to provide a single consistent naming convention throughout the database and to provide a catalogue reference for checking for repeated source listings. The Simple List specificaly identifies this correlation betwen the database J-name of an object and its more common names. The Simple List also provides a listing of an object?s type. The object type follows the hierarchy of Figure 2-5. The order of the objects within the Simple List is in the order of their instalation into the database. 2.3.3.2 Catalogue Detailed List The second list, the Detailed List, provides al the characteristic parameters of a source. This is broken into six major areas: Name and Type, Position, Energy, Stability, Periodicity, and Reference. Each of these areas is discussed in further detail below. The objects in the Detailed List follow the same order as the Simple List. The Name and Type section provides the catalogue specific J-name and its B-name, if it exists. It also provides the object?s type, as wel as object clas and sub-clas. These categories follow the same hierarchy of Figure 2-5. The Position section provides the J2000 inertial frame RA and Dec, as wel as any known uncertainties in these values. The Galactic Longitude (LI) and Latitude (BI) are provided, which are transformed values from the recorded RA and Dec values. These longitude and latitude values represent a sphere of the Milky Way galaxy, with the Galactic plane forming the equator of this sphere. The value of the distance to the source is reported in units of kiloparsecs (1 parsec = 3.262 light years = 3.086?10 16 m). Distances to these sources can only be currently determined on the order of a fraction of a 62 kiloparsec, so these values represent coarse distance measurements. The z-distance to the source is also reported, or its distance above the galactic plane. The measured proper motion of the source is also reported and must be considered if precise position location of a source is required at a particular observation time. The Energy section reports the measured X-ray flux of each source and parameters related to this flux. For the XNAVSC, the flux is separated into two sections of Soft X- rays, those with measured energies < 4.5 keV, and Hard X-rays, those with energies > 4.5 keV. Survey misions use unique instruments that are designed to measure the arival of photons at diferent energies as shown in Table 2-2. Thus, the measured flux of sources is dependent on the mision that observed it. Some sources have X-ray flux measured in both Soft and Hard X-ray energies, while others have measured flux in only one band or the other. The Neutral Hydrogen Column Density (n H ), is the amount of hydrogen atoms per unit area along the direction to the source. This value, along with the photon index, is used to convert the number of photon counts from a mision instrument for an object into energy flux. The measured pulsed fraction, p f , is also recorded. This important parameter is used in determining the acuracy of a pulse time of arival in Chapter 3. The pulsed fraction is the ratio of the pulsed flux to the mean flux, quantifying the amount of flux that is pulsed from a source [27]. To compute the pulsed fraction the X-ray flux, F x , from a source can be determined as a function of the phase cycle of a pulse profile, as, F x =! () ;0"1 (2.1) The minimum flux is defined as the minimum value of flux over this cycle as, x min =F x ! () " # $ % ;0&1 (2.2) 63 The pulsed flux, F x pulsed , is the diference over the phase cycle of the pulse profile betwen the measured flux and the minimum flux, as in F x pulsed = x ! () "F x min # $ % & 0 1 ' d (2.3) The mean flux over this cycle can be computed using, x mean x () " # $ % 0 1 & d (2.4) Therefore, the pulsed fraction is, p f = F x pulsed m (2.5) The pulse width, W , is another important parameter in the arival time analysis, and two forms of this width are listed in the XNAVSC. The 50% width of the pulse profile, or Full-Width Half-Maximum (FWHM) is provided, as wel as the width at 10% of the peak intensity, or Ful-Width 10% Maximum (FW10). Figure 2-10 provides a diagram of a pulse profile along with the identification of these pulse widths. If the magnetic field strength is estimated of the source, this value is also recorded. The Stability section defines the characteristics about the known stability of the source rotation and signal. The source is either characterized as a known steady periodic or transient signal. If the source produces X-ray bursts, or has any known timing glitches, these are also noted. For those sources existing in binary systems, this is highlighted to alert the user of the potential additional complexity in determining pulse time of arivals from the signal of these sources. The Periodicity section provides data on the known pulse cycles and binary orbit parameters. The pulse period, P , is the time interval betwen pulses. Any known first, 64 ! P , and second, ! P , order period derivatives are provided. The epoch, or time, of the determination of this period and its derivatives is recorded. The characteristic age, ! C , is computed using its definition of, ! C = P 2 (2.6) This term provides a measure of the rate of slow down in the rotation rate, as wel as a representative age of the object [118]. If a source is a component of a binary system, then its orbital period in that system is provided. The Reference section of the Detailed List provides information about the references utilized for the catalogued data. Figure 2-10. Pulse profile and widths. 2.3.3.3 Catalogue 2?10 keV Energy List The third list, the 2?10 keV Energy List, of the XNAVSC provides additional information on the X-ray flux from a source. The reported measured flux from each source is provided from the Detailed List. However, since many of these sources have been measured at diferent X-ray energy bands, it is dificult to draw imediate 65 comparisons betwen the sources. It is easier to make these comparisons if flux from each source is determined in the exact same band. Thus to facilitate these comparisons, al the fluxes are converted into the same 2?10 keV energy band. Various methods have been employed to make these conversions, such as the reported conversion rates from source references or the PIMS mision count energy conversion software tool from NASA HEASARC [76]. Although analyses can be pursued using these similar band flux values, caution should be exercised when quoting these values. Although X-ray flux may be measured in a band higher or lower than the 2?10 keV, there is no guarante that the source wil actualy produce similar radiation within this specific band. 2.3.4 X-ray Catalogue Data Characteristics The XNAVSC is designed to provide a listing of celestial X-ray sources that are candidates for use in spacecraft navigation. This section provides an overview of the sources and their data characteristics from the catalogue as a whole. Table 2-5 provides the total number of catalogued sources as of this publication contained in the XNAVSC. Table 2-6 through Table 2-11 provide a breakdown of each major source object type into their clases and sub-clases. Appendix B provides additional information on source clasification and XNAVSC data description. Figure 2-11 provides a plot of al the sources within the XNAVSC database. This figure is presented in Galactic longitude and latitude, where the equator of the plot is along the Galactic plane. X-ray sources exist throughout the X-ray sky, as is evident from Figure 2-11, although the clustering near the Galactic plane is clear. Distances to X-ray objects range from several to thousands of parsecs. Most sources are detected within the 66 Galaxy, however as many as 45 pulsars are located outside the Galaxy in the Large and Smal Magelanic Clouds (LMC and SMC, respectively) ? two iregular dwarf galaxies near Galactic coordinates 80?W?33?S and 60?W?45?S [56]. Figure 2-12 provides this same information using Right Ascension and Declination coordinates for the sources. Figure 2-13 and Figure 2-14 provide views of these source plotted along Galactic longitude and latitude globes, viewed from opposite orientations. Plots of each of the major source object type of NS, LMXB, HMXB, CV, and other types are provided in plots of Figure 2-15 through Figure 2-24. Most types show a distinct distribution mainly centered along the Galactic plane, especialy the HMXB sources. However, the plot in Figure 2-22 shows that CV sources are much more equaly distributed throughout thre- dimensional space. Table 2-5. Sources Within the XNAVSC Database. Object Number of Sources Low-Mas X-ray Binary 290 High-as X-ray Binary 152 Cataclysmic Variable 141 Neutron Star 95 Other Type 67 Unknown Type 8 Active Galactic Nuclei 6 Total 759 67 Table 2-6. LMXB Sources Within the XNAVSC Database. Object Sub- Totals Number of Sources Algol 30 Black Hole Candidate 5 Neutron Star 91 Acretion-Powered Pulsar 9 Binary Pulsar 10 Unknown NS Type 72 RS CVn 82 Unknown LMXB Type 82 Total 290 Table 2-7. HMXB Sources Within the XNAVSC Database. Table 2-8. CV Sources Within the XNAVSC Database. Object Sub- Totals Number of Sources Black Hole Candidate 3 Neutron Star 95 Acretion-Powered Pulsar 62 Binary Pulsar 28 Unknown NS Type 5 Unknown HMXB Type 54 Total 152 Object Number of Sources CV, AM 2 CV, D 3 CV, DN 15 CV, IP 29 CV, N 18 CV, NL 3 CV, P 43 CV, RN 1 CV, S 6 CV, U 5 CV, X 1 CV, Z 3 Unknown CV Type 12 Total 141 68 Table 2-9. NS Sources Within the XNAVSC Database. Table 2-10. AGN Sources Within the XNAVSC Database. Table 2-11. Other Sources Within the XNAVSC Database. Object Number of Sources Anomalous X-ray Pulsar 1 Rotation-Powered Pulsar 68 Soft Gama Repeater 3 Unknown NS Type 13 Total 95 Object Number of Sources Seyfert 2 Type 5 Unknown AGN Type 1 Total 6 Object Number of Sources Black Hole Candidate 5 Magnetar 1 Binary Pulsar 6 BY 9 CHRM 1 FK 1 Pre-Cataclysmic Binary 1 Quasar 1 Super Soft X-ray Source 3 T-Tauri 24 VXS 1 Wolf-Rayet 2 hite Dwarf 3 WU 6 UM 3 Total 67 69 Figure 2-11. Plot of X-ray sources from XNAVSC in Galactic longitude and latitude. Figure 2-12. Plot of X-ray sources from XNAVSC in Right Ascension and Declination. 70 Figure 2-13. Plot of X-ray sources along globe viewed from 45? RA and 45? Dec. Figure 2-14. Plot of X-ray sources along globe viewed from -45? RA and 225? Dec. 71 Figure 2-15. Plot of neutron star sources in Galactic longitude and latitude. Figure 2-16. Plot of neutron star sources in Right Ascension and Declination. 72 Figure 2-17. Plot of LMXB sources in Galactic longitude and latitude. Figure 2-18. Plot of LMXB sources in Right Ascension and Declination. 73 Figure 2-19. Plot of HMXB sources in Galactic longitude and latitude. Figure 2-20. Plot of HMXB sources in Right Ascension and Declination. 74 Figure 2-21. Plot of CV sources in Galactic longitude and latitude. Figure 2-22. Plot of CV sources in Right Ascension and Declination. 75 Figure 2-23. Plot of AGN and other types of sources in Galactic longitude and latitude. Figure 2-24. Plot of AGN and other source types in Right Ascension and Declination. 76 2.3.4.1 X-ray Catalogue Data Analysis Information about the nature and physics of the X-ray sources can be determined by analyzing the data parameters from the XNAVSC. This section discuses several plots of these parameters. Figure 2-25 provides a plot of the period derivative of sources versus their measured period. Although there is some spread in the data points, generaly it can be sen that period derivative gets larger as the period increases. The period derivative is an indicator of the stability of the source, and is used in Chapter 3 for developing pulse time of arival models. As the period derivative increases, it becomes more dificult to predict the arival of a pulse since the period changes more quickly over time. However, it can be se in this figure the many of the fastest rotation period sources, on the order of several miliseconds, are also the sources with the most near-fixed rotation rate since the period derivative is so smal. Due to their fast periods and stable signatures, these types of sources are atractive candidates for time and position determination. Pulse periods range from 0.00156 to 10 seconds for the rotation-powered pulsars, and from 0.0338 to 10,000 seconds for acretion-powered pulsars. Figure 2-26 provides the second period derivative for the sources that have these reported values. For those sources that have reported period and first period derivative values, Figure 2-27 provides a plot of the characteristic age of the source versus its period. The characteristic age of many of the shortest period sources is 10 7 ?10 1 yr. The plot in Figure 2-28 shows the strength of a source?s magnetic field versus its period. Although there are several exceptions, the plot shows that the period generaly increases for larger magnetic 77 fields, and that the fastest rotating sources have field strengths on the order of 10 8 -10 10 Gauss. The X-ray radiation flux measured for each source versus its rotation period is plotted in Figure 2-29. Flux intensity is important for the detection of a source, as wel as its use in producing a time and position solution in navigation. This plot show that several sources emit large amounts of X-ray flux (~10 -2 ph/cm 2 /s and higher) while rotating at rates faster than 100 Hz. The plot in Figure 2-30 shows this X-ray flux versus the magnetic field strength of the source. Due to the spread of values, stronger magnetic fields do not necesarily indicate greater flux intensity. However, for the sub-group of NS sources as the magnetic field increases, the X-ray flux also tends to rise. The pulsed fraction of the signal intensity for each source versus its rotation period is plotted in Figure 2-31. The range of pulsed fraction from a few percent to nearly 100 % indicates the variety of pulsed components of the signals. Figure 2-32 provides a plot of pulse width (FWHM) of each source versus its rotation period. Very litle data on this parameter is presented in the published catalogues, as this figure indicates, thus data analysis usualy estimates this value. 78 Figure 2-25. First period derivative versus period for sources in the XNAVSC. Figure 2-26. Second period derivative versus period for sources in the XNAVSC. 79 Figure 2-27. Characteristic age versus period for sources in the XNAVSC. Figure 2-28. Magnetic field versus period for sources in the XNAVSC. 80 Figure 2-29. X-ray flux versus period for sources in the XNAVSC. Figure 2-30. X-ray flux versus magnetic field for sources in the XNAVSC. 81 Figure 2-31. Pulsed fraction versus period for sources in the XNAVSC. Figure 2-32. Pulse width (FMHW) versus period for sources in the XNAVSC. 82 2.3.4.2 X-ray Milisecond Sources As the previous section ilustrates, a very important sub-category of sources that can be used for spacecraft navigation is those sources that have rotation periods on the order of several miliseconds. Many of these sources rotate at speds greater than 100 Hz, and several of these sources are intense X-ray flux emiters. Therefore, their study is key to understanding the capability of X-ray sources for position and time determination. Table 2-12 provides a listing of the names and periods of the milisecond sources from the XNAVSC with periods shorter than 0.02 s, aranged in order of increasing period. Figure 2-33 provides a graph of these 48 sources plotted in Galactic coordinates. Several of these sources are refered to as milisecond pulsars (MPSR), those whose period in on the order of several miliseconds. These pulsars are asumed to be older neutron stars that have been recycled, and through the proces of acretion have significantly increased their rotation rates [24, 223]. Many exist in X-ray binary (XB) systems, however some are isolated neutron stars [102, 103]. The fastest rotating known source is PSR B1937+21, which has a period of 0.001558 s [151]. Since the sources located in 47 Tucanae have very close positions, they appear as a single point on this plot. Figure 2-34 provides the period derivative versus period for these milisecond period sources from the XNAVSC. This plot shows that many of these sources have very stable periods, as their derivatives are smal (<10 -17 s/s). This provides additional support for the use of these sources in navigation, since acurate models can be created for these sources to predict the arival of pulses from these sources. Figure 2-35 shows the X-ray flux versus period for these sources. Several of the LMXB type milisecond sources have high flux, thus can be more easily identified by detectors developed for navigation. 83 Table 2-12. Milisecond Period Sources in XNAVSC Database. Source Names Source Type Period (s) Reference PSR B1937+21 RPSR 0.0156 [105, 151, 158] PSR B1957+20, Black Widow Pulsar RPSR 0.0160 [19, 20, 159] PSR J023-7203J; 47 Tuc J LMXB 0.0210 [60, 70] XTE J1751-305 LXB 0.0230 [64, 121, 125, 134] PSR J0218+4232 RPSR 0.0232 [19, 20, 105, 151, 158, 159] Sax J1808.4-3658; XTE J1808-369 LMXB 0.0249 [36, 11, 25, 26] PSR J024-7204F; 47 Tuc F RPSR 0.0262 [60, 70] PSR J024-7204O; 47 Tuc O LMXB 0.0264 [60, 70] 4U 1728-34 LXB 0.0276 [11, 22] 4U 1758-25 LMXB 0.0303 [11, 22] PSR B1821-24 RPSR 0.0305 [19, 105, 151, 158, 159] PSR J024-7204N; 47 Tuc N RPSR 0.0305 [60, 70] 4U 0614+091; 1H 0610+091 LMXB 0.0305 [11, 22] XTE J1814-38 LXB 0.0318 [104, 12, 20] PSR J024-7204H; 47 Tuc H LMXB 0.0321 [60, 70] Sco X-1; B1617-15 LXB 0.0323 [11, 22] 4U 1813-14 LMXB 0.0327 [11, 22] 4U 1743-29; 1H 174-293 LXB 0.0340 [22] 4U 1636-53; 1H 1636-536 LMXB 0.0345 [11, 22] PSR J0751+1807 RPSR 0.0347 [19, 20, 158, 159] PSR J024-7204I; 47 Tuc I LMXB 0.0348 [60, 70] PSR J024-7205E; 47 Tuc E LXB 0.0354 [60, 70] 4U 1820-30; 1H 1820-303 LMXB 0.0363 [11, 22] 4U 1908+05 LXB 0.0364 [11, 22] PSR J1740-5340 LMXB 0.0365 [47, 60, 70] PSR J023-7205M; 47 Tuc M RPSR 0.0368 [60, 70] KS 1731-260 LMXB 0.0380 [11, 22] PSR J2019+2425 Binary Pulsar 0.0393 [19] PSR J024-7204Q; 47 Tuc Q LMXB 0.0403 [60, 70] PSR J024-7204G; 47 Tuc G RPSR 0.0404 [60, 70] PSR J174-134 RPSR 0.0407 [158] PSR J024-7203U; 47 Tuc U LMXB 0.0434 [60, 70] PSR J024-7204L; 47 Tuc L RPSR 0.0435 [60, 70] PSR J232+2057 RPSR 0.0480 [19] PSR J030+0451 RPSR 0.0487 [158] PSR J2124-3 RPSR 0.0493 [19, 158, 159] PSR J1024-0719 RPSR 0.0516 [158] PSR J1012+5307 RPSR 0.0525 [19, 20, 158, 159] XTE J1807-294 LMXB 0.0525 [3, 101, 123, 124] PSR J024-7204D; 47 Tuc D RPSR 0.0536 [60, 70] XTE J0929-314 LMXB 0.0540 [64, 169] PSR J0437-4715 RPSR 0.0575 [19, 158, 159] PSR J023-7204C; 47 Tuc C RPSR 0.0576 [60, 70] PSR B1257+12 Binary Pulsar 0.0620 [19] PSR J024-7204T; 47 Tuc T LMXB 0.0759 [60, 70] PSR B1620-26 RPSR 0.0108 [19] PSR 174-24A LMXB 0.0156 [152] PSR J0537-6910 RPSR 0.0161 [158] 84 Figure 2-33. Milisecond period sources from the XNAVSC. Figure 2-34. First period derivative versus period for milisecond period sources. 85 Figure 2-35. X-ray flux versus period for milisecond sources. 86 Chapter 3 Pulse Identification, Characterization, and Modeling ?You may delay, but time wil not.? ? Benjamin Franklin The cyclic emisions generated by variable celestial sources offer measurable signals that can be exploited within a navigation system. To utilize these signals, they must be detectable, such that sensors can be developed that can determine the arival of the emisions from each individual unique source; the signals must be able to be characterized, such that the necesary parameters distinctive to a specific source can be resolved and be used to identify each source as data are recorded; and the signals must be able to be modeled, such that methods can be created to predict the future arival time of the signals at a given location. This Chapter presents methods for asembling the received photons from these sources into a signal that can be utilized for navigation. The Pulse Profile section describes the pulse detection and profile creation proceses. The Pulse Timing Models section provides descriptions of how models are created using the signal detection, as wel as a discusion of the pulse stability that has been shown from long duration observations of several sources. The Pulse Arival Time Measurement Acuracy section 87 presents an analysis on how to determine the acuracy of a measured arival time based upon the SNR value of a specific observation. The final section on Arival Time Comparison discuses the isue of comparing pulse arival times across diferent energy wavelengths, and how this may afect pulse modeling. 3.1Pulse Profile From the variety of variable celestial sources described in Chapter 2, the emision mechanisms and the reception of these signals within the solar system produces an equal diversity of pulse signals. The profile of each pulse is a representation of the characteristics of the pulse. Pulse profiles vary in terms of shape, size, cycle length, and intensities. Some sources produce sharp, impulsive, high intensity profiles, while others produce sinusoidal, elongated profiles. Although many sources produce a single, identifiable pulse, other pulse profiles contain sub-pulses, or inter-pulses that are evident within the signal [114, 118]. Replicating the pulse profile from the detected X-ray photons provides information about the source?s characteristics, the arival time of the pulse, and data that can be utilized for navigation. This section provides methods to reproduce the pulse profile so that this information can be extracted from the source?s signal. 3.1.1Photon Detection and Timing At X-ray energy wavelengths, the measured components of the emited signal from a source are the individual photons released in a source?s energy discharge. The observed profile is created via the detection of these photons from the source as they arive at the navigation system?s detector. 88 The first step in generating the pulse profile is to detect the onset of photons from a source above the nominal X-ray background signal. Appendix E provides a description of several types detector designs that have ben sucesfully demonstrated on spacecraft misions to detect X-ray photons. Typicaly a grid of material detects a photon within two-dimensional aray, providing a measurement of energy produced by the photon and the approximate location of the photon detection event within the detector?s field-of-view (FOV) [59]. Each photon provides a quantized unit of energy that is released within the detector grid. Photon energy magnitude and the number of photons received per unit time provide indications that a source has been detected. To observe a source, an X-ray detector is initialy aligned along the line-of-sight to the chosen source. Once photon events from this source are positively identified, components within the detector system record the time of arival of each individual X-ray photon with respect to the system?s clock to high precision. For acurate systems, this has been demonstrated to the order of one microsecond photon event timing resolution. Future designs wil atempt to resolve the photon timing to even greater precision. During the total observation time of a specific source, a large number of photons, N ph , wil have each of their arival times recorded. The measured individual photon arival times from ! 0 to N"1 must then be converted from the detector?s system clock to their equivalent time in an inertial frame, 0 to N!1 . This conversion provides an alignment of the photon?s arival time into a frame that is not moving with respect to the observed source. The methods of time transfer necesary for this alignment is discused in detail within Chapter 4 and is a crucial component of succesful pulse profile 89 development, as wel as a central algorithm within the time and position determine proceses discussed in later chapters. 3.1.2Profile Creation The N ph number of photons detected within a given observation spans numerous pulse cycles if the observation time is much greater than the pulse cycle period. Each photon is a component of an individual pulse, and detecting a single photon does not imediately provide an indication of a given pulse. The photon event data are esentialy a table of arival times for these N ph photons. To create the pulse profile, these photons must be asembled together to align their arival times with respect to one individual pulse. The proces of asembling al the measured photon events into a pulse profile is refered to as epoch folding, or averaging synchronously al the photon events with the expected pulse period of the source. A binned pulse profile is constructed by dividing the expected pulse phase into M equal bins and dropping each of the N ph recorded photon events into the appropriate phase bin. The bins can be either created within the time domain or the frequency domain. Through the folding proces, for sources that produce identifiable pulse signatures, some phase bins within the pulse cycle length wil acumulate more photon events than others. The resulting histogram over the pulse cycle length renders the profile of the pulse from the source. Thus, the pulse profile is a representation of the phase average of multiple detected pulses from a source. Once produced, characteristics of the pulse can be determined from a profile, or set of profiles. These characteristics include pulse amplitude above the averaged signal and 90 number and shape of peaks. Variability in parameters such as period length and noise, as wel as continuity of pulsed emision can be determined. The unique characteristics of each source?s pulse profile aids in the identification proces of the source. 3.1.2.1 Pulse Profile Template To asist an individual pulse time of arival measurement, pulse profiles with very high signal-to-noise ratio (SNR) can be created. These standard profile templates are produced similarly to observation profiles using epoch folding. However, these templates utilize much longer observation times and posibly multiple observations folded together in order to gain a high SNR value. These templates often present a much clearer representation of the pulse profile, as the noise on this signal is reduced through the repeated observations. Figure 3-1 shows a standard pulse template for the Crab Pulsar (PSR B0531+21) in the X-ray band (1?15 keV) created using multiple observations with the USA experiment onboard the ARGOS vehicle. The intensity of the profile is a ratio of count rate relative to average count rate. This image shows two cycles of the pulsar?s pulse for clarity. The Crab Pulsar?s pulse is comprised of one main pulse and a smaler secondary sub-pulse with lower intensity amplitude. The phase of the main peak of pulse within this template has been aligned to a phase equal to zero. This was chosen so that arival times correspond to the peak of the main pulse. Contrasting this image, Figure 3-2 shows an observation profile of the Crab Pulsar produced using a shorter observation close to the same epoch as the standard template. This observation has not been aligned for zero phase, as was done for the standard 91 template. This image shows that standard observation contains significant amounts of noise when compared to the standard pulse template of Figure 3-1. As another example, Figure 3-3 shows a two-cycle image of the pulse profile of PSR B1509?58 created using data from the RXTE spacecraft. This profile shows that the pulse from this pulsar is a broad sinusoidal shape, and only one single peak per period is clearly visible. The image shows quantization within the curvature of the pulse shape. In order to be used as a pulse template, folding with additional data would be neded to reduce the noise within the profile. 3.1.3Pulse Arrival Time Measurement The fundamental measurable quantity for time and position determination within a variable source-based navigation system is the arival time of an observed pulse at the detector. It is necesary to determine the time of arival (TOA) of the pulse so that navigation algorithms can compare the measured TOA to the expected TOA and use the information acordingly. A pulse TOA measurement is initiated by observing a source for multiple pulse periods and producing an epoch folded profile, as described in the previous section. Prior to this observation, it is asumed a standard pulse template defined at a specified epoch has been created and is available for comparison to the observed profile. The observed profile, p () , wil difer from the template profile, () , by several factors. Typicaly the observed pulse wil vary by a shift of time origin, ! S , a bias, b , a scale factor, k , and 92 Figure 3-1. Crab Pulsar standard pulse template. Period is about 33.5 miliseconds (epoch 51527.0 MJD). Figure 3-2. Crab Pulsar observation profile. 93 Figure 3-3. PSR 1509-58 pulsar standard pulse template. Period is about 150.23 miliseconds (epoch 48355.0 MJD). random noise !(t) [204, 205]. The relationship betwen the observed profile and the standard template profile is given by, t () =b+k!" S () # $ % & +' ( (3.1) For X-ray observations that records individual photon events, Poison counting statistics typicaly dominates the random noise in this expresion. The objective of the observed and template profile comparison proces is to determine the constant values of bias, scale factor, and particularly the time shift in Eq. (3.1). The time shift necesary to align the peaks of within the two profiles is added to the start time of the observation to produce the TOA of the first pulse within this particular observation. 94 The discrete Fourier transforms of the two profiles can be compared using the method described by Taylor [204]. After converting time to phase of the pulse period, this proces measures the phase offset of the observed profile with respect to the high SNR standard profile template. This is based upon the asumption that, after averaging a sufficiently large number of pulses, a pulse profile recorded in the same energy range is invariant with time. The template can be aligned with an arbitrary point in the profile as phase zero, but two conventions are commonly used. Either the peak of the main pulse can be aligned as the zero phase point, or the profile can be aligned such that the phase of the fundamental component of its Fourier transform is zero. Although it reduces to the former in the case of a single-symmetric pulse profile, the later method using the fundamental component is prefered because it is more precise and generaly applicable. This method also alows for simpler construction of standard templates by measuring the phase of the fundamental Fourier component, applying a fractional phase shift to the profile, and summing many observations to produce the template. An estimate of the acuracy of the TOA measurement can be computed as an outcome of this comparison proces. This estimate provides an asesment on the quality of the TOA measurement, and can be useful in the navigation algorithms. Although the time domain could be used to determine the computed time shift, Taylor?s method is prefered as its eror estimate in the TOA measurement can be expresed independent of the photon event sampling time interval. 95 3.2Pulse Timing Models The pulsed emision from variable celestial sources arives within the solar system with sufficient regularity that the arival of each pulse can be modeled. These models predict when specific pulses from the sources wil arive within the solar system. For navigation, these models can be used as a method to predict when pulses are expected to arive at an observing station. These models provide information about the characteristics of the sources, including their period duration, and the rate of change of this duration. Using this information, elements of the evolution and nature of a source can be determined. After a source?s model has been produced, new observations of the source can be conducted and results compared against the model. As discussed in the previous section, the proces of pulse epoch folding uses the expected pulse period from these models to create acurate pulse profiles, which are in turn used to compute acurate TOAs. For navigation, it is necesary to have a database of predetermined pulse timing models for al sources planned to be used within the system to avoid requiring this information to be determined during a spacecraft?s mision. Many sources already have wel determined models, as was shown in Chapter 2. These external observations and models provide a significant resource for developing this navigation system. As an example, the Jodrel Bank Observatory performs daily radio observations of the Crab Pulsar, and publishes a monthly ephemeris report [115]. This published report lists model parameters that describe the pulsar?s timing behavior since the beginning of their observations in May 1988. Information similar to this would need to be maintained for al sources and continualy provided to the navigation system onboard a vehicle. 96 3.2.1Frequency and Period Forms of Models Pulse timing models are often represented as the total acumulated phase of the source?s signal as a function of time. A starting cycle number, ! 0 =t () , can be arbitrarily asigned to the pulse that arives at a fiducial time, t 0 , and al subsequent pulses can be numbered incrementaly from this first pulse. Asigning a cycle number to individual pulses is necesary since the celestial sources do not directly provide this information. The total phase of ariving pulses, ! , is measured as the sum of the fractions of the period, or phase fraction, ! , and the acumulated whole value cycles, N . These can be expresed as functions of time as, !t () ="+Nt () (3.2) From a chosen reference time, 0 , the phase fraction varies from 0 to 1 for each pulse period whereas the number of whole value cycles continue to increase. Thus, the total phase, ! , has both periodic and secular efects from these two components. The total phase can be specified at a specific location using a pulsar phase model of, !t () = 0 +ft" 0 [] ! f 2 t 0 [] 2 + ! f 6 t" 0 [] 3 (3.3) Eq. (3.3) is known as the pulsar spin equation, or pulsar spin down law [114, 118]. In this equation, the observation time, , is in coordinate time, discussed in more detail in Chapter 4. The model in Eq. (3.3) uses pulse frequency, f , and its derivatives. From the relationship of frequency and period, their derivatives can be computed simply as [114], 97 f= 1 P ;= 1 f ! f 2 ; ! f 2 f= 3 ;= f 3 ! (3.4) Using Eqs. (3.3) and (3.4), the pulse timing models can also be represented using pulse period, P , (also angular velocity !=2"f ) as, !t () = 0 () + 1 P t" 0 [] ! 2 t 0 [] 2 + ! P 3 " 6 2 # $ % & ' ( t 0 [] 3 (3.5) The specific model parameters for a particular object are generated through repeated observations of the source until a parameter set is created that adequately fits the observed data. The acuracy of the model prediction depends on the quality of the known timing model parameters and on the intrinsic noise of the pulsar rotation [114, 194]. Since the pulse phase depends on the time when it is measured as wel as the position in space where it is measured, the location of where the model is valid must be supplied in addition to the parameters that define the model for acurate pulsar timing. Typicaly, this location is chosen as the solar system barycenter (SB), however, other locations can be utilized as long as this is declared along with the model. The pulsar phase model of Eq. (3.3), or (3.5), alows the determination of the phase of a pulse signal at a future time t , relative to a reference epoch 0 , at a specified position in space. Thus, it is possible to predict when any peak amplitude of a pulsar signal is expected to arive at a given location. The model shown in Eq. (3.3) utilizes pulse frequency and two of its derivatives (equivalently, Eq. (3.5) uses period and its two derivatives); however, any number of derivatives may be required to acurately model a 98 particular pulsar?s timing behavior. Additionaly, sources that are components of multiple star systems, such as binary systems, require parameters that include the periodic orbits of the source within the systems. It is necesary to have precise models in order to acurately predict the pulse arival times. However, as long as these parameters can be sufficiently determined, any source with detectable pulsations can be used in the time and position determination scheme. 3.2.2Pulsar Timing Stability The acuracy of the pulse timing models depends significantly on whether the intrinsic nature of the source or the extrinsic efects acting on the source continues to match the model?s predicted rotation rates. As some pulsars have been observed for many years, it has been shown that the stability of their spin rates compares wel to the quality of today?s atomic clocks [7, 96, 112, 113, 127, 163]. An acurate timer or clock is important to many spacecraft sub-systems and is often a fundamental component to the spacecraft navigation system. Figure 3-4 presents the stability of several of today?s atomic clocks [127]. Atomic clocks provide high acuracy references and are typicaly acurate to one part in 10 9 -10 15 in stability over a day. Figure 3-5 plots the stability of two wel studied pulsars, PSR B1937+21 and PSR B1855+09 in the radio band [95]. Figure 3-6 provides both sets of this data on the same plot [112]. The metric used here for comparing the signal stability from these clocks and pulsars is computed using third diferences, ! z () , or third-order polynomial variations ? as opposed to second diferences for the standard clock Alan variance statistic ? of clock and pulsar timing residuals [6, 127]. This metric is sensitive to variations in frequency drift rate of atomic clocks and pulsars; the standard Alan variance is sensitive to 99 variations in frequency drift. With this metric and these plots, it can be sen that some pulsars approach the stability of today?s atomic clocks for the long term (on the order of one or more years). For the short term (on the order of days to a year), these pulsars match the stability of a few of today?s atomic clocks, with more acurate atomic clocks having improved stability in this short term. With these long term comparisons, the high quality stability of these variable celestial sources has led some researchers to consider new time standards based upon these sources [163, 167, 203]. Older pulsars, particularly those that have undergone a long period of acretion in a binary system that spins them up to a milisecond period, have extremely stable and predictable rotation rates. The plots in Figure 3-5 and Figure 3-6 use data from radio pulsars, however, PSR B1937+21 is also detected in the X-ray band. Its X-ray stability is expected to be similar, or perhaps beter because of a reduction of propagation efects from the interstelar medium efect on X-ray photons. Figure 3-5 and Figure 3-6 demonstrate that several pulsars compare wel to typical atomic clock stabilities. This stability asures that the pulse timing models created for these sources wil sufficiently predict arival times of pulses, such that a navigation system can use these predictable pulse observations for either correcting time or position on the spacecraft. 100 Figure 3-4. Stability of several atomic clocks (Courtesy of Matsakis, Taylor, and Eubanks [127]). Figure 3-5. Stability of two pulsars (Courtesy of Kaspi, Taylor, and Ryba [96]). T h i r d - O rd e r Al l a n Va ri a n c e T h i r d - O rd e r Al l a n Va ri a n c e 101 Figure 3-6. Stability of atomic clocks and pulsars (Courtesy of Lommen [112]). 3.3Pulse Arival Time Measurement Acuracy Once pulse profiles and timing models are provided, pulse TOAs can be computed. An important aspect of this arival time measurement for navigation is its estimated acuracy. This estimation is used to weight the procesing of each TOA either in a batch estimation proces or Kalman filter implementation to improve solutions of spacecraft navigation data as presented in Chapters 6 through 8. This section provides discussion on the methods used to compute TOA acuracy and demonstrates these methods using pulsar observations and characteristics. T h i r d - O rd e r Al l a n Va ri a n c e 102 3.3.1Pulse Profile Fourier Transform Analysis It is important to determine the TOA with an acuracy that is determined by the SNR of the profile, and not by the choice of the phase bin size. A standard cross-correlation analysis does not alow this to be easily achieved. However, the method given by Taylor [204] is independent of bin size and can be implemented into a navigation system. The technique employs the time shifting property of Fourier transform signal pairs. The Fourier transform of a function shifted by an amount !t S is the Fourier transform of the original function multiplied by a phase factor of e 2if" , where f is frequency of the signal. Since the observed profile difers from the template by the constant values of the bias, the scale factor, the time shift, and random noise, as in Eq. (3.1), it is straightforward to transform both the profile and the template into the Fourier domain. The parameters in Eq. (3.1) are then determined by a standard least squares fiting method. Chi-squared tests are pursued to minimize the fiting statistics for determining these observation and template profile comparison model parameters. The final measured TOA of the pulse is then determined by adding the fited offset !t S to the recorded start time of the data set t 0 . Chapter 7 and Appendix C provide sample observations made by the NRL USA experiment of the Crab Pulsar. Measurements produced using this Fourier transform analysis are provided, along with estimated acuracies based upon this method. Using this experiment?s data, TOAs on the order of a few microseconds are computed. As is explained in Chapters 4 and 7, if al the TOA measurement eror is asumed to be directly related to spacecraft position, then these erors convert to a couple of kilometers of range eror along the Crab Pulsar?s unit direction. 103 Possible future enhancements to this Fourier transform ethod may include improved parameter-fiting methods. The description of the comparison of the observed and template profiles of Eq. (3.1) can be implemented within a Kalman filter. This implementation approach could incorporate higher order parameters and additional system dynamics, such as detector motion, in order to compute additional model parameters and produce covariance estimates of the TOA acuracy. A Kalman filter may alow analysis at the individual photon level, as opposed to the full pulse profile analysis used here. New research should be considered to determine if new approaches to determining parameter models might generate improved results. 3.3.2SNR From Source Characteristics Analysis The method presented by Taylor [204] creates a computation of TOA acuracy based upon the observed profile characteristics compared to the template profile. This method does not provide an imediate asesment of a source based upon its known characteristics of a source?s energy flux and pulsations. An alternative method is presented here for asesing a specific X-ray source's characteristics that are used to produce high acuracy TOAs. This method uses the computation of the SNR of a source. An added benefit of this analysis is that enhanced implementations could incorporate the eficiency of a detector. The pulsed signal component from a source is determined by the number of photons that are received through the detector area, , during the observation time, ! obs . The source parameter of pulsed fraction, f , defines the percentage of the source flux that is pulsed. The duty cycle, d , of a pulse is the fraction that the width of the pulse, W , spans the pulse period, P , or 104 d= W P (3.6) The noise of the pulsed signal is comprised of a fraction of both the background radiation flux and the total observed flux from this source. The background flux and the non-pulsed component of the signal contribute to the noise during the duty cycle of the pulse. The pulsed signal contribution to the noise exists throughout the full pulse period. Using this interpretation of signal noise, the SNR can be determined from the source due to the observed X-ray photon flux, F X , and the X-ray background radiation flux, B X . This ratio relates the pulsed component of the signal source photon counts, N S pulsed , to the one-sigma eror in detecting this signal as [59, 161], SNR= N S pulsed ! noi N S pulsed B + no"lse () dutycl + S pulsed F X A f #t obs X 1p f () $ % & ' () Xf t obs (3.7) For a given observation, the TOA acuracy can be determined from the one-sigma value of the pulse and the SNR via, ! TOA = 1 2 W SNR (3.8) In this equation, the one-sigma value of the pulse has been estimated as one-half the pulse width (or Half-Width Half Maximum, HWHM), which asumes the pulse shape is approximately Gaussian and the full width is equal to two-sigma. The TOA acuracy represents the resolution of the arival time of a pulse based upon a single observation. 105 A TOA measurement can be used to determine range of the detector from a chosen reference location along the line-of-sight to the pulsar. The acuracy of the range measurement can be computed using c to represent the speed of light as, ! RANGE =c TOA (3.9) 3.3.2.1 Required Observation Time For TOA curacy Based upon the SNR calculation of Eq. (3.7), the required observation time to achieve specific range acuracy in Eq. (3.9) can be determined. This proces is useful for evaluating candidate sources, by initialy selecting sources that can produce high acuracy range measurements in short observation spans. This section presents pulsar sources of both RPSR and XB types along with their catalogued characteristics, and determines their potential for producing good range measurements. One analysis method is to solve Eq. (3.8) in terms of !t obs using the relationship for SNR from Eq. (3.7). This produces an expresion of, !t obs = W 2 B X +F1"p f () # $ % & d+ Xf {} 4' TOA 2 Xf (3.10) By selecting a desired TOA acuracy and knowing the parameters for a specific source, Eq. (3.10) can be used to determine the amount of observation time required to atain this acuracy. Alternatively, a set of observation times can be chosen and the acuracy from Eq. (3.8) or (3.9) can be computed based upon these time and source parameters. This second method is presented in further detail below. Table 3-1 and Table 3-2 provide source parameters for 25 RPSRs from the XNAVSC. These sources were chosen to have high flux output and short rotation periods, and are listed based upon increasing period length. Similarly, Table 3-3 and Table 3-4 provide 106 source parameters for 25 sources in X-ray binary systems, including several APSRs, Atoll, and Z sources, also listed in increasing period. The data for al these sources is reported in the XNAVSC, and its asociated reference catalogues and papers. However, since not al parameters for these sources are provided by these references, several of the values of pulsed fraction and pulse width have to be estimated. These estimates are created based upon reported values from corresponding similar types of pulsars. Pulsed fraction was chosen to be 10% if not reported. For sources with pulse periods greater than 0.1 s, the pulse width was set to 0.0182 times the period. For sources with periods les than 0.1 s, the pulse width for RPSRs was set to 5% of period, and the pulse width of XBs was set to 20% of period. These conservative estimated values were chosen based upon similar sources with known data and to avoid labeling a source with unknown characteristics as a highly potential navigation candidate. For this TOA acuracy analysis, a common X-ray background rate of 0.005 ph/cm 2 /s (3?10 -1 erg/cm 2 /s) over 2?10 keV energy range was used for al sources. This representative background rate is a conservative value, and for this analysis is considered fixed throughout the celestial sky. Choosing two detector areas of 1-m 2 and 5-m 2 , Eqs. (3.7) and (3.9) were utilized for varying observation times in order to determine a source?s achievable range measurement acuracy. The plots of Figure 3-7 and Figure 3-8 provide range acuracies for the RPSRs with a 1-m 2 and 5-m 2 detector, respectively. These plots show the top ten sources from the data in Table 3-1 and Table 3-2 that produce the best range acuracies. Values of SNR > 2 are shown on the plots for each source. These plots show that several sources achieve range acuracies beter than 1 km within 1000 s of observation. These plots show that although 107 increasing the detector area collects additional X-ray background radiation, larger detector areas can improve the range acuracy of each source. Using the data for XBs from Table 3-3 and Table 3-4, the plots in Figure 3-9 and Figure 3-10 show the achievable range measurement acuracies for SNR > 2 and 1-m 2 and 5-m 2 detector areas, respectively. The ten XB sources from these tables with the best range acuracies are shown in these plots. Within 1000 s of observation, al the ten sources produce beter than 1 km acuracies for either size detector. Comparing RPSR to XB sources from these figures, there are several XBs that could provide good, or higher, range acuracy based upon these table parameters. Although these XB sources introduce additional complexity in their timing models, their potential for producing acurate range measurements cannot be ignored. However, additional investigation of these sources must be pursued to determine the true values of pulsed fraction and pulse width in order to make an improved asesment of al these sources. The plots of these figures alow unlimited SNR values. However, limits may exist of the maximum SNR atainable for a given source. Thus, Rappaport [161] suggests limiting the SNR to a maximum value of 1000 for al sources. Based upon this limitation, a low- pas filter for SNR of the following can be used for this limit, SNR filterd = 1000SNR + (3.11) The plots in Figure 3-11 and Figure 3-12 provided the range acuracies based upon this filtered SNR values for RPSRs and XBs, respectively. Both these plots use a 1-m 2 detector area. In Figure 3-11, several RPSRs have reduced achievable range acuracy due to the limitation on SNR, and no further observation time would improve these values. In Figure 3-12, al the XBs have this reduced range acuracy due to SNR limits. 108 The listings in Table 3-5 and Table 3-6 provide the range acuracies for the top 10 RPSRs and XBs for a 1-m 2 detector. These tables provide data for the unlimited and limited SNR scenarios over a range of 500 s, 1000 s, and 5000 s observation lengths. Navigation methods can use these range acuracy values from the sources in order to weight each measurement from individual sources. The analysis presented here asumes an area for a theoretical detector with perfect eficiency, no internal losses or noise, and no background rejection. Each source is asumed in this analysis to produce a single, identifiable pulse shape per pulse period, and the pulse period is asumed to be acurate over the observation duration. It asumes that sources have no intrinsic noise, as it is not yet wel understood how this noise wil directly afect the range acuracy. However, a conservative estimate of X-ray background noise was chosen in part to incorporate the efects of the pulsar signal noise, and other erors that may not be fully modeled in the above equations. For sources with wel- modeled signals, their range acuracy may improve if the true X-ray background present near that source is implemented in the SNR and range acuracy equations. Further source investigation must be pursued to verify the specific SNR limitation for each source. Limitations on the SNR may also be included due to a specific detector?s viewable area and photon detection and timing eficiency, which may reduce the range acuracy for some sources. 109 Table 3-1. List of Rotation-Powered Pulsar Position and References. Name Galactic Longitude (deg) Galactic Latitude (deg) Distance (kpc) References PSR B1937+21 57.51 -0.29 3.60 [105, 151, 158] PSR B1957+20 59.20 -4.70 1.53 [19, 20, 159] PSR J0218+4232 139.51 -17.53 5.70 [19, 20, 105, 151, 158, 159] PSR B1821?24 7.80 -5.58 5.50 [19, 105, 151, 158, 159] PSR J0751+1807 202.73 21.09 2.02 [19, 20, 158, 159] PSR J030+0451 13.14 -57.61 0.23 [158] PSR J2124?358 10.93 -45.4 0.25 [19, 158, 159] PSR J1012+5307 160.35 50.86 0.52 [19, 20, 158, 159] PSR J0437?4715 253.39 -41.96 0.18 [19, 158, 159] PSR J0537-6910 279.5 -31.76 47.30 [158] PSR B0531+21 184.56 -5.78 2.0 [19, 158, 159] PSR B1951+32 68.7 2.82 2.50 [19, 158, 159] PSR B1259?63 304.18 -0.9 2.0 [19, 159] PSR B0540?69 279.72 -31.52 47.30 [19, 90, 158, 159] PSR J181-1926 1.18 -0.35 7.80 [158] PSR J0205+649 130.72 3.08 2.60 [158] PSR J1420-6048 313.54 0.23 2.0 [158] PSR J1617-505 32.50 -0.28 4.50 [158] PSR B083?45 263.5 -2.79 0.25 [19, 158, 159] PSR B1823?13 18.0 -0.69 4.12 [19, 158, 159] PSR B1706?4 343.10 -2.68 1.82 [19, 158, 159] PSR J124-5916 292.04 1.75 4.80 [31, 158] PSR J1930+1852 54.10 0.27 5.0 [32] PSR B1509?58 320.32 -1.16 4.30 [19, 158, 159] PSR J1846-0258 29.71 -0.24 19.0 [131, 158] 110 Table 3-2. List of Rotation-Powered Pulsar Periodicity and Pulse Atributes. Name Period (s) Flux (2?10 keV) (ph/cm 2 /s) Pulsed Fraction (%) Pulse Width (FWHM) (s) PSR B1937+21 0.0156 4.9E-05 86.0 0.0021 PSR B1957+20 0.0160 8.31E-05 60.0 0.0080 a PSR J0218+4232 0.0232 6.65E-05 73.0 0.00350 PSR B1821?24 0.0305 1.93E-04 98.0 0.005 PSR J0751+1807 0.0347 6.63E-06 70.0 0.0017 a PSR J030+0451 0.0487 1.96E-05 10 a 0.0024 a PSR J2124?358 0.0493 1.28E-05 28.2 0.0025 a PSR J1012+5307 0.0525 1.93E-06 75.0 0.0026 a PSR J0437?4715 0.0575 6.65E-05 27.5 0.0029 a PSR J0537-6910 0.0161 7.93E-05 10 a 0.0081 a PSR B0531+21 0.0340 1.54E+0 70.0 0.01670 PSR B1951+32 0.03953 3.15E-04 10 a 0.020 a PSR B1259?63 0.0476 5.10E-04 10 a 0.024 a PSR B0540?69 0.05037 5.15E-03 67.0 0.025 a PSR J181-1926 0.06467 1.90E-03 10 a 0.032 a PSR J0205+649 0.06568 2.32E-03 10 a 0.03 a PSR J1420-6048 0.06818 7.26E-04 10 a 0.034 a PSR J1617-505 0.06934 1.37E-03 10 a 0.035 a PSR B083?45 0.08929 1.59E-03 10.0 0.045 a PSR B1823?13 0.10145 2.63E-03 10 a 0.018 a PSR B1706?4 0.10245 1.59E-04 10 a 0.019 a PSR J124-5916 0.13531 1.70E-03 10 a 0.025 a PSR J1930+1852 0.13686 2.16E-04 27.0 0.025 a PSR B1509?58 0.15023 1.62E-02 64.6 0.027 a PSR J1846-0258 0.32482 6.03E-03 10 a 0.059 a a Estimated value. Refer to text. 111 Table 3-3. List of X-ray Binary Source Position and References. Name Type Galactic Longitude (deg) Galactic Latitude (deg) Distance (kpc) References XTE J1751-305 LMXB 359.18 -1.91 8 [64, 121, 125, 134] SAX J1808.4-3658 LMXB 35.39 -8.15 4 [36, 11, 25, 26] B1728-37 LXB 354.30 -0.15 ? [11, 22] B1758-250 LMXB 5.08 -1.02 [11, 22] B0614+091 LXB 20.8 -3.36 ? [11, 22] XTE J1814-38 LMXB 358.75 -7.59 8 [104, 12, 20] B1617-15 LXB 359.09 23.78 ? [11, 22] B1813-140 LMXB 16.43 1.28 [11, 22] B1636-536 LXB 32.92 -4.82 ? [11, 22] B1820-303 LMXB 2.79 -7.91 [11, 22] B1908+05 LXB 35.72 -4.14 ? [11, 22] B1731-260 LMXB 1.07 3.6 [11, 22] XTE J1807-294 LXB 1.94 -4.27 8 [3, 101, 123, 124] XTE J0929-314 LMXB 260.10 14.21 6 [64, 169] PSR B174-24A LXB 3.84 1.70 ? [152] PSR J0635+053 HMXB 206.15 -1.04 [10] 1E 1024.0-5732 HXB 284.52 -0.24 ? [10] AO 0538-6 HMXB 276.86 -31.87 50 [141] GRO J174-28 LXB 0.04 0.30 ? [11] B015-737 HMXB 30.41 -43.56 [10] B1656+354 LXB 58.15 37.52 ? [11] GRO J1750-27 HMXB 2.37 0.51 [10] B119-603 HXB 292.09 0.34 8.5 [10] PSR B1627-673 LMXB 321.79 -13.09 ? [64, 11] GRO J1948+32 HXB 67.48 3.28 [10] 112 Table 3-4. List of X-ray Binary Source Periodicity and Pulse Atributes. Name Period (s) Flux (2?10 keV) (ph/cm 2 /s) Pulsed Fraction (%) Pulse Width (FWHM) (s) XTE J1751-305 0.0230 1.81E-01 5.50 0.0046 a SAX J1808.4-3658 0.0249 3.29E-01 4.10 0.0050 a B1728-37 0.0276 4.49E-01 10 a 0.005 a B1758-250 0.0303 3.74E+0 10 a 0.0061 a B0614+091 0.0305 1.50E-01 10 a 0.0061 a XTE J1814-38 0.0318 3.8E-02 12.0 0.0064 a B1617-15 0.0323 4.19E+01 10 a 0.0065 a B1813-140 0.0327 2.10E+0 10 a 0.0065 a B1636-536 0.0345 6.58E-01 10 a 0.0069 a B1820-303 0.0363 7.48E-01 10 a 0.0073 a B1908+05 0.0364 2.9E-04 10 a 0.0073 a B1731-260 0.0380 2.9E-02 10 a 0.0076 a XTE J1807-294 0.0525 1.18E-01 7.50 0.015 XTE J0929-314 0.0540 1.05E-02 5.0 0.01 a PSR B174-24A 0.0156 1.09E-03 10 a 0.023 a PSR J0635+053 0.0380 1.65E-03 10 a 0.068 a 1E 1024.0-5732 0.0610 1.65E-03 10 a 0.012 a AO 0538-6 0.06921 4.27E-01 10 a 0.014 a GRO J174-28 0.4670 3.80E+01 10 a 0.085 a B015-737 0.7160 1.50E-03 10 a 0.013 a B1656+354 1.2400 4.49E-02 10 a 0.023 a GRO J1750-27 4.4500 8.08E-02 10 a 0.081 a B119-603 4.81793 2.9E-02 10 a 0.08 a PSR B1627-673 7.700 7.48E-02 10 a 0.14 a GRO J1948+32 18.700 7.31E-01 10 a 0.34 a a Estimated value. Refer to text. 113 Figure 3-7. Range measurement accuracies using RPSRs versus observation time [Area = 1 m 2 , X-ray background = 0.005 ph/cm 2 /s (2?10 keV)]. Figure 3-8. Range measurement accuracies using RPSRs versus observation time [Area = 5 2 , X-ray background = 0.005 ph/cm 2 /s (2?10 keV)]. 114 Figure 3-9. Range measurement accuracies using XBs versus observation time [Area = 1 m 2 , X-ray background = 0.005 ph/cm 2 /s (2?10 keV)]. Figure 3-10. Range measurement accuracies using XBs versus observation time [Area = 5 2 , X-ray background = 0.005 ph/cm 2 /s (2?10 keV)]. 115 Figure 3-11. Range measurement accuracies using RPSRs, with SNR limited to 1000 [Area = 1 m 2 , X-ray background = 0.005 ph/cm 2 /s (2?10 keV)]. Figure 3-12. Range measurement accuracies using XBs, with SNR limited to 1000 [Area = 1 2 , X-ray background = 0.005 ph/cm 2 /s (2?10 keV)]. 116 Table 3-5. RPSR ange Measurement Acuracy Values (1-m 2 Detector). ! RANGE Range Measurement Acuracy (m) No SNR Limit ! RANGE Range Measurement Acuracy (m) SNR Limit of 100 Name 50 s 100 s 500 s 50 s 100 s 500 s PSR B0531+21 109 7.9 34.8 359 328 285 PSR B1821?24 325 23 104 34 241 12 PSR B1937+21 34 247 10 347 250 13 PSR B1509?58 1807 1294 578 217 1704 98 PSR B1957+20 186 136 597 187 1348 609 PSR B0540?69 307 2153 962 384 2531 139 PSR B1823?13 9367 6708 296 964 6985 3273 PSR J0218+4232 13701 9812 4383 13754 9865 435 PSR J124-5916 16485 1805 5273 16854 12174 5642 PSR J0437?4715 17293 12384 532 1736 12427 575 Table 3-6. XB Range Measurement Acuracy Values (1-m 2 Detector). ! RANGE Range Measurement Acuracy (m) No SNR Limit ! RANGE Range Measurement Acuracy (m) SNR Limit of 100 Name 50 s 100 s 500 s 50 s 100 s 500 s B1617-15 35.4 25.3 1.3 132 12 108 B1758-250 11 79.5 35.5 202 170 126 B1813-140 160 15 51.2 258 213 149 B1728-37 293 210 93.7 376 293 17 B1820-303 298 214 95.4 407 32 204 B1636-536 302 216 96.7 406 320 20 GRO J174-28 315 26 101 1589 150 1375 B0614+091 565 404 181 656 496 272 XTE J1751-305 657 470 210 726 539 279 SAX J1808.4-3658 690 494 21 764 569 295 117 3.3.3X-ray Source Figure of Merit Based upon the SNR calculation in Eq. (3.7) and the TOA acuracy of Eq. (3.8), an algorithmic representation to ases each source can be created. This figure of merit (FOM) for each source can be computed to asist identifying X-ray sources with potential to provide good timing and range acuracy. The FOM can be computed by squaring the TOA acuracy Eq. (3.8) to produce, ! TOA () 2 = 1 4 W 2 SNR 2 B X d Fp f () A"t obs + W 2 F X 1#p f () d+ f $ % & ' 4 f 2 A"t obs (3.12) By asuming that the X-ray background rate, a given detector area, and fixed observation time are nearly constant for this calculation, these common terms can be ignored in developing a general FOM expresion for al sources. Using Eq. (3.12) and only the terms that a unique to each source, this FOM, Q X , can be represented as, Q X = F X p f 2 W 2 f + P 1! f () " # $ % & ' (3.13) Using this X-ray variable celestial source FOM provides a means to evaluate and rank sources that provide high acuracy timing and range. Although this FOM is not dimensionles, it can be normalized with respect to the value of a reference candidate. Normalizing by the Q X Crab value for the Crab Pulsar (PSR B0531+21), 118 Table 3-7 and Table 3-8 provide the rank of the sources of the ten best RPSR and XB sources from the previous section. The sources in these tables are listed in increasing pulse period. Though it lacks the full representation of signal noise from the SNR equation, the listed ranking based upon the FOM calculations compares wel with the ranking based upon the plots of the full range acuracy equation. Although there are a few RPSRs that have slightly diferent rankings from each method, the XBs match perfectly. Thus, the FOM computation of Eq. (3.13) provides an eficient, quick calculation for evaluating sources. Highly ranked sources have large flux, large pulsed fraction, short duty cycles, and narow pulse widths, which can produce acurate timing and range estimates in Eq. (3.9). The FOM of Eq. (3.13) does not include X-ray background flux. If background flux needs to be included in the source evaluation, then a FOM based upon Eq. (3.12) must be investigated. A simpler form of this metric could be used for even quicker source evaluations. The simple form of this figure of merit ignores the pulsed fraction component of the signal and is evaluated as, Q X = Fp f 2 W (3.14) However, this simpler form has les acuracy of predicting source quality than the FOM in Eq. (3.13). Although the FOM of Eq. (3.13) is recommended, using either of these forms of the X-ray source quality FOM provides a means to evaluate and list hierarchicaly the catalogued sources. Then those sources that are expected to provide high acuracy timing and position can be chosen for further investigation. 119 Table 3-7. RPSR FOM Rankings (1-m 2 Detector). Name Q X Crab FOM Ratio x - Based Ranking Plot-Based Ranking PSR B1937+21 0.26 2 3 PSR B1957+20 0.020 4 5 PSR J0218+4232 0.009 7 8 PSR B1821?24 0.17 3 2 PSR J0437?4715 0.0052 8 10 PSR B0531+21 1.0 1 1 PSR B0540?69 0.014 6 6 PSR B1823?13 0.0018 9 7 PSR J124-5916 0.006 10 9 PSR B1509?58 0.037 5 4 Table 3-8. XB FOM Rankings (1-m 2 Detector). Name Q X Crab FOM Ratio x - Based Ranking Plot-Based Ranking XTE J1751-305 0.028 9 9 SAX J1808.4-3658 0.025 10 10 B1728-37 0.14 4 4 B1758-250 0.96 2 2 B0614+091 0.038 8 8 B1617-15 9.50 1 1 B1813-140 0.46 3 3 B1636-536 0.13 6 6 B1820-303 0.13 5 5 GRO J174-28 0.12 7 7 3.3.4Source Selection Criteria An important property of candidate sources is their ability to provide an acurate TOA within aceptable observation duration. From the current X-ray catalog, it is possible to determine which are viable candidates for use in a navigation system. Not al sources can be used however, due to their individual characteristics or due to lack of sufficient parameter information. There are 759 sources in the current catalog, which includes 459 sources within binary systems and 8 with known glitches. From the TOA acuracy models from either the Taylor Fourier transform method or the source FOM based upon observation SNR, sources with certain characteristics 120 provide improved ability for time and position determination within a navigation scheme. Perhaps the two most important criteria of a source are its wel-determined position location and its high X-ray flux output. Additionaly, sources with fast pulse periods and with pulse shapes that feature sharp, narow peaks provide additional benefits during a given observation. Sources that are stable over long durations such that pulse-timing models predict acurately the arival of pulses within the solar system are also atractive. For these types of navigation solutions, it is necesary to sek out sources that match these criteria. Of the sources listed in the current catalog, for acurate and eficient time and position determination, sources could be deselected based upon the folowing criteria: - Choose only those sources with defined pulse timing models. - Choose only those sources with period les than 10000 seconds. - Choose al those with detected flux over specified energy range. - Remove al bursters (49 bursters) The above selection proces results in 247 remaining sources. Of these remaining, there are 129 sources with measured flux above 0.001 ph/cm 2 /s (2?10 keV), and 57 sources with measured flux above 0.01 ph/cm 2 /s (2?10 keV). Removing al the 175 sources with known transient signals from the catalogue further reduces the number of available candidates. There are 27 sources that remain with measured flux above 0.01 ph/cm 2 /s (2?10 keV) after removing the sources with transient characteristics. Many of the acreting pulsars in Table 3-3 and Table 3-4 are known transient sources. If the potential benefits of al these sources were ignored however, the ability to pursue spacecraft navigation using variable celestial sources would diminish. 121 Signals from transient sources could be utilized when the source is producing sufficient X-ray flux to be detected. Time spans when these sources produce high flux can last for days to months, thus a navigation system that can provide fast updates to the source almanac data may alow the limited use of these sources. In order to make use of al sources, continual monitoring and database updates must be maintained for this navigation system. Some of the sources from the current catalog lack available parameter information. As investigation into these sources continues, the parameters can be included in the database and the sources reconsidered as potential navigation candidates. 3.4 Arival Time Comparison Sources that emit pulsed radiation in multiple wavelengths do not necesarily produce the exact same signal in each band, as discussed in Chapter 2. During this research, a study was pursued using observed data to determine whether the measured pulse TOAs agre across the radio, visible, and X-ray bands for the Crab Pulsar [164, 165, 187]. This section presents results from this study, as wel as a discusion about potential consequences of these results. The methods used to compute the measured TOAs follow the Fourier transform ethod of Section 3.3. There are four sets of observation station data used in this study. These are the following: ? Radio: Jodrel Bank Observatory, Jodrel Bank Pulsar Group (Crab Pulsar Monthly Ephemeris data and Reference Notes) (610 MHz and 1396 MHz observations) [115]. 122 ? Visible: Palomar Observatory, optical telescope [30]. ? X-ray: RXTE Satelite, Guest Observer Facility, NASA Goddard Space Flight Center (GFSC) [144]. ? X-ray: USA Experiment by NRL aboard the ARGOS vehicle. The radio data supplied by Mark Roberts of the Jodrel Bank Observatory provided the pulse-timing model, as wel as the radio telescope observations for the months of November and December 1999 and January 2000. A few observations were provided by Dae Sik Moon using the optical telescope at Palomar Observatory during this same time span. Also during these months, the USA experiment and the RXTE spacecraft completed observations. Using the data furnished by each observation station, the measured pulse arival times were fited to a model using the Princeton TEMPO pulsar timing package [206, 207]. This software program provides a means to compare al the measured TOAs in each observation wavelength to one another. TEMPO reads a file of arival times, transfers the observed arival times to the SB inertial frame if needed, and completes a least squares fit to a pulse timing model [8]. The output of this package is timing residuals, or diferences betwen the measured and predicted pulse TOAs. A plot of the TOA residuals for these four data sets during the thre months is provided in Figure 3-13. The gren asterisks are the fiducial arival times published in the Jodrel Bank Monthly Ephemeris for November, December and January [115]. The red crosses and cyan triangles represent the Jodrel Bank radio TOAs at 610 MHz and 1396 MHz respectively. The radio data represent the baseline for comparison to the other wavelengths. The pulse timing model based upon the Jodrel Bank Observatory monthly 123 pulsar ephemeris was chosen to fit al of the provided radio observations [115]. The model used in this plot is f= 29.84670409339285200 Hz, ! f= = -3.746098445932E-10 Hz/s, and ! f= = 1.019126284E-20 Hz/s 2 , with epoch of 51527.0 MJD. The dispersion measure of the interstelar medium used in the radio observations is 56.767 pc/cm 3 . With more data available during the selected time span, the USA X-ray data appears to follow the general shape and trends of the radio data. However, it can be sen from Figure 3-13 that both the RXTE and the USA data are offset from the radio data. More significantly, however, the RXTE and USA data sets are not offset by the same amount. Computing these offsets using the JUMP option within the TEMPO program, Figure 3-14 provides an overlay plot of the RXTE, USA, optical data, and radio data. From this plot, it can be sen that al diferent measurement types follow the same general trend over the time span. Table 3-9 lists the computed offsets and the estimated eror for the observed data compared to the radio data. Since the RXTE leads the radio data by 533 ?s while the USA data lags the radio data by 108 ?s, no definitive conclusion can be reached about X-ray versus radio signal transmision of the Crab Pulsar. Since these observations were made with overlapping X-ray energy bands and contemporaneously, some kind of calibration or analysis eror must be responsible for the diference. The single optical observation also leads the radio data, by 253 ?s. With only one observation point however, it is dificult to draw any conclusions from this data set at this point. 124 Table 3-9. Ofset of X-ray and Optical Data from Radio Data for Crab Pulsar. Measurement Station Ofset from Jodrel Bank Radio Data (?s) Computed Eror in Ofset (?s) RXTE +53 ?28 USA -108 ?23 Palomar +253 ?125 3.4.1TOA Comparison Discussion Although no imediate conclusions can be drawn about the TOA diferences betwen the radio and X-ray observations, some remarks can be discussed, especialy about the potential diferences in the two X-ray measurement sets from USA and RXTE. These are discussed in further detail below and must be further considered for future navigation system implementations. 3.4.1.1 Absolute Time Stamp Erors An absolute systematic timing eror could exist within either spacecraft?s system. An undiscovered, constant time stamp eror in photon event timing could be present. These erors are naturaly much more dificult to discover since the relative timing for each instrument wil be acurate. It has been asumed that the absolute time of the photon events from each station has been calibrated to the same absolute reference. However, if references or calibrations to the same absolute time reference are incorrect, this may explain some of the computed offset betwen stations. The Jodrel Bank Observatory, the NRL USA experiment, and Palomar Observatory al claim to acurately calibrate their system clock using GPS as their absolute time reference. The GPS system has a civilian timing acuracy of about 40 ns [49]. 125 Figure 3-13. Radio, X-ray, and optical Crab Pulsar TOA residual comparisons. Figure 3-14. Comparison plot with offsets in TOA residuals removed. 126 The RXTE satelite uses its Misions Operation Center to calibrate its clock, and additionaly verifies the clock via cosmic sources. The quoted acuracy of this timing is 5 or 8 ?s [144]. Since, the ARGOS mision was known to have navigational erors as discussed in Chapter 7, potential timing erors may be present also if its GPS receiver produced inacurate absolute time and pased these on to the USA experiment. 3.4.1.2 Spacecraft Position Erors The Earth-fixed observatories, Jodrel Bank and Palomar, use their known coordinates relative to Earth center and solar system data from the JPL DE200 ephemeris to complete the time transfer task for acurate pulse timing. The Earth-orbiting observatories, the USA and RXTE experiments, must provide an acurate orbit position solution to complete the time transfer task. Position erors within the navigation solution of each of these spacecraft would produce inacurate pulse TOA calculations. However, position eror on the order of 100 km is necesary to produce a timing eror of 33 ?s. It is unlikely this magnitude of position eror would not be discovered during each spacecraft?s mision, unles position erors were significant in the along-track direction of the orbit. The navigation erors discussed in Chapter 7 for the ARGOS could contribute to some of the USA experiment timing offset. 3.4.1.3 Software Procesing Erors Although al atempts were made to minimize the number of diferent software analysis packages used in this data procesing, it is posible that the few separate packages could handle the RXTE and USA X-ray data diferently and introduce a time offset. Future studies could make similar comparisons with other pulsars that have been 127 observed nearly simultaneously by both experiments. Computed time offsets with these new data may identify isues with the analysis programs. 3.4.1.4 Pulsar Position and Model Erors Pulsar position and pulse timing models may be in eror by some amount. The quoted position by the Jodrel Bank Observatory was used for al data procesing. Any eror in this position would be consistent throughout al measurement station data procesing. A standard pulse model was also used for each measurement set procesing. It is evident in Figure 3-14 that there is variation in the time residuals of al sets of data. Removing some of this variation by using higher order model parameters, however, does not afect the offset betwen each measurement station. Higher order terms only act to flatten the residual plot of each respective set, but does not adjust the offset. This variation is probably due to the Crab Pulsar?s rotational instabilities during the observing time span and is consistent within each measurement station set. 3.4.1.5 Energy Range Diferences The two X-ray experiments used slightly diferent energy ranges for their observations. If the pulse profile had significant energy dependence, this may acount for some of the time offset. The USA experiment observed the source within the 1?15 keV band, while the RXTE single-bit data observed within the 2?15 keV band. However, RXTE data at the higher band of 15?60 keV shows litle change in the TOA ofset for this experiment, which may indicate no energy dependence on the signal exists for the Crab Pulsar. 128 3.4.1.6 Dispersion Measurement Erors The radio wavelength emisions from variable celestial sources is delayed by the ionized gas of the interstelar medium [114, 118]. A dispersion measure, DM, of this delay can be estimated, or computed, using multiple radio wavelength observations. Eror in this computed value could acount for some of the offset eror betwen the radio and X-ray observations. However, the DM of the Crab Pulsar varies by about 0.01 pc/cm 3 per month [164, 165]. An eror of this magnitude would cause an offset of 110 ?s in the 610 MHz data. However, the multi-wavelength observations by Jodrel Bank Observatory in Figure 3-13 do not have this significant ofset betwen the two radio observations. Thus, DM does not fully explain the radio and X-ray observation offsets. 129 Chapter 4 Time Transformation and Time of Arival Analysis ?The only reason for time is so that everything doesn?t happen at once.? ? Albert Einstein Timing the arival of photons from the celestial sources is the fundamental measurable component within a variable celestial source-based navigation system. Acuracy of this timing is critical for a high performance navigation system. An onboard pulsar-based navigation system would be comprised of a detector and instrumentation to detect ariving photons, a high performance clock or oscilator (such as an atomic clock), and a computer to facilitate the data collection and recording. Once recorded, the arival time of these photons must be transformed to an appropriate time frame so that pulse profiles may be established. The comparison of pulse arival times to existing pulse timing models requires the transfer of time to the location where the model is defined. The first order analysis presented in the previous Chapters represents an estimate of TOA acuracies that produce spacecraft position estimates. This Chapter presents detailed time conversion and transfer techniques to insure high acuracy TOA measurements. These time transfer methods include relativistic corrections in order to produce timing resolution of pulse photons on the order of a few nanoseconds. 130 4.1 Inertial Coordinate Reference Systems In order to compute acurate arival times of pulses, measurements must be made relative to an inertial frame ? a frame unacelerated with respect to the pulsars [15, 79, 113, 137, 138, 201, 202, 209]. This frame represents the thre-dimensional inertial position coordinates as wel as the fourth dimension of coordinate time. Most observations of variable celestial sources have ben made on Earth for radio wavelength sources, or on a spacecraft moving about Earth for X-ray wavelength sources. The data collected while in these moving frames must be first transformed into an inertial frame and subsequently transfered to where the pulse model is defined. Options exist for inertial coordinate frames that can be used for acurate pulse timing, and several are presented below. Appendix A also provides lists of time scales and standards that may be used for pulse timing. 4.1.1 Parameterized Post-Newtonian Frame The parameterized post-Newtonian (PN) coordinate system is one framework for reference time and inertial position [135, 153, 170-173, 228]. This system is useful for general relativistic analysis, and can be used as a tool in studying pulse arival times. The Post-Newtonian time (PNT) can be used as the time coordinate within this system. 4.1.2 Solar System Barycenter Frame The solar system barycenter (SB) frame is a more suitable coordinate system for spacecraft navigation than the PN. This is a comon inertial reference system chosen for many pulsar observations and simplifies some of the general relativistic equations used for high acuracy time transfer. 131 The SB frame is refered to as the International Celestial Reference Frame (ICRF) and its axes are aligned with the equator and equinox of epoch J2000 [183]. The origin of this ICRF frame is the position of the center of mas for the whole solar system, or barycenter. The Sun and Jupiter are the primary contributors to this location, with al other planets, moon, and asteroids contributing only secondary efects. Due to the large mas of the Sun, the barycenter position is very near the surface of the Sun. The center of the Sun rotates around this barycenter position with a period equal to the ~12 yr orbit period of Jupiter. For operations and measurement of pulsar timing within the solar system, the efects of Earth?s motion on detectors must also be removed to produce acurate models. Two time scales exist which support solar system timing, and each have their origin at the SB. These are the Temps Coordonn?e Barycentrique (TCB, Barycentric Coordinate Time) and the Temps Dynamique Barycentrique (TDB, Barycentric Dynamical Time) [23, 183]. Many current pulsar observations are computed using the TDB time scale. Recent improvements in time-ephemeris models may prove that the TCB scale produces increased pulsar model acuracy [87]. 4.1.3 Terrestrial Time Standards Earth-based telescopes can reference their observations to specific epochs by initialy using terestrial time standards, such as Temps Atomique International (TAI, International Atomic Time) or Coordinated Universal Time (UTC). These times are then often converted to Earth-based coordinate time of either Terestrial Time (T) [once refered to as Terestrial Dynamical Time], or Temps Coordonn?e G?ocentrique (TCG, Geocentric Coordinate Time). TCG is the coordinate time scale with respect to Earth?s 132 center, and TCG difers from T by a scaling factor [183]. Standard corrections can then be applied to convert recorded terestrial time to TCB or TDB [57, 63, 87, 183, 199]. For spacecraft in operation near-Earth or within the solar system, additional corrections must be applied to transform the spacecraft?s clock time to these inertial reference times. These correction methods are discussed in the following sections. 4.2 Proper Time to Coordinate Time To produce an acurate navigation system, the efects on time measured by a clock in motion and within a gravitational potential field must be considered. The general relativistic theory of gravity provides a method for precisely comparing the time measured by a spacecraft?s clock to a barycentric standard time reference, such as TCB or TDB. Reference standard time, refered to as coordinate time, is the time measured by a standard clock at rest (fixed or not moving) in the inertial frame and not under the influence of gravity (located at infinite distance) [148, 156]. The spacecraft clock, although often very precise, does not truly measure perfect coordinate time. Corrections must be applied to acount for the vehicle?s motion, as wel as diferent gravitational perturbations, so that the clock?s measured time can be compared to other known time standards. A spacecraft?s clock, while in motion and at a diferent gravitational potential than the standard reference clock, measures proper time, or the time a clock measures its detected events as it travels along a four-dimensional spacetime path [156, 220]. The following sections provide methods to transform spacecraft proper time to coordinate time, for both near-Earth and interplanetary mision applications. 133 4.2.1 Spacetime Interval The four dimensions of the spacetime coordinate frame can be generalized to x 0 , 123 {} =ct,xyz {} (4.1) In this representation, the superscripts on the generalized coordinates, x , are indices, not exponents. The coordinate ct represents the dimension related to time, and x,yz {} represent the spatial coordinates. The path taken by a light ray or particle in four-dimensional spacetime is refered to as a world line. A geodesic path is the path betwen two points a light ray or particle takes while in fre fal within a gravitational field. For a particle, the geodesic path is typicaly the shortest path betwen the two points. For a light ray, these paths have zero spacetime length and are refered to as null geodesics. Generaly within a gravitational field these geodesics have some curvature in space [148, 149, 156]. In the theory of general relativity, this notion of a spacetime interval in curved space is invariant with respect to arbitrary transformations of coordinates. This spacetime interval can be defined as [148, 149, 156, 220], ds=g !" dx 0 3 # (4.2) In this definition, the metric g !" =,xyz () is a function of the time and spatial coordinates, and the elements of form a symmetric, covariant tensor that defines the geometry of spacetime. The dx terms are the diferentials of the spacetime coordinates and define the path of an object through spacetime. In this representation, the Grek 134 indices ! and ! range from 0 to 3 and the Latin indices of i and j range from 1 to 3 [148, 149, 220]. Eq. (4.2) can be expanded using these definitions as, ds 2 =g !" dx 0 3 # = 00 c 2 dt+g 0j cdtdx j j=1 3 +g ij dx j =1 3 # i (4.3) For Minkowski?s flat space of special relativity (absence of gravity), the symmetric tensor is simply the four terms of g 00 =!1, 11 g 2233 =1 , with al other terms equal to zero [148]. Since the spacetime interval is invariant with respect to arbitrary coordinate transformations its value remains constant for these transformations. Thus, the proper time measured by a clock, ! , as it moves along a world line, s related to the invariant spacetime interval and the coordinate time in special relativity via, ds 2 =!cd" 2 dt 2 +dxdy 2 dz (4.4) From the theory of general relativity the relationship for the spacetime interval with clock proper time and coordinate time is general with respect to the geometry of spacetime from Eq. (4.3) as, ds 2 =!cd" 2 g 00 c 2 dt+g 0j cdtdx j j=1 3 # +g ij dx j =1 3 i (4.5) In a weak-gravitational field and nearly flat space, which is appropriate for the solar system, a Post-Newtonian metric tensor is suitable and can be expresed to linear order of the total gravitational potential within the system. Therefore, the spacetime interval relationship of Eq. (4.3) has been shown of the order O(1/ 2 ) to be [148, 149], ds 2 =!cd" 2 1 U c 2 # $ % & ' ( dt+1 2 c # $ % & ' ( dx 2 +dydz 2 () (4.6) 135 The total gravitational potential, U , acting on the spacecraft clock is the sum of the gravitational potentials of al the bodies in the solar system, and is defined in the positive sense U=GMr+higher orde terms ( ) . The total speed, v , of the spacecraft?s local frame through the solar system can be writen as, v 2 = dx dt ! " # $ % & 2 + dy 2 dz dt ! " # $ % & 2 (4.7) Using this expresion for sped, the spacetime interval of Eq. (4.6) can be divided by dt 2 to yield, ds dt ! " # $ % & 2 =' d( dt ! " # $ % & 2 1' U 2 $ % & + 2 ! " # $ % & v (4.8) Taking the square root of the terms in Eq. (4.8) the relationship betwen proper time of the spacecraft?s clock and coordinate time can be established. Through a binomial series expansion for the square root terms and retaining only terms of O(1/ c 2 ) yields the two expresions, d!=1" U c 2 v # $ % & ' ( 2 ) * + , - .dt (4.9) dt 2 !$ 2 ' ( * + d- (4.10) These expresions are valid with a maximum eror of 10 -12 s [137]. The expresion in Eq. (4.9) demonstrates that a moving clock is slowed by the relativity concept of time dilation, as d! is smaler than the elapsed coordinate time dt [148]. By integrating Eq. (4.10) a solution of the coordinate time relative to the proper time can be determined for a spacecraft clock. Integrating Eq. (4.10) over time yields, 136 dt t 0 ! ="t 0 () 1+ U c 2 v # $ % & ' ( 2 ) * , - .d/ / 0 ! =" 0 () + U c 2 1v # $ % & ' ( 2 ) * , - .d/ / 0 ! (4.11) Various methods have ben employed to solve this remaining integral, including near- Earth applications [9, 10, 156, 157], a vector-based solution using positions of various planetary bodies relative to the SB [137, 138], and a solution for an Earthbased ground telescope and its clock used for pulsar timing [15, 79]. 4.2.2 Near-Earth Mission Applications Eq. (4.11) is the general conversion equation for clocks in motion. This equation can be solved based upon knowledge of the spacecraft?s orbit type. The speed of an Earth- orbiting spacecraft with respect to inertial space can be related to the inertial velocity of Earth, v E , and the relative spacecraft velocity, !r SCE , using, v 2 = E +!r SC () v E !r SC () (4.12) This expresion can also be represented as, v 2 = E ! () +2 d dt v E !r SC ) " d dt v E () !r SC # $ % & ' ( +! E r SC () (4.13) The total gravitational potential acting at the spacecraft?s location within the solar system, U SS , can be expresed as the sum gravitation potential of Earth, U , acting at the spacecraft?s position relative to Earth, and the total potential due to al other solar system bodies, SS!E . This can be presented as, U= SSSC () ESC () +U SS!E r SCE (4.14) 137 Using the substitutions for speed and gravitational potential from Eqs. (4.13) and (4.14), as wel as expresing the magnitude of a vector as r=!r () 1 2 , the conversion of proper time of an Earth-orbiting spacecraft clock to coordinate time is, t! 0 () =" 0 () + 1 c 2 U E r SC () + SS!E r () 21 v 2 # $ % & ' ( d" " 0 ) + 1 c 2 v E *r SC () (4.15) The gravitational potential for non-Earth bodies has been expanded in this expresion, and terms involving Earth aceleration cancel with one of the expanded terms [137, 209]. The integral term can be replaced by the standard corrections based upon planetary ephemeredes [137, 183]. Additional correction terms are required if comparisons of the proper time of a spacecraft clock are made with reference to the proper time read by a clock on Earth?s surface, the geoid [149]. The third term on the right-hand side is often refered to as the Sagnac efect and is the correction applied to elapsed time of a light signal in a rotating reference frame, in this case the spacecraft?s clock in orbit about Earth [156]. These relativistic efects upon clocks in orbit about Earth are appreciable and cannot be ignored if acurate time comparison is required. For example, the net secular relativistic efect on the clocks of GPS satelites amount to 38.6 ?s per day (equivalent to 11.6 km in range eror) [148, 149]. Ignoring this significant value would eventualy produce large navigation eror in GPS-based solutions. 4.2.3 Interplanetary Mission Applications For a spacecraft in orbit about another planetary body, Eq. (4.15) can be represented using the body?s absolute velocity, v PB , and spacecraft?s relative position, SCPB , as, 138 t! 0 () =" 0 () + 1 c 2 U PB r SC () + SS!PB r () 21 v 2 # $ % & ' ( d" " 0 ) + 1 c 2 v PB *r SC () (4.16) This would be useful for example for applications of spacecraft in orbit around Mars or within the Jovian system. For spacecraft on heliocentric orbits, the velocity term can be converted using the vis- viva energy, or energy integral, equation of the orbit [17, 213]. The integral can then be directly evaluated using the ecentric anomaly angle, E , such that, ! 0 () =" 0 () 1! ? S 2 # $ % & ' ( + 2S E! 0 () (4.17) In this equation, ? S =GM S () is the Sun?s gravitational parameter (and the primary gravitational influence), and a is the semi-major axis of the heliocentric orbit. Using additional descriptions of the Keplerian orbit parameters and how they relate to time, this expresion may also be writen as [148, 156, 188], t! 0 () =" 0 () 1+ 3? S 2ca # $ % & ' 2 r)v! 0 ) () (4.18) 4.3 Time Transfer To Solar System Barycenter As discussed in the Chapter 3, once a pulsar?s model is defined, in order for this model to be utilized by another observer, the coordinate time scale and the valid location for this model must be stated. The common frame utilized is the SB coordinate frame and either the TCB or TDB time scales. The models are often described to be valid at the origin of the SB frame. In order to compare a measured pulse arival time at a remote observation station with the predicted time at the SB origin, the station must project 139 arival times of photons by its detector onto the SB origin. This comparison requires time to be transfered from the observation station, or spacecraft, to the SB. Alternatively, the SB pulse-timing model could be transfered to another known location. For example, at a given time instance, the pulse timing model could be transfered to Earth?s center, in order to create pulse arival time comparisons with the position of Earth. To acurately transfer time from one location to another, geometric and relativistic efects must be included in this transfer. These efects acount for the diference in light ray paths from a source to the detector?s location and to the model?s location. These light ray paths can be determined using the existing theory of general relativity and the efects of the solar system [171-173]. The discussion below describes a method of transfering detected arival times to the SB origin. 4.3.1 First Order Time Transfer Figure 4-1 shows the relationship of pulses from a pulsar as they arive into the solar system relative to the SB inertial frame and a spacecraft orbiting Earth. The positions of the spacecraft, r , and the center of Earth, E , with respect to the SB are shown, as wel as the unit direction to the pulsar, ? n . From the known angular positions of the celestial objects, the line-of-sight to the pulsar can be determined relative to the SB inertial coordinate system. Figure 4-2 depicts a simple representation of the position of the spacecraft relative to the origin, as wel as the range of the spacecraft from the origin along the line-of-sight vector to the pulsar ? n! () . Using the Right Ascension, ! , and Declination angles, ! , of the pulsar?s position, the line-of-sight unit vector ? n to the pulsar can be computed as, 140 ? n=cos! () " ? i+cos! () sin ? j+i! () ? k (4.19) Since the pulsar is so distant from the origin within the solar system, first order analysis alows the line-of-sight from the origin to the pulsar to be asumed paralel with the line-of-sight from the spacecraft to the pulsar. Therefore, the spacecraft measured pulse-timing diferences betwen the spacecraft and the origin (or another reference observation station) represents a measure of the spacecraft?s position offset along the direction towards the pulsar. Figure 4-3 provides a diagram of this offset time and distance betwen the spacecraft and the origin. Using the spacecraft?s position relative to the SB, the offset of time a pulsar signal arives at a spacecraft compared to the arival time of the same pulse at the SB to first order is, SSB = SC + ? n! (4.20) In this representation, t SSB is the coordinate time of the pulse TOA at the SB, t SC is the coordinate time of the pulse TOA at the spacecraft, and c is the speed of light. Since many pulsars are so distant from Earth, in this simple expresion, the unit direction to the pulsars may be considered constant throughout the solar system. However, paralax and any apparent proper?motion should be included when determining the direction of closer pulsars. To transfer time from the spacecraft to the barycenter, the simple geometric relationship of Eq. (4.20) determines the time offset as, !t= SSB "t SC ? n#r c (4.21) This expresion also represents the time of arival diference betwen the two locations. 141 Figure 4-1. Position of spacecraft upon pulse arrival within solar system. Figure 4-2. The unit direction to a pulsar and the position of a spacecraft [50]. 142 Figure 4-3. Spacecraft position offset distance in direction of pulsar signal. 4.3.2 Higher Order Time Transfer A time transfer equation with improved acuracy over Eq. (4.21) can be created using theory the general relativity, which provides a method of acurately transfering time data within an inertial frame. The equations from this theory relate the emision time of photons that emanate from a source to their arival time at a station and define the path of the photons traveling through curved spacetime [15, 79, 140]. The goal of a pulsar-based navigation system would be in part to provide acurate position information of the spacecraft. This could only be acomplished by acurately timing pulsar signals and then correctly transfering this time to the SB. If a performance goal of the navigation system is to provide acurate position information on the order of 300 meters or les, then the system must acurately time pulses to at least 1 ?s (? 300 c ). The relativistic efects on time transfer neglected in Eq. (4.21) acount from tens to thousands of nanoseconds thus must be included to achieve this time and position determination goal. Thus, general and special relativistic efects on a clock in motion relative to an inertial frame and within a gravitational potential field must be 143 considered. A derivation of these efects on time is provided below, and follows the models of Helings, Moyer, Murray, and others [15, 79, 126, 137, 138, 140], which are specific to Earth-based ground telescopes and their use for pulsar timing analysis. From the theory of general relativity, the solar system can be estimated as a weak- gravitational field and nearly flat space. Within this type of system, the spacetime interval, ds , which is invariant with respect to arbitrary transformations of coordinates to order O1c () , is given by Eq. (4.6). An individual pulse is composed of an asemblage of photons from a variable celestial source. Each single photon travels along a light ray path, or world line. For electromagnetic signals, this world line takes the path of a null geodesic, as the photon travels from the emiting source to the receiving location of an observer [148, 156]. Transfer of time can be acomplished by using the light ray path betwen these two locations. Along this null geodesic the spacetime interval equals zero, or ds=0 [148]. Therefore the time coordinate relates to the path coordinates using Eq. (4.6) as, c 2 dt= 1+ U 2 ! dxdy 2 +dz () (4.22) Using a binomial expansion, this relationship is valid to order O1 2 () as, cdt=1+ 2U ! " # $ % & dx 2 dy+dz 2 (4.23) Considering a single pulse from a source, the transmision time of one photon is related to the reception, or observed, time of the photon by the distance along the path this photon has traveled. Figure 4-4 presents a diagram of a emiting source and the observation of the photon at a spacecraft near Earth. The vector to the source from the 144 Sun is D , the position of the spacecraft relative to the Sun is p , and the line-of-sight from the spacecraft to the pulsar is ? n SC . Since a pulse is an ensemble of these photons, by measuring the arival times of al the photons within a pulse period, the arival time of the pulse peak can be determined. Figure 4-4. Light ray path arriving from distant pulsar to spacecraft within solar system. By integrating Eq. (4.23), an algorithm can be developed to determine when the N th pulse is received at the spacecraft at time, t SC N , relative to when it was transmited from the pulsar at time, T N . This is represented as, cdt t T N SC ! =1+ 2U c " # $ % & ' dy 2 dx + dz( ) * , - 1 2 D x p (4.24) In this expresion, x and D x are the x-axis components of the p and D vectors of Figure 4-4, respectively. The solution to this equation depends on the null geodesic light ray path and the gravitational potential of bodies along this path. For a pulse ariving into the solar system, the integrated solution betwen a pulsar and an observation spacecraft is [15, 79, 113, 126, 170-173, 188], 145 t SC N ! T () = 1 c ? n SC "D N !p () 2GM k c 3 k=1 PB S # ln ? SC "p N k + k D + 2? S c 5 D N y ? SC " N () ? SC " () N $ % & ' ( ) 2 1 * + , - . / n" p ! N y arct N x D y $ % & ' ( ) arctn N x y $ % & ' ( ) 0 1 3 4 5 6 2 (4.25) In this equation, p N represents position of the spacecraft when it receives the N th pulse from the pulsar relative to the center of the Sun (not the SB). The first term on the right hand side of Eq. (4.25) is the geometric separation betwen the source and the observer. The second term is the summation of Shapiro delay efects of al the bodies within the solar system [184]. This summation term is taken over al planetary bodies in the solar system, PB SS . The terms p N k and D k are the respective positions of the spacecraft and the source relative to the k th planetary body in the solar system. The third large term in this equation is the deflection of the light ray path of the pulse due to the Sun, which is the primary influencing gravitational force within the solar system. This term is typicaly a smal value (< 1 ns). Similarly, the elapsed time of the pulse travel betwen the emision of the N th pulse from the pulsar and the SB origin can be computed using Eq. (4.24). However, the position of the SB origin relative to the Sun, b N , and the direction to the pulsar from the SB, ? n SSB , are used instead of the corresponding values for the spacecraft. The term b N k is the position of the SB relative to the k th planetary body. This elapsed time can be represented as, 146 t SSB N ! T () = 1 c ? n SSB "D N !b () 2GM k c 3 k=1 PB S # ln ? SSB "b N k + k D + 2? S c 5 D N y B ? SSB " N () ? SSB " () N $ % & ' ( ) 2 1 * + , - . / n SSB " b ! N y SB arct N x D y SB $ % & ' ( )arctn N x SB y $ % & ' ( ) * + , - . / 0 1 3 2 4 5 2 6 2 (4.26) In order to compare the pulse arival time at the spacecraft relative to the arival time at the SB, time must be transfered from the spacecraft to the SB. This time transfer can be acomplished by diferencing the transmit time of the N th pulse from a pulsar, t T N , to its arival at each of the spacecraft, t SC N , and the SB, t SSB N , as in t SSB N ! T () t SC N T () =t SSB N ! SC (4.27) Figure 4-5 presents a diagram of the positions of the pulsar, the spacecraft, and the SB with respect to the Sun. The time transfer relates t SC N and t SSB N , as wel as the relative position betwen these two locations, r . 147 Figure 4-5. Spacecraft position relative to Sun and SB origin. Diferencing Eq. (4.25) from Eq. (4.26) yields the necesary transfer time of Eq. (4.27) betwen the spacecraft and the SB, t SSB ! SC () = 1 c ? n SSB "D!b () 1 c ? n SC "!p () 2GM k 3 k=1 PB S # l SSBk + ? " 2GM k c 3 k=1 PB S # ln ? SC "p k + D + 2? S c 5 D y B n SSB "!b () ? SSB " () D $ % & ' * + , - . /? SSB " () b !1 * + , - . / y SB arct x y SB arctn x SB y $ % & ' , / 0 3 4 5 2 6 ! 2? S c 5 y ? n SC "!p () ? SC " () $ % & ' 2 +1 * + - . ? SC "D () p !1 $ % & ' ( D y arct x y arctn x y $ % & 0 1 3 4 5 2 6 (4.28) In this expresion, the subscript for the N th pulse received at each location has been dropped for clarity. Eq. (4.28) is the full high acuracy time transfer equation betwen the 148 spacecraft and the SB, and should be acurate to sub-nanosecond if al terms are retained. 4.3.2.1 Simplified Analytical Time Transfer Simplifications to algorithm of Eq. (4.28) can stil produce acurate time transfer. These simplifications reduce the computational complexity of the algorithm, but also reduce the acuracy to the order of a few nanoseconds or microseconds. The first simplification can be neglecting the diference in the light ray bending efect terms. Since these terms from Eqs. (4.25) and (4.26) are smal (< 1 ns), the diference of these two smal values can be efectively ignored. The proper-motion of the emiting source can also be included for the change of the pulsars location from its position, D 0 , at the emision of the 0 th pulse, t T 0 , and it position, D N , of the th pulse, t T N [79]. Asuming a constant value of proper motion, V , and that the diference in transmision time T N ! 0 () is equal to the diference in reception time SC N ! 0 () , the pulsar position can be represented as, D= 0 +V T N0 () "D+V SC N ! 0 () =D+V# N (4.29) If the line-of-sight to the emiting source is considered constant within the solar system, then the direction becomes ? n SC ! SSB ? S n!D 0 . Using the position of the SB origin relative to the Sun?s center as b , the position of the spacecraft relative to the SB as such that p=b+ ), then these simplifications modify the time transfer equation to relate and SSB , to the following, 149 t SSB ! SC () = 1 c ? n"r! 2 D 0 + ? "r () 2 0 "V#t N 0 ! ? n"t N () ? "r ( D 0 () 0 2 "t N ) 2 $ % & ' ( ) "t 2 () 0 "V#t ) "t N () 0 2 b"r 0 + ? n"r ( 0 " () D 0 2 !" b 2 "V#t N () $ % & ' + ? n" 0 2 "r () 2 +"t ? n"t N b"r () D 0 2 ' ) ) ) GM k c 3 k=1 PB S * l ? " k b 1 (4.30) Ignoring al terms of order O1D 0 2 () yields a time transfer algorithm of, t SSB ! SC () = 1 c ? n"r! 2 D 0 + ? "r () 2 0 "V#t N 0 ! ? n"t N () ? "r ( D 0 b () "n $ % & ' ) + 2GM k c 3 k=1 PB S * l ? "r k +b 1 (4.31) Since the values of proper motion, V , are typicaly smal, such that D 0 >V!t N , and the Sun imposes the primary gravitational field within the solar system, the expresion in Eq. (4.31) may be further simplified as, t SSB ! SC () = ? n"r c + 1 2D 0 ? "r () 2 !+ ? n"b () r!2" () # $ % & ? S 3 l ? "b (4.32) 150 In Eq. (4.32), ignoring the efects of the outer planets can have erors as large as 200 ns depending on the photon?s flight path [79]. This simplified time transfer equation is acurate to about roughly 10 ?s with respect to the full equation of Eq. (4.28). The first term on the right-hand side of Eq. (4.32) is the first order Doppler delay, and represents the simple geometric time delay betwen these two locations. The second term is due to the efects of paralax. Together these two terms are refered to as Roemer delay. The last term is the Sun?s Shapiro delay efect, which is the additional time delay from the curved light ray path due to the Sun?s gravity field [184]. The interstelar medium dispersion measure term, appearing as a correction to this equation for al radio observations, is considered zero (~10 -3 nanoseconds) for high frequency X-ray radiation [114, 118]. Eq. (4.32) requires acurate solar system ephemeris information to provide the SB location and the Sun?s gravitational parameter. If the relativistic efects and terms of order O1D 0 () are ignored, Eq. (4.32) reduces to the first order approximation of Eq. (4.21). Using any of the simplified expresions from Eq. (4.30), (4.31), or (4.32) provides a method to transfer time from the spacecraft?s position to the SB position. When using one of these equations to operate within a navigation system, it is important to consider reference time scales, pulsar phase timing model definitions, and desired acuracy in order to insure correct time transfer results. Since pulse timing models could be described at any known location, such as Earth? center, Earth?Moon barycenter, Mars?center, even other spacecraft locations, it may be necesary to implement time transfer to locations other than the SB. These equations can be used to transfer time betwen the spacecraft and another reference position, by 151 replacing the position of the SB?s origin, b , with the new reference position (ex. r E , if the model is defined at Earth?center). Thus, these expresions provide a method to acurately compare the arival time of a pulse at the spacecraft with those of pulsar timing models that can be defined at any known location within the solar system. Time transfer is an important aspect for acurate navigation using variable celestial sources. However, as can be sen in these equations, this time transfer requires knowledge, or an estimate, of detector position in order to be implemented. It wil be shown in Chapters 6 through 8 that this dilema can stil be addresed in order to determine spacecraft position. 4.3.2.2 Numerical Acuracy of Time Transfer Expresions The equations of time transfer in the solar system of Eqs. (4.28), (4.30), (4.31), and (4.32) provide decreasing complexity of computation, however, these also produce diminishing acuracy. Depending on the performance required by a specific application, the algorithm with adequate acuracy should be utilized. Table 4-1 provides a summary of the comparison of acuracy among the four time transfer algorithms. For this comparison, the specific position in the orbit of the ARGOS vehicle was chosen at time = 2451538.96769266 JD, and the results are only valid for this specific location. The single source used in this analysis was the Crab Pulsar, along with its proper motion of ? ! = -17 mas/yr and ? ! = 7 mas/yr and a distance of 2 kpc [34]. A value of N = 100 days was selected as a representation of the elapsed time betwen the measured 0 and the current time. From this table it can be sen that for this specific instance and position in space, the diference betwen the simplified expresion of Eq. (4.32) and the full expresion of Eq. 152 (4.28) is about 5.3 ?s. The values in the fourth row of this table show that by adding the Shapiro delay efect of al the bodies in the solar system, instead of considering only the Sun?s efect, acounts for as much as 10 ns of diference. The reported eror of 200 ns by Helings [79] of ignoring al solar system planets is realistic when considering another point in the vehicle?s orbit, where Jupiter?s or other large planet?s position would create a greater efect on the delay. Table 4-2 lists the values of the terms within the simplified expresion of Eq. (4.32). For this specific instance, the values in the table shows that the geometric delay term provides the majority of the time transfer, whereas the Shapiro delay term acounts for nearly 51 ?s of correction. In order to produce the results of these tables it was required to utilize variable precision arithmetic to compute the diferences betwen large and smal values. This was implemented to avoid the potential numerical truncation, which ignores smal remainders, when using fixed double precision. It is recommended that at least quadruple precision (128 bits of floating point representation) be used if any of the Eqs. (4.28) through (4.31) are implemented. Since Eq. (4.32) does not require any of these types of computations for near-Earth applications, this equation could be implemented using double precision (64 bit), however this asesment should be verified when data is collected from deep space misions. A full study should be further pursued to determine the acuracy of the time transfer algorithms at diferent times, implying diferent locations of the spacecraft, Sun, and planetary bodies, and diferent celestial sources. This comprehensive study should further ases the performance of these algorithms. Although it may be desired to utilize the algorithm with the asumed best performance, Eq. (4.28), the limitations of this 153 expresion include the required acurate knowledge of source position. Unfortunately, no observed source has thre-dimensional position knowledge that would alow this equation to be truly applicable. Table 4-1. Time Transfer Algorithm Acuracy Comparison. Algorithm Diference from Eq. (4.28) Diference from Preceding Algorithm Eq. (4.28) -- -- Eq. (4.30) -3.59 ?s -3.59 ?s Eq. (4.31) -3.59 ?s +0.71 ps Eq. (4.31) with !t N =0 -5.32 ?s -1.73 ?s Eq. (4.32) -5.31 ?s +9.43 ns Table 4-2. Simplified Time Transfer Algorithm Component Contributions. Term Value (s) ? ! +481.2174080369 1 2D 0 ? n! () 2 "r# $ % & -0.000019854 c 0 !b!! () [] +0.00001493 ? S 3 l + 1 +0.0050898463 Total 481.21790960471 4.3.3 Pulse Arrival Time Comparison Summary The preceding sections provide methods to time observed pulsar pulses and compare this time to pulse prediction models. This section provides a summary of how to implement this pulse comparison in a manner that would be utilized by a pulsar-based navigation system. A navigation system would include of a sensor that would detect 154 pulsar pulse photons at the spacecraft, a clock onboard the vehicle that would time the photons? arival, and a database of known timing models for pulsars. Table 4-3 provides the steps necesary to complete time transfer of observed pulsar data and comparison to pulsar phase timing models. In order to compute a pulse TOA and compare this measured TOA to the predicted TOA of a timing model, al time measurements must be converted to in inertial coordinate time frame, such as TCB or TDB. Also, al pulses must be timed as if they would arive at the inertial frame?s origin, such as the SB. Table 4-3. Pulse Time Transfer and Comparison Proces. Proces Steps Photon Arival in TDB ? Colect and time pulsar X-ray photons at the spacecraft?s detector using onboard clock. ? Corect spacecraft clock proper time to SB cordinate system TDB time using standard corections and spacecraft velocity efects. Time Transfer to Barycenter ? Using spacecraft position and velocity and gravitational potential of solar system, corect measured photon TDB arival time for ofset of vehicle from SB origin. TOA Measurement and Ofset ? Coherently fold photons into an observed pulse profile. ? Compare observed pulse profile to standard template profile of pulsar to determine measured TOA of detected pulse, as it would arive at SB origin. ? Using pulsar-timing mode, compare predicted TOA of pulse closest to measured TOA to determine diference in pulse arival time. 4.4 Pulsar Timing Analysis Equations Previous astrophysical researchers have pursued the timing analysis of pulsar signals. Much of the previous work was concerned only with observations made by telescopes on Earth?s surface, and the corrections to the clocks at those stations necesary to compute acurate pulse TOA comparison. This section presents an overview of these previous 155 results, as wel as a discusion about the relationships of these previous algorithms to the time transfer equations presented above. Helings and Backer [15, 79], and Murray [140] present the most detailed discussion on pulsar signal timing analysis. Helings derivation in [79] builds upon the relativistic work acomplished by Richter and Matzner [170-173]. The acuracy of the resulting algorithm is stated as ? 100 ns. Both these analyses only determine the coordinate arival time of a photon at the observation station on Earth, but could be applicable to spacecraft if the spacecraft?s position is substituted for Earth position. There have been several other articles on the development of photon arival timing for pulsar pulse timing [22, 94, 95, 113, 162, 206]. Al have presented simplified SB transfer equations for Earth-fixed clocks based upon the work by Helings, Backer, and Murray. Al directly relate to radio telescope observations, thus include the additional efects of the interstelar dispersion measure. Taylor and Weisberg state the terms of the proper time and relativistic efects, whereas others leave these as generalized terms in their equations [206]. If only the Roemer delay and part of the Shapiro delay terms are considered, most of these simplified transfer expresion match wel with the transfer equations derived in the previous sections. There are several papers that present the timing of pulsars that exist within binary systems [28, 54, 74]. Binary system pulsars add additional complexity to their timing models, as wel as considerations of the additional relativistic efects produced by the companion star?s mas. The Shapiro delay terms in these systems can be represented similarly as the isolated pulsar sources. However these papers present considerations of 156 only the time-varying portion of the Shapiro delay efects, and do not create a time diference betwen the pulse arival at Earth-based telescopes and the SB. Helings Eq. (32) [79] is the same as Eq. (4.25), and is similar to the equations presented by Murray [140]. A time transformation algorithm is then derived based upon this equation. However this algorithm is not the diference betwen the arival times at the SB and the observation station, but rather the actual arival time of the photons at the observation station. This results in equations for both Helings and Murray that retain the full position of the pulsar, D , and the transmision time, t T N . Since these cannot be determined to the acuracy required by the pulsar timing analysis or are unknown, new terms are introduced to the algorithm in order to gather these unknown terms into values that can be efectively ignored within pulsar timing analysis. The term that Helings introduces is the 0 th order pulse TOA into the solar system as (Helings uses the symbol for transmision time as T=t ), t SC 0 = T + 1 c ? n SC 0 !D () " 2GM k c 3 k=1 PB S # ln 1 ? SC !D N k + k (4.33) Ignoring the last term in Eq. (4.25), Helings arival time equation becomes the following using Eq. (4.25) and (4.33), t SC N ! 0 () =t T N0 () + 1 c ? n SC "D N ! 0 () 1 c ? n SC "p N () 2GM k 3 k=1 PB S # l"p k + k (4.34) Implementing the proper motion expresion of Eq. (4.29), this expresion becomes Helings? Eq. (46), except that Helings replaces the observations station?s Sun relative position, p , with its SB relative position, r . 157 Although this time transformation equation presented in Eq. (4.34) is used currently for many pulsar data analyses and may be sufficient for spacecraft clock applications, the diferences betwen this method and the derivations presented in the previous section should be considered. The derivation of the relativistic light ray paths used in the timing derivations in the previous section and by Helings from Richter and Matzner are developed for the frames that are centered at the Sun, not the SB [170-173]. Thus, simple replacement of the relative position from the Sun to the relative position from the SB may not be valid. Since the transmision times from the pulsar, t T N and t T 0 , are unknown, these have to be ignored when using Eq. (4.34). The 0 th order pulse TOA, t SC 0 , cannot be directly measured, only estimated. But perhaps the largest isue with utilizing these existing pulsar analysis equations is due to their computational erors at the location of the SB origin. From Figure 4-4, if the spacecraft were hypotheticaly at the center of the Sun approximated as a point mas, then there would be no bending efects of the light ray path and only the geometric elapsed time betwen the pulsar and the spacecraft would exist. For a spacecraft hypotheticaly located at the SB origin, the time transfer equation betwen the vehicle and the origin should produce zero time diference. However, replacing p with its SB relative position r in Eq. (4.34) and seting r=0 for the SB origin, the Shapiro delay term becomes undefined in this expresion currently used by many pulsar-timing analyses. However, in the newly derived transfer Eqs. (4.30), (4.31), or (4.32), the Shapiro delay term correctly is computed as zeo in this scenario. The fundamental diference is that pulsar timing analysis equations of Helings, Backer, and Muray determine the photon TOA with respect to the pulsar as in Eq. (4.25) 158 by ignoring the unknown transmision time, whereas the time transfer Eq. (4.28) uses the measured TOA of a photon and projects this arival time to the SB origin. Further analysis may be required in order to determine how to resolve these discrepancies. 159 Chapter 5 Variable Celestial Source-Based Navigation ?We shall not cease from exploration, and the end of all our exploring wil be to arrive where we started and know the place for the first time.? ? T. S. Eliot 5.1 Navigation Having investigated and developed the relevant physics, modeling, and analysis that characterize variable celestial sources in the preceding four chapters, it is necesary to determine how the measured data can be used to determine a navigation solution for spacecraft. Various techniques can be employed to facilitate the use of the periodic signals from these sources. An overview of the concepts for determining components of a full navigation solution is provided in this chapter. As identified in Chapter 1, navigation is the proces of determining when, where, and the orientation of a person or vehicle in relation to a fixed reference object. The time determination proces solves for the acurate absolute time at a given instance, or epoch. Position determination is the proces that solves for the location of the vehicle. Atitude determination is the proces of determining the orientation of the vehicle with respect to a chosen to set of reference coordinate axes. Additionaly, navigation may include 160 determining the velocity of the vehicle, or the direction and speed of its current motion. These proceses determine the state of the vehicle at a given instance. Once resolved, the navigation information can be utilized to guide the vehicle to its planned destination. In order to pursue their intended mision, spacecraft utilize navigation information for asisting the computation of the optimal guidance path required to achieve its target orbit or rendezvous with an object. Once the necesary path has been calculated, the control of the vehicle can be implemented via spacecraft maneuvers, which may include re- orientation and/or impulsive engine thrusts [93, 195, 224]. Precise control is necesary so that the vehicle wil acurately maintain its position and atitude along the intended path. Navigation updates computed as the vehicle traverses the path identifies any necesary corrections that are fed back into this navigation, guidance, and control procesing loop. A navigation system that can determine position in an absolute navigation sense can determine where a vehicle is at any instance, without necesarily requiring any a priori information about its location or motion. Methods that provide a user with absolute position information are critical for many applications, including situations where a spacecraft is lost-in-space, or when no position information is known at al. However, determining position in a relative navigation sense, such that a spacecraft can maneuver with respect to a target planet or other vehicle is also useful for many applications. Celestial navigation is the proces of navigation based upon the positions of persistent radiation celestial objects. This disertation provides information on how to determine a navigation solution of a spacecraft utilizing the signals of celestial sources whose signal intensities vary periodicaly. Most of the discussion is presented with 161 respect to time, position, and velocity determination, although aspects of atitude determination are presented in limited scope. Chapters 3 and 4 have provided models and methods to compare the measured pulse TOA from a variable celestial source to a predicted TOA within an inertial frame. This Chapter provides additional discussion on how these comparisons can be used for each aspect of spacecraft navigation. Chapters 6 through 8 provide further details on the specific methods of absolute, relative, and delta-correction position determination, as wel as empirical and simulated examples to demonstrate performance. 5.2 Time Determination It has been shown that an acurate clock is a fundamental component of a spacecraft navigation system. The plots in Chapter 3 show that the stability of the pulses from several pulsars match the stability of several of today?s atomic clocks over the long term. The signal from these pulsars can be used to stabilize an onboard spacecraft clock. Therefore, perhaps the most significant benefit of pulsars is to provide acurate atomic clock quality time based solely upon celestial observation [127, 167]. Detecting pulsations from celestial sources does not provide a direct measurement of absolute time; however, the stable pulsations can adjust the drift of spacecraft?s clocks to maintain acurate time. A method of correcting clock time using a phase-locked loop can be implemented [72]. As shown in Figure 5-1, within this fedback loop, the phase diference betwen the local clock?s oscilator and the reference signal from the pulsar is driven towards zero. Using repeated pulsar observations, the phase diferences are continuously computed and 162 any local clock erors are removed. However, this method must coordinate the measured pulsar phase information with the velocity of the vehicle and potentialy the orbital dynamics information, as phase shifts are present in the signal from pulsars as the vehicle moves toward or away from the source in its orbit. Figure 5-1. Phase-locked loop for clock adjustment [72]. Alternatively, individual pulse arival times can be used to correct clock time. The offset betwen the measured pulse arival time and the predicted arival time provides a measure of the eror within a spacecraft clock. This asumes that most, if not al, of the offset is timing eror. Using the model of the spacecraft clock?s expected behavior, such as clock drift or known efects due to temperature variations, the measured pulse arival time offset can adjust the clock?s output acordingly. For example, given initial estimates of clock bias, b C , scale factor, k C and jiter, j C , a filter that incorporates the dynamics of these parameters, such as a Kalman filter, can be created to update these clock parameter values. The true time, ! T , can be represented using the spacecraft clock time, ! C , and a reference time, 0 , by the following, 163 ! T = C +bk! C " 0 () + 1 2 j C !" 0 () 2 +# C ! () (5.1) The measurement provided to the filter would be the diference betwen the true time and the measured clock time, and this relates to these parameters where noise is ignored as the following, !"= T # C $" P =b C +k"# 0 () 1 2 j C "# 0 () 2 (5.2) In this representation and within the filter, the true time is estimated using the predicted pulse arival time, ! P , from one or several pulsars. The clock model dynamics and measurement could be further incorporated into a Kalman filter that includes other navigation states, such as vehicle position and velocity. Acurate time determination using the relativistic efects presented in Chapter 4 requires position and velocity information. Incorporating time determination within this larger Kalman filter design alows these proceses to be combined and operated simultaneously. Chapter 8 provides additional discussion on estimating clock parameters within a Kalman filter. 5.3 Atitude Determination Determining atitude of a spacecraft can be acomplished using pulsar observations through several methods. Much of the discusion throughout this disertation has concentrated on celestial sources that produce variable intensity signals. However, for atitude determination persistent, or non-variable, X-ray sources provide equaly good candidates that can be identified due to their specific characteristics of flux and image. Chapter 2 identifies several types of X-ray celestial sources with low variability in their 164 intensity. The orientation of the image of these nearly persistent sources provides a method to determine the atitude of the detector. Pulsars are also potential source candidates for atitude determination, as long as their pulse signal can be identified during the observation time window. The methods suggested here for these sources are similar to the proceses employed by existing optical star cameras and trackers except that X-ray wavelengths are measured instead of visible wavelengths. Asuming a static, or fixed, detector on a spacecraft, atitude of the vehicle can be determined by detecting a source in the sensor?s FOV and comparing the resulting signal against a database of known X-ray source characteristics, profiles, and images. Once the source is identified, its image on the detector plane determines angles within the sensor coordinate frame. The line-of-sight to the source is known in inertial frame coordinates, and the sensor to inertial frame transformation provides vehicle atitude. A detector pointed randomly in the sky wil either detect a recognizable source or the X-ray background. For detected signals above the background level, comparisons can be made which wil help determine which, if any, source is in the FOV of the detector. For a static detector it may take some time for a detectable source to enter its FOV, which wil depend on vehicle rotation rate and FOV size. Because X-rays are very short wavelength, they cast sharp shadows such that difraction is not the limiting factor for atitude determination. The achieved acuracy depends on the detector area, aceptable integration time, detector position resolution, and detector mask scale and distance. Plausible systems could achieve atitude acuracies of arcminutes to arcseconds depending on the particular design. Once a pulsar is detected and identified, however, the pulsar location information provides a means of determining the sensor?s, and hence the 165 vehicle?s, atitude. The line-of-sight to the pulsar wil be known in inertial frame coordinates, and once detected by the sensor, the sensor to inertial frame transformation provides vehicle atitude. Very slowly rotating spacecraft could also use this type of atitude determination proces. Atitude rate information may also be derived by observing the slew of the image of a source across the detector?s FOV [72]. Alternatively, a gimbaled sensor system can be used to scan various X-ray source locations in the sky to hasten the proces of detecting a suitable source [72]. However, a gimbaled system requires a high performance drive and control system in order to maintain fine pointing resolution while on a moving platform, which may impact vehicle design. The USA experiment used a two-axis gimbal system to point its detector to desired source locations [72, 166, 232]. During its mision, the USA experiment was used to detect an offset in the roll axis of the host ARGOS satelite by sweping the detector past a known source. Since the vehicle?s navigation system atitude solution was incorrect by a smal amount, the source detection did not occur at the expected atitude. By adjusting the values of roll and yaw of the ARGOS vehicle, the USA detector was then re-oriented and again pointed at the known source. This proces was continued until satisfactory source detection occurred based upon determined gimbals and vehicle atitude. This iterative, or fedback, method could be employed for atitude determination systems. 5.4 Velocity Determination Various mision applications may require knowledge of a vehicle?s velocity, or speed and direction. For instance, when a spacecraft requires an orbital maneuver, the velocity 166 of the vehicle is used to determine the appropriate point in its orbit to acomplish the rocket firing. A straightforward method to determine a spacecraft?s velocity is to acumulate a sequence of position estimates using any of the methods described within this disertation using variable sources. The velocity can then be computed using the diference of succesive position estimates divided by the time interval betwen estimates. Thus by determining the diferential of position over time, vehicle velocity can be established. Since position determination inherently contains noise from the pulse measurements, this diferentiation proces wil amplify this noise in the system, which reduces the acuracy of the velocity calculation. This position derivative method may have only limited use, such as a verification technique, or for start-up mode in a lost-in- space scenario. Velocity may also be determined using a pulsar?s signal Doppler shift. Because pulsars transmit pulse signals that are periodic in nature, as a spacecraft moves toward or away from the source, Doppler efects wil be present in the measured pulsar signal. Second-order and higher Doppler efects may be significant depending on the pulsar signal and vehicle motion. Measuring the pulse frequency from a pulsar and comparing this to its expected model can determine the Doppler shift. The Doppler shift can then be converted to speed along the line-of-sight to the pulsar. Asembling measurements from several pulsars alows full thre-dimensional velocity to be determined. Whereas some proceses wil atempt to minimize the Doppler efect by selecting sources that are perpendicular to the vehicle?s plane of motion, this velocity determination method pursues sources that produce the maximum Doppler efect. Higher order relativistic Doppler efects should also be included for increased acuracy [148, 149]. 167 For systems that evaluate pulse cycle ambiguities, the triple diference calculation can also produce an estimate of spacecraft velocity. This method is presented in Chapter 6 [189]. Although this method may amplify measurement noise as in the position- diferenced method above, once acurate pulse cycles are known, only the cycle phase measurements are procesed. These types of measurements wil most likely have les noise than full position estimates. 5.5 Position Determination Given the unique, periodic signatures of pulsars, it is possible to determine position of a spacecraft. The position, or location, of the vehicle is determined with respect to a desired inertial frame. Position knowledge is necesary for spacecraft mision operations such as verifying the correct trajectory path, scheduling observations of science objectives on planetary bodies, rendezvousing with other spacecraft of orbiting bodies, etc. The succes of these operations typicaly depends on the achievable position knowledge acuracy. This section discuses several possible methods using variable celestial sources for computing the position of a spacecraft. The two methods of occultation and pulsar- elevation are similar to existing visible source celestial navigation methods. However, these methods offer an advantage over optical systems since X-ray signals are dificult to blind in a conventional manner. A major disadvantage of these methods is their requirement of having another celestial body simultaneously in view with a pulsar. Due to the characteristics of the body, detectors in diferent wavelengths, such as visible, may be required to detect both the body and the pulsar at the same time. 168 Two new methods are presented based upon the periodic pulse generated by these celestial objects. In these methods, pulse-timing diferences betwen the spacecraft and the reference origin provide a measure of the spacecraft?s position offset along the direction towards the source. These methods use acurate pulse TOA measurements from these sources, which requires coordinate time conversion and the barycenter offset corrections to be applied as presented in Chapter 4. However, these corrections require spacecraft position knowledge in order to be correctly implemented. This requirement of position information presents a dilema if trying to resolve spacecraft position. Resolution of this dilema is discused in these methods described below. Additionaly, the proces of position determination may require the additional navigation components of time, atitude, and velocity to be determined. However, this depends on the type of detectors that are implemented within the navigation system and their available FOV. Although the SB provides one inertial coordinate frame and reference origin, it is also useful for mision operations to also relate vehicle position to Earth?s position. Several of the methods discussed here can produce position relative to Earth. Methods for determining position of spacecraft on interplanetary trajectories or misions about other planets can be extended from these Earth-based methods. 5.5.1 Source Occultation Method Ocultation of an X-ray source by Earth?s limb provides position information for Earth-orbiting spacecraft [17, 229]. As a vehicle revolves about Earth in its orbit, X-ray sources move behind the limb and then reappear on the other side. The time spent behind Earth represents a chord length of Earth?s disc. Knowing the source position and Earth?s dimensions, it is possible to determine the position of the vehicle relative to Earth. 169 In the Earth-limb occultation method, a detector on the spacecraft is pointed towards Earth?s limb and sources are observed as they pas behind the limb. A short duration of occultation can be interpreted as either a source only grazing Earth?s limb, or the spacecraft is far from Earth such that Earth?s disc creates only a very smal area in the detector?s FOV. A long duration of occultation can be interpreted as a source traversing the full diameter of the occultation disc, or the spacecraft is so close to Earth that its disc nearly covers the detector?s FOV. Expected visibility durations can be computed using the visibility algorithms of Chapter 8. Figure 5-2 provides a diagram of a pulsar being occulted by Earth as the viewer moves along an orbit path. Constituents of Earth's atmosphere absorb X-ray photons from these sources. Thus, knowledge of Earth?s atmosphere is required since the X-ray signals would begin to be absorbed by the atmosphere as the source pases close to the limb [231]. The science of aeronomy must be used in this method, as information about the constituents of the atmospheric regions can be studied. Alternatively, this occultation method could be used about any planetary body that occults the visibility of a pulsar. The body must have known dimensional parameters, positional ephemeredes, and atmospheric elements to be a good candidate for this method. 170 Figure 5-2. Ocultation of pulsar due to Earth's disc and atmosphere. 5.5.2 Source Elevation Method A vehicle with known inertial atitude can point its detector in the direction of a chosen X-ray source. By simultaneously observing a reference planetary body, elevation angles betwen the source and reference body, as wel as the apparent diameter of the body, can be used to determine the range of the detector relative to the body [17]. Nearly persistent X-ray sources, as wel as identifiable pulsars are candidates for this method, and multiple sources are required for full position determination. Figure 5-3 shows a diagram of this method, where ! E is the apparent angular diameter of Earth, and A E is the measured angle from the line-of-sight to a pulsar with respect to the spacecraft, ? n , and the edge of Earth?s limb. Using the known radius of Earth, R E , the range of the spacecraft from Earth can be represented as, r SC/E = R sin! () (5.3) This component of this spacecraft position along the pulsar?s line-of-sight from the spacecraft is related to the full position by the following, 171 ? n!r SC/E =" / cosA E +# () (5.4) It can be sen from Figure 5-3 that the two angles are functions of the spacecraft?s distance from Earth, as ! ESC/E () and E =! SC/E () . Diferentiating these expresions with respect to the spacecraft position vector, solutions for components of the position vector can be computed [17]. Adding measurements with other pulsars and other celestial bodies, such as the Moon shown in Figure 5-3, alows determination of the full thre-dimensional position vector. Since this method determines relative position with respect to the planetary body, absolute vehicle position can be determined by using the knowledge of absolute position of the body. Sensors that can detect objects within multiple wavelengths may be required for this method ? X-ray for the source and optical for the planetary bodies. However, Earth and the Moon are bright in X-ray wavelengths on their sun-lit sides, which may alow an X- ray-only system. The simultaneous observation of multiple objects within the FOV requires a complex system of detectors and procesing. This method may only be useful when orbiting a planetary body, as during interplanetary trajectories planetary bodies may not be adequately viewable. 172 Figure 5-3. Spacecraft position with respect to Earth and elevation of pulsar. 5.5.3 Absolute Position Determination An onboard navigation system that can operate in an absolute, or cold-start, mode is very desirable for many spacecraft applications. In this mode, the navigation system generates a complete thre-dimensional position solution using its equipment and source measurements. This type of system does not require asistance from external navigation systems, such as DSN or GPS. Absolute position determination alows a spacecraft to navigate and guide itself to its intended target with complete autonomy. It is also very advantageous after abnormal circumstances, such as a computer reset or vehicle power failure. To determine absolute position from variable celestial sources it is necesary to determine which specific integer phase cycle, or pulse period, is being detected at a certain time. A celestial source does not uniquely identify each of its pulses, so techniques must be developed to identify a detected pulse relative to a chosen reference pulse. By tracking the phase of several pulsars and including the pulsar line-of-sight 173 directions, it is possible to determine the unique set of cycles that satisfies the combined information to compute absolute position relative to the inertial origin. The cycle identification, or resolution, proces determines the numbered cycle through its selection criteria and testing. Once it is determined which specific cycle is detected, then range betwen the origin and the spacecraft can be determined along a source?s unit direction. Multiple simultaneous pulsar observations may be required for this proces. Succesive observations should be corrected for time diferences, and may be used if vehicle motion is relatively smal betwen observations. This identification proces is similar to the GPS integer cycle ambiguity-resolution method. Ofering an advantage over GPS, pulsars can provide many diferent cycle lengths, some very smal (few miliseconds) to very large (many thousand of seconds). These diverse cycle lengths asist the pulse integer cycle resolution method. Chapter 6 provides an in depth study and analysis of the absolute position determination proces using variable celestial sources. 5.5.4 Relative Position Determination As important as determining the absolute position of a spacecraft, resolving its relative position with respect to another known object (other spacecraft, observation station, planetary body, etc.) can be equaly important. This method alows relative navigation with respect to this object in the object?s frame of reference, without requiring full inertial positional knowledge. An advantage of this method is that only relative position diferences or range diferences may be needed for this application instead of a full thre-dimensional solution. Also, techniques similar to those used for absolute position determination can be implemented within this method. The computation of the number of integer phase cycles 174 betwen the spacecraft and the known object can determine the range betwen the two positions. Since this would typicaly be a shorter distance than the range betwen the spacecraft and the inertial origin, the cycle resolution proces in this relative position method may be simpler due to the fewer number of cycle candidates. Chapter 6 provides further detail on the algorithms for relative navigation position determination. 5.5.5 Delta-Correction To Position Solution A more subtle but equaly important method of position determination is the correction of an existing, approximate position solution. These delta-correction techniques are used to update, or correct, a working solution of position such that improved solutions are produced. Various schemes can be implemented to produce an approximate solution. These include onboard orbit propagators, range measurements from DSN, other position determination methods described above such as source occultation, source elevation, absolute, and relative navigation. The signals emited by variable celestial sources can then measure the eror within the estimated solution, such that succesive measurements refine the estimated solution to an aceptable level of acuracy. Spacecraft launched on predictable trajectories or on known orbits around planetary bodies with few anticipated disturbances can utilize the methods of the delta-correction techniques to asure the computed path is acurate. Additionaly, time and velocity components of navigation can be updated through the same delta-correction techniques. Chapters 7 and 8 provide additional description of this technique, as wel as a simulation study that presents the expected navigation performance based upon this method. 175 5.6 Variable Celestial Source-based Navigation System Description A navigation system based upon the signals of variable celestial sources, including pulsars, would be comprised of a sensor to detect pulsar photons at the spacecraft, a clock onboard the vehicle to time the photons? arival, and a database of known timing models for pulsars. Once a pulsar is identified and a pulse TOA is determined, this information can be utilized to update or determine atitude, velocity, time, and/or position. Figure 5-4 presents a simplified data procesing flow chart using pulse TOA measurements. The necesary sequence of navigation solution determination is the following: ? Time Determination ? Neded to align pulse information, select appropriate pulse models, ensure acurate photon event time tagging. Pulse timing can update clock estimates. ? Atitude Determination ? Necesary to determine orientation of spacecraft and detector gimbal angles to place pulsar within FOV of detector. Determines if vehicle is rotating or tumbling at an aceptable rate. ? Velocity Determination ? Determines direction and speed of vehicle. Asists with selecting sources perpendicular to vehicle path to decrease Doppler efects. ? Position Determination ? Determines instantaneous position of vehicle. Used to improve estimates of position and velocity. Interelated with acurate time determination and time transformation. 176 For a spacecraft that has no navigation solution, or for a start-up or calibration mode of the navigation system, the system must progres through this sequence to complete the full navigation solution. The order of time and atitude determination could be interchanged depending on the criticality of mision operations, or if time were already provided by onboard clock or an external provider. The methods described in this disertation show that the determination of the navigation components of time and position are coupled. Independent methods of determining each of the components are desirable, and future research may provide alternative options for their computation. In order for this navigation system to operate correctly, the system must provide continuous output of time, as this is the most fundamental component for navigation using the methods presented here. A fre-running clock that is started upon initialization from an external reference and is independent of the spacecraft sub-systems may be required. This would be especialy important after unforesen circumstances such as a vehicle power failure, or a computer procesing system reset. Figure 5-5 provides a diagram of the schematics for a pulsar-based navigation system for a spacecraft. Various detector types could be used in this system. Appendix E provides descriptions of these detectors that could be used for X-ray source-based navigation. Additional instrumentation may be required for each type of detector in order to reduce the efects of the X-ray background and succesfully time the arival of each photon. Since most designs are planar arays of detector components, the detector could be mounted upon a one-axis or two-axis gimbaled system to provide continuous viewing of a source independent of the vehicle?s motion or current atitude. This may require additional power, procesing, and gimbal sensors to maintain the fine alignment of 177 detector with the source, but the benefits of increased performance and viewing potential would offset these disadvantages. If multiple detectors are integrated into a single system, future designs may not require the detector to incorporate a gimbaled system for pointing. Since a complete spacecraft navigation system is rarely comprised of only a single detector or sensor, many spacecraft utilize complementary and redundant components to enhance the overal navigation solution. External sensors such as GPS or DSN could be used when available. Onboard sensors such as atomic clocks, gyros, and acelerometers would increase overal autonomy. Sensors historicaly used for spacecraft navigation such as magnetometers, sun sensors, horizon sensors could aid these onboard sensors. Other types of celestial navigation sensors, such as optical star cameras and trackers could supplant navigation information when necesary or provide a traditional backup system [221]. Blending of al the navigation sensor?s data could be acomplished within a central navigation Kalman filter. Upon producing its best solution, the navigation system would pas this solution onto the vehicle?s guidance and control system to ensure the intended trajectory path and mision objectives are being met. The navigation system would include a database of source ephemeris and characteristic data to be used as needed. Thus, maintenance of this database would be provided by an external entity, most likely the entire astronomical community. As new sources are discovered, the database could be updated via communication by the spacecraft?s ground operations, or perhaps an orbiting base station that periodicaly broadcasts up-to-date source information. 178 Figure 5-4. Pulsar-based navigation system data procesing flowchart. 179 Figure 5-5. Navigation system schematic. 180 Chapter 6 Absolute and Relative Position Determination ?Each thing is of like form from everlasting and comes round again in its cycle.? ? Marcus Aurelius 6.1 Description The absolute position of an object is its thre-dimensional location specified in an inertial frame. Determining the absolute position of a spacecraft alows the vehicle to imediately recognize its relationship to other nearby objects, alows the vehicle to safely control itself around potential obstacles, and most importantly asists the vehicle in pursuing its intended mision. Navigation systems that can report the absolute position of the vehicle to its guidance and control systems provide increased vehicle autonomy, safety, and reliability. Various existing methods solve for absolute position of a user, include using fixed visible star references; map reading; time references; Earth-bound navigation system such as LORAN or OMEGA; and Earth-orbiting systems, such as GPS, GLONAS, and the proposed European Galileo system. Via the radio signal provided by the GPS or GLONAS systems, users can triangulate their location from the acurate range measurements betwen the user and the known locations of the orbiting, transmiting 181 satelites. These systems have shown to provide impresive navigation acuracies for time, position, velocity, and atitude [156, 157]. However, limitations do exist for these systems, including limited signal visibility and availability, low source signal strengths, and these systems only operate near-Earth, since the primary function of these systems is to provide for Earth-bound users. For applications far from Earth, or where GPS/GLONAS signals are unatainable, diferent methods of determining absolute position determination is necesary. In this Chapter, it is shown that variable celestial sources, including pulsars, can be utilized to determine acurate absolute position [189, 193]. In order to utilize sources for absolute position determination, the specific pulse cycle received from a source must be identified. Methods are developed to show how the unknown, or ambiguous, number of pulse cycles can be determined. Once any unknown cycles are resolved, absolute position of a user can be produced with respect to a reference frame origin. An important atribute of this method is that it is applicable to al regions of space. The method is valid throughout the solar system, as wel as further into the Milky Way galaxy, and perhaps beyond, as long as sufficient measurements can be procesed to solve for the ambiguous pulse cycles. The determination of unknown cycles for variable celestial sources, or pulse phase cycle ambiguity resolution proces, is in some manner similar to the methods used in GPS/GLONAS navigation systems, including particularly those used for surveying and diferential positioning systems. However, the ambiguity resolution proces for variable celestial sources is unique in many ways from the GPS/GLONAS systems, including the following: 182 ? Antennas vs. Models: GPS/GLONAS systems use multiple antennas and receivers to determine cycle ambiguities measured betwen the antenna locations. Pulsar-based systems would primarily use the measured pulse arival at a detector and compare this to the expected arival time produced by a model at another location in order to determine absolute position of the detector. No detector is physicaly located at the model?s location. A relative positioning system, however, may be able to use multiple detectors at diferent locations to determine the offset of each detector relative to one another. ? Diferent Frequencies: The GPS system currently uses one, or perhaps two, cycle periods, or frequencies, to complete its ambiguity resolution proces. Each pulsar, however, has a unique signature, thus each cycle period can be quite diferent. The pulsar-based ambiguity resolution proces must evaluate each diferent signal and utilize this diferent period length. These many diferent pulse cycle lengths, some very smal (few miliseconds) to very large (many thousands of seconds), can asist the cycle ambiguity resolution proces. ? Availability and Control: The GPS and GLONAS systems are developed and maintained by humans. The satelites within each system are bound to an Earth-orbit and their signal strength primarily alows for near-Earth observations. Celestial sources have been developed and maintained by the Universe. Although control of these sources is unavailable, their imense 183 distance and high signal strength alow them to provide usable signals throughout the Milky Way galaxy and beyond. ? Multiple Wavelength Observations: Radio band emisions from these celestial sources can be received in space and on Earth?s surface. X-ray emisions from these sources are absorbed by Earth?s atmosphere, thus use of this wavelength is limited to space or planetary body applications. A pulsar-based navigation system can use the diferent wavelengths of these sources, anywhere from radio through gama-ray bands. Diferent pulse detection methods and hardware may be required in diferent wavelength bands. ? Range vs. No Range Measurements: The GPS/GLONAS methods make use of direct measurements of range betwen the orbiting satelite and the receiving antenna through the acurate time tagging of data from the satelites. Celestial sources, however, are very distant from the solar system and these distances are not known to sufficient acuracy. These sources do not provide labeled time information with their signal, thus no direct measurement of range is made from these sources. ? Carier Wave vs. Signal Pulse: The GPS/GLONAS cycles are determined from the radio wavelength carrier wave combined with the code signal. Pulsars emit pulses directly at a specified frequency. Although the carier signal from pulsars could be monitored, the pulse cycles themselves are used in the ambiguity resolution proces. ? Phase Rate vs. Doppler Efects: GPS/GLONAS receivers can acurately track the carier wave of the signal transmited from the orbiting satelites. 184 Thus, measurements of carier phase rate can be used in GPS/GLONAS cycle ambiguity resolution. Since the carier wave is not directly tracked from pulsars, this phase rate cannot be measured. However, it may be possible to determine the rate of change of pulse phase as the detector is in motion due any observed signal Doppler efect. Alternatively, this navigation proces can be applied to determine the position relative to another translating or rotating object. The proces of relative navigation is similar to absolute navigation in that it determines information relative to another object. However, in the relative navigation case, this object may or may not be fixed. For example, absolute navigation of a ship on Earth?s oceans determines the vehicle?s location ? such as latitude, longitude, and perhaps altitude ? at a given time with respect to the fixed Earth coordinate system. However, relative navigation of this ship would apply in the case of a tugboat approaching the vesel in order to match its speed and direction. These examples also apply to spacecraft in orbit. On a heliocentric orbit, absolute navigation of a spacecraft would include determining the exact position of the vehicle at a given instance with respect to the solar system barycenter (SB) inertial reference frame. Relative navigation of this same spacecraft would be the proces of determining the position offset of a sister spacecraft as the two vehicles maneuver in coordinated flight to acomplish their intended mision. Both the absolute and relative navigation proceses are diferent from navigation proces that use either integrated vehicle motion, a priori navigation information, or an estimate of vehicle navigation data. These proceses use estimates of navigation values, and new measurements are generated to refine, or update, the estimated values in order to 185 determine a more acurate complete navigation solution. Since no initial estimate is required for absolute, or relative, navigation, many applications benefit from these directly available solutions. This Chapter provides details of the methods and algorithms to determine the phase cycle ambiguities from pulsars. The following section on Observables and Erors provides a description of quantities that are measured from variable celestial sources. Erors that can be significant in this proces are also presented. It also discusses the isue of creating pulse profiles and determining pulse TOA without acurate or unknown position knowledge. The section on Measurement Diferences computes al the necesary diferences that are used in the proces of computing absolute position. The Search Space and Cycle Ambiguity Resolution section describes how to asemble the candidate cycle search space and then test individual candidate cycles in order to determine the most probable location for the user. Various techniques that can be implemented in this resolution proces are provided. The Relative Position section discusses the use of these navigation techniques for applications where relative position information is required, instead of absolute information. The section on Solution Acuracy provides computations that provide estimates of the acuracy of the navigation solution, including methods that help choose optimal sets of sources. The final section of Numerical Simulation discusses results of the performance of the described algorithms. 186 6.2 Observables and Erors Variable celestial sources emit periodic radiation that can be detected using various methods. Each source produces a unique signal. Due to the stability of the emision mechanisms of the sources, the arival time of this pulsed radiation is often predictable. For a pulse ariving into the solar system to the position of the spacecraft relative to the Sun center, p , the relationship of the transmision time, t T , to the reception time, t R SC , is the following from Chapter 4 [188, 192, 193], t R SC ! T () = 1 c ? n SC "D!p () 2GM k c 3 k=1 PB S # ln ? SC "p k + D + 2? S c 5 y ? SC " () " () $ % & ' ( ) 2 1 * + , - . /?n SC " () p D !1 $ % & ' ( ) y arctn p x y !arct x y $ % & 0 3 4 5 2 6 (6.1) For the discussion in this Chapter, the second and third terms in Eq. (6.1) can be combined together into a single parameter, RelEf , which represents al the relativistic efects along the light ray path such that, t R SC ! T () = 1 ? n SC "!p () + 1 RlEf (6.2) 6.2.1 Range Measurement The range, ! , from the source to the observer can be computed from the transmit and receive times of Eq. (6.2) as the following, !=c R SC " T () (6.3) 187 Using the representation of these times from Eq. (6.2), range can also be expresed in terms of the position vectors as, != ? n SC "D#p () +RelEf (6.4) The unit vector along the direction from the observer to the source can be writen in terms of the pulsar and observer positions as, ? n SC = D!p (6.5) Using this representation for unit direction, the range from Eq. (6.4) becomes, !=D"p+RelEf (6.6) The range vector is defined to be in the direction from the source to the observer. Since the magnitude of a vector is equal to the magnitude of the opposite direction vector, or x!" , Eq. (6.6) can be more properly stated as the following, !=p"D+RelEf (6.7) This form of the equation wil be utilized because of the choice of the direction of the range vectors, and wil be shown in more detail in the following Measurement Diferences section. Eqs. (6.3), (6.4), and (6.7) represent the total path length, or range, that a pulse must travel from a source to the observer. If the observer?s position and the source position vectors are acurately known, then the range can be directly determined from Eq. (6.4). Conversely, if a range measurement can be computed betwen the source and the observer along with using knowledge of the source position, rearanging Eq. (6.4) or (6.7) alows a portion of the observer?s position rative to the Sun to be computed. Thus 188 any method that can provide an absolute range measurement can contribute to determining observer position. An absolute range measurement can be computed using Eq. (6.3), if the transmision and reception times are known for an individual pulse, and this measurement could be applied to Eq. (6.4) to determine observer position. However, any measurement system that atempts to use transmision and reception times is limited primarily by the major complication that pulsars do not provide a means to determine when an individual pulse was transmited. Thus, although the reception time can be measured, the transmision time, t T , is unknown. Contrastingly, navigation system such as GPS, GLONAS and Earth-bound systems provide the signal transmision time, which alows direct computation of range betwen a user and the transmiting satelite or station. Nonetheles, as wil be shown, enough information is provided such that observer position can stil be determined using measurements from pulsars. 6.2.1.1 Range Measurement Eror Within a navigation system, the range measurement, ! , wil difer from the true range, ! , by some eror amount, !" . The relationship of the true and measured range can be writen as, = ! + (6.8) In terms of measured, or estimated, transmit and reception time for the i th pulsar, the measured range from Eq. (6.3) is, ! i =t R SC i " ! T i () (6.9) The measured range using transmit and receive time wil difer from the true range by several erors, including station clock and signal timing erors at the observer?s station, 189 !t SC , intrinsic timing model erors or unknowns for a specific pulsar, !T i , and range measurement noise, ! i . Asuming that these erors behaving linearly with respect to the measurement, the true range can be represented as the sum of the measurement and its erors as, ! i =ct R SC i " ! T i () +c#t SCi $ i (6.10) Similarly, in terms of measured, or estimated, source and observer position for the i th pulsar, the measured range from Eq. (6.7) is, i pD i elEf " i (6.11) This form of measured range wil difer from the true range by several erors, including observer position eror, !p , and source position eror, !D i , along the direction to the source, relativistic efects eror, RelEf i , as wel as range measurement noise. If these erors sum linearly with the measurement, then the true range is represented as, !=p" ! D i +RlEf i #p+D i RlEf+$ i (6.12) The range measurement of Eq. (6.11) uses the magnitude of the geometric diference betwen the source and the observer. Alternatively, the estimate of line-of-sight direction to the source can be used from Eq. (6.5), such that the measured range is, !=n SC i " ! i #p+RlEf " i (6.13) The erors for this equation include those from Eq. (6.12) and the additional efect of the line-of-sight eror, n SC i , such that the true range is, ! i =n SC i " ! D i #p () +RelEf " i !n SC i "$D i +! SC i "p $ i i i % (6.14) 190 It has been asumed that these representative erors sum linearly. Any non-linear eror efects that may prove significant must be included appropriately, which may complicate procesing. 6.2.2 Phase Measurement Variable celestial sources produce pulsed radiation that arives periodicaly at a detector. It is this periodic nature of these sources that make them valuable as navigation beacons. Since the periodicity of these sources is stable, it is possible to identify individual pulse cycles. At any given measurement time however, the peak of the pulse, or other identifying structure of the pulse, may not be detected. Instead, a certain instance within the pulse cycle wil be measured, which can be represented as the phase of the cycle, or the fraction of the pulse period often measured in dimensionles units from zero to one. As presented in Chapter 3, at a given measurement time, a series of cycles can be represented as the total cycle phase, ! . This total cycle phase is the sum of the fraction of a pulse, ! , plus an integral number, N , of ful integer cycles that have acumulated since a chosen initial time. Thus, total cycle phase can be writen as, !="+N (6.15) The phase of a cycle, or series of elapsed cycles, emanating from the source and ariving at the observer is related to the range betwen the source and observer by the wavelength, ! , of the cycle, !="#$+N (6.16) Therefore, if the number of cycles plus the fraction of the current pulse could be determined betwen the pulsar and the observer, the range can be computed from Eq. (6.16). This equation provides an alternative method of determining range, rather than 191 using transmit and receive time in Eq. (6.3) or source and receiver positions as in Eq. (6.4). However, celestial sources provide no identifying information with each pulse, so that there is no direct method of determining which specific cycle is being detected at any given time. As an example of this relationship, Figure 6-1 provides a diagram of a train of pulse cycles and shows the asociation of phase and range along certain points relative to the origin. Figure 6-1. Range and phase measurement along a train of pulse cycles. 6.2.2.1 Phase Measurement Eror The total measured cycle phase, ! , of a celestial source pulse from a detector system wil difer from the true phase, , by any phase eror, !" , unresolved within the system, such as, !=+" (6.17) This phase eror can be separated into erors, and !N , within the measured fraction of phase, ! , and the measured number of full cycles, ! , respectively as, !+N= ! "+N (6.18) 192 Using Eqs. (6.11) and (6.16), the measured phase fraction and cycle number relate to the measured source and observer position as, ! i "= i ! #+N i () !p$D i +RelEf " i (6.19) Since the measurement of phase is directly related to the timing of ariving pulses and the distance to the source, the combined efects of the erors from the range measurement of Eqs. (6.10) and (6.12), along with the specific phase measurement noise eror, ! i , relate the true phase to the measured phase by the following, ! i "= i #+N i p$ ! D i RelEf " i c%t SC +T i %pD i +RelEf i & (6.20) The measured phase can also be computed in terms of the source line-of-sight as in Eq. (6.13) to produce, ! i "= i ! #+N i () !n SC i $D i %!p () +RelEf " i (6.21) By including the line-of-sight erors from Eq. (6.14), the true phase can be represented as the following, ! i "= i #+N i () n SC i $ ! D i %p () RelEf " i +c&t SC T i !n SC i $&D i +! SC i $p & i i ! i ' i (6.22) 6.2.3 Pulse Arrival Time Determination As discussed previously in Chapters 3 and 4, acurate determination of the pulse arival time from a pulsar requires time at the detector to be transfered to the SB and compared to a pulsar-timing model. Utilizing a clock onboard a spacecraft, the timing of photons can be directly determined as these arive at the detector. In order to create a 193 pulse profile for model comparison, each photon arival time must be transfered to the model?s defined location, in most cases this is chosen as the SB. However, this time transfer requires knowledge of the spacecraft?s position. In the absolute position determination proces, it is asumed that no prior knowledge of the spacecraft?s position is available, thus the time transfer cannot be implemented as previously presented. The methods of determining absolute position rely on the diference of range or phase betwen the spacecraft and the model?s defined location. If this location is far from the spacecraft, then many pulse cycles wil exist betwen the two locations. If this location is relatively close to the spacecraft, then it is possible that only a fraction of a pulse cycle exists betwen the two locations. But in order to calculate these diferences, the photon arival times at the detector must be transfered to this location. For spacecraft orbiting Earth, one method to avoid acumulating pulse cycles betwen the vehicle?s detector and the SB is to use pulsars with large periods. Using sources with periods greater than 500 sec !1AUc () ensures there is only one cycle betwen the SB and Earth. Long period pulses, however, also require longer observation time, which may be detrimental to spacecraft operations if a fast absolute position solution is required. An improved method for ensuring that only a few cycles exist betwen the spacecraft and the pulse model location is to keep the model?s defined location close to the spacecraft. For spacecraft orbiting Earth, or near-Earth, beter pulse model locations would be at the geocenter (Earth-center) or the Earth-Moon barycenter. Although these locations are not truly inertial locations, compensations in the pulse models as wel as short observation times would alow these locations to be used. Alternatively, any location near the 194 spacecraft could be used for the model location. For example, a spacecraft orbiting Mars or Jupiter could use the center of those planets or their system?s barycenter. These methods require redefining existing pulsar timing models defined at the SB to these new locations. Creating pulse profiles with varying asumptions of position knowledge demonstrates the efects of position on profile acuracy. Figure 6-2 provides a high SNR template plot of the pulse cycle of the Crab pulse detected using the NRL USA experiment. The clarity of the pulse is evident from this profile. Figure 6-3 shows the profile results of an observation of the Crab Pulsar made by the USA experiment with time transfered from the spacecraft to the SB. This observation was made on December 19, 1999, starting at 08:54:05.78 AM and lasting for 483.57 seconds. To create this image, the navigation system onboard the vehicle provides one second updates on the vehicle position and velocity and this information was used to transfer time to the SB. If however, spacecraft navigation data were unknown, then this time transfer could not be completed acurately. A starting asumption could be made that the vehicle was located at the geocenter. Figure 6-4 provides a diagram of the same Crab Pulsar observation that uses Earth?s center location as the position to transfer time to the SB. The pulse shape is altered when compared to either the template in Figure 6-2 or the barycentered observation in Figure 6-3. The noise within the pulse has grown. Asuming no knowledge of spacecraft position, Figure 6-4 provides the Crab Pulsar observation using no time transfer at al. Pulse shape is significantly altered, with pulse height intensity being reduced, as wel as obviously substantial noise increase. These efects are 195 due to ignoring the spacecraft?s position and motion within the inertial frame when computing the photon arival time. Table 6-1 provides a summary of the calculated pulse TOA values for these observations. These TOAs were computed by comparing the observed pulsed to the high signal-to-noise template of Figure 6-2. Choosing the geocenter as the location of the pulse detector and transfering this arival time to the SB results in a TOA diference of 0.0188 s. This value is les than the pulse period of 0.0335 s, and les than the maximum possible time diference betwen the geocenter and the 833 km altitude orbit of the ARGOS spacecraft of 0.024 s =833+6378 () /c! " # $ . An improved comparison could be created by developing a pulse arival-timing model that exists at the geocenter. Then the diference of the pulse arival time at the spacecraft to the predicted arival time at the geocenter could be made, instead of the distant SB. The pulse cycle wavelength is 10,043 km =0.0335*c () , thus the ARGOS vehicle orbit wil remain within ?one cycle with respect to the geocenter. Using the known actual position of the spacecraft, the true time diference betwen the spacecraft and the geocenter is 0.0167 s = ? n! SCE () . The diference betwen this true time diference and the measured TOA diference asuming the vehicle is at the geocenter is 0.0021 s (= 0.0188 ? 0.0167). This corresponds to either 630 km of position eror along the line-of-sight to the Crab Pulsar, or 6.3% of phase diference for a Crab Pulsar pulse cycle. Thus, by asuming that the spacecraft is at the geocenter creates at Crab TOA measurement that computes a range estimate with eror les than 10% of the ARGOS orbit radius of 7213 km. Appendix C presents additional sets of data and shows several phase eror values. 196 Figure 6-2. High signal-to-noise profile template of two pulses from Crab Pulsar. Figure 6-3. Crab Pulsar profile with photon arrival times transfered from ARGOS position to SB. 197 Figure 6-4. Crab Pulsar profile with photon arrival times transfered from geocenter to SB. Figure 6-5. Crab Pulsar profile with no time transfer on photon arrival times. 198 Table 6-1. TOA Calculations and Diferences for Crab Pulsar Observation. Time Transfer TOA (MJD) TOA Eror (10 -6 s) TOA Diference wrt SC to SB (s) TOA Diference wrt GEO to SB (s) From SC to SB 51531.372976203982 9.98 -- -0.018 From GEO to SB 51531.372974026506 7.93 0.018 -- None 51531.371643466494 15.98 48.5189 48.501 If a spacecraft is moving in a plane perpendicular, or nearly perpendicular, to the direction to a pulsar, then ariving pulses wil not be afected by the vehicle?s motion. However, with motion towards or away from the pulsar, the pulses, as wel as the folded pulse profile, would be afected by the Doppler efect produced by the motion. If a folded profile is corrected for this motion by transfering the individual photon arival times to the SB, then clear profiles are evident, as in Figure 6-2 or Figure 6-3. If a profile is not corrected to the inertial origin and created only at the vehicle?s location, the Doppler efect esentialy smears, or distorts, the folded profile. Figure 6-5 provides an image of a Crab Pulsar observation at the ARGOS vehicle with no SB time transfer when the vehicle?s motion is close to perpendicular to the pulsar line-of-sight. This motion implies the dot product of the direction and spacecraft velocity is smal. For the observation in Figure 6-5 ? n!v SC/E =0.13km/s . Figure 6-6 provides an image of another observation on January 3, 2000 at 16:50:00 when the spacecraft?s motion distorts the profile due to a higher Doppler efect. In the observation of Figure 6-6 ? n!v SC/E ="4.8km/ . In order to create TOA measurements for use in the following sections, only observations should be utilized when the vehicle?s motion is primarily within this perpendicular plane or for sections of the orbit where the Doppler efect is reduced. Thus, a measure of this Doppler efect must be considered when creating pulse TOAs at the vehicle with no correction to the SB. It is obvious from these images that the pulse height intensity and shape gives a 199 measure of this profile distortion and presumably the measurement of the size of the Doppler efect. Creating an iterative scheme involving observations may improve the absolute position determination proces. If the first iteration asumes the vehicle is at some predefined location, such as the geocenter, then the TOA diferences can be used to correct some of this position estimate. Subsequent iterations of the same observations using these corrected position estimates could further remove position eror until a solution is determined that satisfies al observations from diferent pulsars. Figure 6-6. Second Crab Pulsar profile with no time transfer on photon arrival times. Profile is distorted due to Doppler efect on pulses arriving at vehicle. 6.3 Measurement Diferences In order to compute the absolute position of a detector using variable celestial sources, it is necesary to determine which specific pulse is ariving at the detector from a 200 source. Since sources do not identify any of the pulses that they emit, specific pulses must be identified by the way a set of pulses coordinate with respect to the orientation of a set of pulsars. Figure 6-7 shows the arival of pulses at a spacecraft from thre pulsars. At any given instance, there is only one unique set of pulses from this group of pulsars that solves for the exact location of the vehicle. By identifying this set of pulses, the position of the vehicle can be determined. Due to the significant distances betwen the celestial sources and the solar system, the pulse waves that arive into the system are asumed to be planar, not spherical. Ignoring the spherical efects of the wave propagation is only significant if the spacecraft and location of the model used for comparison are very far apart. Figure 6-7. Pulse arrivals from individual pulsars at spacecraft location. 201 Since no identifying information is provided with each pulse from a pulsar, determining which specific pulse is ariving at a given instance is not possible. However, by choosing a pulse-timing model at a known location, it is possible to identify the set of diferences in pulses betwen the spacecraft and the known location. For a single pulsar, a measured diference can be created with the pulse arival time at the detector and the predicted arival time at the known location. The diference in these values imediately identifies a set of candidate positions along the line-of-sight to the pulsar. These candidate locations are the value of measured fraction of pulse phase plus or minus multiple whole value pulse cycle lengths. Only one unique position satisfies measured diferences from a set of pulsars; and once this unique position is identified, the corect set of diferenced cycles are imediately determined. Alternatively, a phase cycle ambiguity search space can be created, either by choosing these search spaces based upon a prefered geometry, or by selecting a maximum number of search cycles to be considered. Al the candidate cycles that exist within this search space can be tested to determine whether the corresponding location satisfies the measured phase diferences. This method of position determination is similar to the navigation concept of Time Diference of Arival (TDOA). In TDOA, the diference of two sets of time arival measurements is used to determine the optimum location that satisfies specified criteria. However, in most TDOA concepts, two detectors or sensors are used to measure the source?s signal, and data from these two systems are diferenced. Contrastingly, in the celestial source methods described below, one of the detectors in the TDOA configuration is replaced by a model of pulse arival that is defined to exist at a specified 202 location, thus there is only one actual detector in the system. In these methods, no data needs to be transmited betwen the detector and the model location. Using a supplied pulsar almanac containing these models, the navigation system on the spacecraft can compute the entire absolute position. This is a true absolute positioning system, since the navigation system?s detector needs only to observe celestial source data, and determine its location within a given inertial frame. Although two detectors could be used for the absolute positioning system and data communicated betwen them, this would be more correctly represented as a relative positioning system. Several types of measurement diferences are described below. The Single Diference is the diference betwen the measured phase at the detector and the phase predicted at a model location for a single pulsar. The Double Diference is the subtraction of two single diferences from two separate pulsars. The Triple Diference is the subtraction of two double diferences betwen two separate time epochs. The benefits of computing these diferences include removing imeasurable erors, with higher order diferences removing additional erors. The complexity of using higher order diferences includes requiring more observable sources to produce solutions, which may take additional observation time. 6.3.1 Single Difference Measurements of the pulsed radiation from variable celestial sources can be diferenced with the predicted arival time from a pulse-timing model. The pulse-timing model is defined at a specific location within an inertial frame. Any specified location can be used, however, the most common location is the SB origin. For the examples shown below, the location of Earth within the SB inertial frame wil be used for 203 ilustrative purposes. Many spacecraft misions are in Earth orbit, or are for near-Earth applications. Although Earth is used for these examples, any known location in the solar system can be used, such as the Moon, Mars, Pluto, etc. In addition, the known location of another spacecraft or base station may be utilized. The single diference removes any values common to both the spacecraft and the model location. Primarily it removes the pulsar distance, which is often not known to any great acuracy. Measurement diferences can be created using measured range from the source or measured cycle phase. Primarily, since range measurements are dificult to compute from celestial sources, the phase measurements wil be used to compute spacecraft position. However, the range measurement algorithms are provided to help ilustrate the methods described here. The erors that are expected to be present in an actual navigation system are also identified and are shown within the diference computations. 6.3.1.1 Range Single Diference The range vectors betwen the pulsar source and Earth and betwen the pulsar and the spacecraft are shown in Figure 6-8. The source is asumed to be extremely far away from the solar system. Consequently the diference in these range vectors provides an estimate of the ofset betwen Earth and the spacecraft, !x . 204 Figure 6-8. Range vectors from single pulsar to Earth and spacecraft locations. 6.3.1.1.1 Geometric-Only Considering only the geometric representation from Figure 6-8, the position of the spacecraft relative to Earth can be represented using the spacecraft?s position, r SC , and Earth?s position, r E , within the SB inertial frame as, !x=r SCE "r E (6.23) This position can also be represented by the range vectors from the i th celestial source as, iSC i # E i (6.24) Within the SB inertial frame, the line-of-sight, or unit direction, to the source can very nearly be considered as a constant, due to the extreme distances to the sources. Thus the unit direction to the source can be represented using its known position within the inertial frame. The unit direction is in the opposite direction from the source to either the spacecraft or Earth as, ? n i = D !" ? # SC i E i (6.25) 205 The range vector can be represented using its magnitude and direction, as != , or != ? . Using the unit direction from Eq. (6.25), the diference in range magnitude represents the spacecraft?s position along the line-of-sight to the pulsar as, !" i = E i # SC i ? n i $!x (6.26) It is important to note the distinction betwen symbols for the range vector diference, !" i , from Eq. (6.23) and the range magnitude diference, " i , from Eq. (6.26). Since the line-of-sight from the SB to the source is in opposite direction with respect to the range vectors, the range vector diference is in opposite sense as the range magnitude diference. This is clear from the diagram in Figure 6-8. 6.3.1.1.2 Relativistic Efects As was discussed in the Observables and Erors section above, the relativistic efects on the path of a photon from the source to either the spacecraft or Earth cannot be considered negligible if acurate position determination is required. With the addition of these efects, the range diference using Eq. (6.7) becomes, !" i = E i # SC i r E D i +Relf E i $ % & ' #r SC D i +RelEf SC i $ % & ' iSCi lf i i (6.27) The position magnitude diference in the first term of Eq. (6.27) can be represented as, r E !D i SC " # $ % & '=r E (!2(D i + i ( ) 1 2 SC (r SC ( ii ( 1 2 i E 2 i 2 ) * + , - . 1 2 ! i r SC 2 (D i 2 +1 * + , - . 2 (6.28) 206 Using a binomial expansion of the square root terms and the line-of-sight simplification from Eq. (6.25) produces, r E !D i SC " # $ % & '( i 1+ 2 r E i ! )D i 2 * , - . / " # $ % & ' i SC i 2 ) i 2 + +O 1 i 2 * , - . / ( 1 2D i r E ! SC () ) i D !r E ) i * , D i 2 ? n i ) () 1 2 i SC 2 () + 1 i * , - . / (6.29) Therefore the range diference expresion can be simplified from Eq. (6.27) as, !" i # ? i $ SC % E () + 1 2D i E % SC 2 () +Rlf E i %lf SC i & ' ( ) +O 1 D i 2 * , . / (6.30) A further simplification that the second term of Eq. (6.30) is smal in most cases yielding, !" i # ? n i $x+RelEf i %lf SC i & ' ( ) + 1 i () (6.31) The expresion for the single diference in Eqs. (6.30) or (6.31) shows the main reason for its implementation. The poorly determined and very inacurate pulsar position vector, D i , has been removed from the equations. Thus spacecraft position computations no longer rely on the measurement of range directly from the pulsar. From these expresions, the range diference is only related to both the spacecraft position diference and the diference in relativistic efects to order O1D . 6.3.1.1.3 Range Single Diference Measurement with Erors Actual measurements made within the navigation system wil contain some erors. Thus the true range diference is a function of the actual measured values and their erors. From the range expresion of Eq. (6.12), the range diference becomes, 207 !" i =r E # ! D i +Relf " E i $r+D E i $Relf E i +% i & ' ( ) SCiSC i SC i SC ii ! Ei ! i & ' ( ) elf E i #lf i & ' ( ) r E #$ SC & ' ( ) +$ i # SC i +$ i SC i + ii (6.32) From the representation of the first term in Eq. (6.32) from Eq. (6.29), the range single diference can be estimated as, !" i # ? n i $x+RelEf ! i %lf SC i & ' ( ) +*r E % SC & ' ( ) *D i SC i ( ) *e i Rlf i & 'E i + i & ' (6.33) 6.3.1.2 Phase Single Diference The phase of the ariving pulse from a celestial source can be diferenced betwen the spacecraft and a known model location, similar to the range diference created above. The phase diference represents the fraction of cycle phase, or fraction of phase plus a fixed number of integer cycles, from an ariving pulse betwen the spacecraft and the model location. Figure 6-9 provides a diagram of ariving pulses from a single celestial source at a spacecraft and Earth. By measuring the phase diference, the spacecraft?s position with respect to Earth along the line-of-sight to the source is determined. Using multiple measured phase diferences from diferent sources provides a method of determining the spacecraft?s thre-dimensional position with respect to Earth in an inertial frame. 208 Figure 6-9. Phase diference for individual pulses arriving at the spacecraft and Earth. 6.3.1.2.1 Geometric-Only Phase diference is directly related to range diference when the wavelength, ! i , of the cycle is included. From Figure 6-8 and Figure 6-9, the geometric relationship of phase with respect to range from a source can be expresed as, !" i = E i # SC i $ i % i !& i +N i () =$ i & E i # SC i () +N E i SC i () ' ( ) * (6.34) The geometric relationship of phase with respect to spacecraft position is then ! i "#= i $ i +N i () = ? n i %"x (6.35) 6.3.1.2.2 Relativistic Efects Analogous to the range calculations, improved acuracy is atained when the relativistic efects on the light ray paths from the source are included. From Eq. (6.27), the phase diference becomes, ! i "#= i $ i +N i () r E %D iSCi & ' ( +RelEf i %lf SC i & ' ( ) (6.36) If the simplifications to the first term are included as was considered in Eqs. (6.29) and (6.31), and the line-of-sight is included from Eq. (6.25), this phase diference becomes, 209 ! i "#= i $ i +N i () % ? n i &"x+RelEf i 'lf SC i ( ) * + O 1 D i () (6.37) 6.3.1.2.3 Phase Single Diference Measurement with Erors Actual phase measurements made at the detector of a spacecraft wil contain erors, similar to an actual range measurement. Refering to the measurement erors for phase from Eq. (6.20), the phase diference calculation is related to these erors as, ! i "#= i $ i +N i () !r E %D i ! SCi & ' ( ) +RelEf " i %lf SC i & ' ( ) +c*t E % SC [] c*T ii [] *r ESC *D ii +Relf E i lf i &( ii &( (6.38) It should be noted from Eq. (6.38) that the term involving pulsar intrinsic model eror, c!T i , cancels when computing a phase single diference. This is significant since any model erors that exist in the pulse-timing model for a specific pulsar do not afect the computation of position when using a phase diference. With the additional simplification of the first term on the right hand side of Eq. (6.38) using Eq. (6.29), the phase single diference equation becomes, ! i "#= i $ i +N i () % ? n i &xRelEf ! i 'lf SC i * + c,t E ' SC [] +,r E ' SC ( ) * + ,D i SC i) * + ,e i Rlf i (* - ii (6.39) Alternatively, the geometric representation of phase can be stated in terms of the line- of-sight and its related erors from Eq. (6.22), as, 210 ! i "#= i $ i +N i () %!n E i &D i '!r E () n SC i & ! i 'r SC () ( ) * + RelEf " i 'lf SC i ( ) * + c,t [] ii &,D i ( ) !n i &r! i &, + ? E i & ! iE () ? SC i ! iSC () Relf i 'lf i ( ) * + - E i ' i * + (6.40) With the additional asumption that the line-of-sight is constant throughout the solar system such that !n iE i ! SC i , the above representation can be simplified to the following, ! i "#= i $ i +N i () %!n i &xRelEf " i 'lf SC i ( ) * + c,t E ' SC [] +!n i &,r E ' SC () ( ) * + , ? i [] i e i - ii ( ) * (6.41) The fourth term on the right hand side of Eq. (6.41) is related to the eror in spacecraft position, or !r E " SC () #$x . If the position of Earth is acurately known, then the eror in Earth position is efectively zero, or !r E "0 . Thus, this expresion simplifies directly to spacecraft position eror. An interesting observation is that the delta-correction position method of Chapter 7 [192, 193], can be implemented utilizing Eq. (6.41). Using phase single diference measurements and an estimate of spacecraft position, x , Eq. (6.41) can be used to solve for any unknown spacecraft position eror, ! SC . 6.3.2 Double Difference The primary benefit of the single diference computation is the removal of the poorly known pulsar position vector, D i from the computations. Implementing a double diference can provide additional benefits. A double diference is the subtraction of two 211 single diferences from two separate pulsars. This diference removes values that are common to both pulsars, such as navigation system dependent values. However, double diferences require observations from multiple sources to be conducted contemporaneously, such that the pulse arival time measurements from these sources are computed simultaneously and at the same position of the spacecraft. Otherwise, methods must be employed to adjust arival times for observations made at diferent times to the same time epoch. This may require multiple detectors to be integrated into a single system for full absolute position determination. 6.3.2.1 Range Double Diference The range double diference is computed betwen these two sources, the i th and j th pulsars. The diagram in Figure 6-10 shows the ariving pulses from two pulsars into the solar system. Figure 6-10. Pulse plane arrivals within solar system from two separate sources. 212 6.3.2.1.1 Geometric-Only If only the geometric relationship for two pulsar range vectors and the spacecraft position is considered as in Figure 6-8 and Figure 6-10, the range vector double diference can be expresed as, !"# ij = i $ j # SC i E i () $ SC j # E j () (6.42) In this expresion, the symbol ! is used to represent a double diference, and should not be misinterpreted as the gradient operator. From the representation of a range vector single diference from Eq. (6.24) it can be sen that the range vector double diference equals zero, or, ji " j =x0 (6.43) Although the double range vector diference is zero, this is not true of the double range (scalar) diference. Since the line-of-sight vectors are diferent for each pulsar, the double range diference is not zero. Instead, in a purely geometric-sense, the range double diference using Eq. (6.26) is the following, !"# ij = E i $ SC i () # E j SC j () = ? n i $ j () %"x (6.44) 6.3.2.1.2 Relativistic Efects Including the efects of relativity on the light ray path for range single diferences as in Eq. (6.31), the range double diference for two pulsars becomes, !"# ij $ ? n i % j () &"x+RelEf i %"lf j ' ( ) * +O 1 D i % j, - . / 0 (6.45) 213 6.3.2.1.3 Range Double Diference Measurement with Erors Including the measurement erors for the range single diferences, the double diference betwen two pulsars from Eq. (6.32) becomes, !"# ij = !r E $D i ! SCi j +r j % & ' ( ) * "RelEf i $lf " j % & ( ) + r E $ SC % & ' ( ) * E i SC i $ jj % & ' ( ) * lf i lf j %( , E i SC i jj % & ' ( ) * (6.46) This expresion can be further simplified, since the terms involving Earth location eror and spacecraft position eror cancel, to produce, !"# ij = !r E $D i ! Ej () SCi r SCj % & ' ( ) * +"RelEf i $lf " j % & ( ) + E ij () $ SC i + SC j % & ' ( ) * lf i lf j % & ( ) +", i $ j % & ( ) (6.47) If the line-of-sight vectors are utilized instead, as in Eq. (6.33), then this range double diference becomes, !"# ij = ? n i $ j () %"x+RelEf ! i $"lf j & ' ( ) *D E ij () SC i SC j & ' + ( ) , *lf i RelEf j ( ) +"- i $ j & ' ( ) (6.48) The range double diference of Eqs. (6.47) and (6.48) involve diferences of smal values. It is likely that in practical situations many, if not al, of the diferences other than spacecraft position and noise can be ignored. 214 6.3.2.2 Phase Double Diference As was shown for range, double phase diferences can be calculated for the i th and j th pulsars. Figure 6-11 provides a diagram of the phase single diference for two pulsars, which can be subtracted from one another to produce a phase double diference. Figure 6-11. Phase diference at the spacecraft and Earth from two sources. 6.3.2.2.1 Geometric-Only The total phase double diference is composed of the fractional phase double diference and the integer cycle double diference, and is given by, !"# ij = i $ j !"% ij +N ij =% i +" i () $% j N j () (6.49) From Figure 6-9 and Figure 6-11, the geometric relationship of phase with respect to spacecraft position is ijiii () $ jjj () ? n ij () &x (6.50) or, by dividing through by cycle wavelength, 215 !"# ij =$ ij +"N ij = ? n i % & j ' ( ) * + ,-"x (6.51) 6.3.2.2.2 Relativistic Efects Analogous to the range calculations, improved acuracy is atained by including the relativistic efects on the light ray paths from the source. From Eq. (6.36), the phase diference becomes, ! i "#$ j =! i "% i +N i () $! j "% j + j () r E D iSCi j r j & ' ( ) * RelEf i $"lf j & ' ) * (6.52) If the simplifications to the first term are included as was considered in Eq. (6.37) and the line-of-sight is included from Eq. (6.25), this phase double diference becomes, ijiii () jj N j () ? n j 'x lf i ( , - O 1 D ij . / 0 2 3 (6.53) or, by dividing through by cycle wavelength this becomes, ij =$ ij + ij % ? i ' ( ) * , -. Relf lEf / 0 1 2 3 4 i ' & j ( ) * + , - (6.54) 6.3.2.2.3 Phase Double Diference Measurement with Erors Actual phase measurements made at the detector of a spacecraft wil contain erors, similar to an actual range measurement. From Eq. (6.38), the phase double diference equation becomes, 216 ! i "#$ j =! i "% i +N i () $! j "% j + j () & ? n ij () 'xRelEf i lf j ( ) * + c,t E $ SC t ( ) - * + . + ,r ESC $ ( ) - * + . ,D i SC i $ E jj) - + . "Relf i elf j "/ ij (* (6.55) Observing the terms within Eq. (6.55), the spacecraft and Earth time erors cancel, as wel as the spacecraft and Earth position erors. Removing these terms yields, ! i "#$ j =! i "% i +N i () $! j % j +" j () & ? n ij () 'x RelEf i j ( ) * , - .D E i $ SC i j + j ( ) * , - + .elf i $" j ( ) * + , - / i $" j (+ (6.56) In terms of double phase diference, the Eq. (6.55) becomes, !"# ij =$ ij +"N ij % ? n i & ' j ( ) * , -.x RelEf ! i & ' "lf j / 0 1 2 3 4+c5t E ' SC () 1 & ij ( * + , - / 0 1 2 3 4 + 5D E i SC i ' jj & / 0 1 2 3 4 +5r ESC () & ij) * + , - / 0 1 2 3 4 "5RelEf i elf j / 1 2 4 "6 i ' j / 0 1 2 3 4 (6.57) Alternatively, the geometric representation of phase can be stated in terms of the line- of-sight and its related erors from Eq. (6.41) such that the phase double diference becomes, 217 ! i "#$ j =! i "% i +N i () $! j "% j + j () &n ij () 'x RelEf i j ( ) * , -! n i $ j ( '.r ESC () ( ) + , +. ? i $ j ' ( ) + .lf i "e j + / i " j (6.58) If this is represented as phase only, this expresion becomes, !"# ij =$ ij +"N ij % !n i & ' j ( ) * , -.x RelEf i & ' "lf j / 0 1 2 3 4+c5t E ' SC () 1 & ij ( ) * + , - / 0 1 2 3 4 + ! i j + .5r ESC () / 0 1 2 3 4 ? n i j & ( ) * , -.x / 0 1 4 "Relf i & ' elf j 14 + "6 i ' j 1 2 3 (6.59) For most practical systems, the phase double diference of Eqs. (6.55) or (6.58) are very beneficial, since the time erors cancel in these representations. However, some applications may only produce direct phase double diference measurements in which case there would be no alternative but to use Eqs. (6.57) or (6.59). However, in these equations the time erors do not cancel, so al terms must be retained for acurate position determination. 6.3.3 Triple Difference The triple diference is created by subtracting two double diferences over time. This diference removes any values that are not time dependent. For a static system or when measurements are made over fairly short diference in time, many of the time independent terms wil cancel. 218 6.3.3.1 Range Triple Diference with Erors The triple diference for range can be computed from Eq. (6.48) at time t 1 and 2 as, !"# ij t 2 () $ ij t 1 () % ? n i $ j {} &"xt 2 () t 1 ' ( ) * + !"RelEf ij t 2 () $ 1 ' ( ) * , + !-RelEf ij t 1 () (* ,. ij t 2 () ij t () ') (6.60) This representation of Eq. (6.60) asumes that the triple diference of pulsar position eror, with respect to Earth and the spacecraft, is negligible. The triple diference of the relativistic efect and its erors can also be considered to be very smal, so for most applications the range triple diference can be stated as, !"# ij t 2 () $ ij t 1 () % ? n i $ j {} &"xt 2 () t 1 ' ( ) * + !" ij t 2 () $ 1 ' ( , ) * - (6.61) 6.3.3.2 Phase Triple Diference with Erors Similarly as with range described above, a phase triple diference can be computed using Eq. (6.57). If al the triple diferences with respect to relativity efects and its erors, time erors on Earth and the spacecraft, and position erors are considered negligible, then the phase triple diference can be writen as, !"# ij t 2 () $ ij t 1 () =!"% ij t 2 () $ ij t 1 () & ' ( +!"N ij t 2 () $ ij t 1 () & ' ( * ? n i + j , - . / 0 3x 2 & ' 4 i t () i t 1 () $ 4 j t 2 () j t 1 () + ' 5 6 (6.62) If the time diference is short enough, and the phase cycle is long enough, then the integer cycle wil not change betwen measurements and the integer cycle triple diference from 219 Eq. (6.62) wil be zero, or !"N ij t 2 () # ij t 1 () $ % & ' =0 . This simplifies the expresion, and spacecraft position can be determined using only the fractional phase measurements. 6.3.4 Velocity Measurement An interesting aspect of the triple diferences is that by subtracting values over time this diference introduces the potential for spacecraft velocity determination. Rewriting Eq. (6.62) with the time diference betwen and 2 as !"# ij t 2 () $ ij t 1 () % & ' ( ) * = !"+ ij t 2 () $ ij t 1 () % & ' ( ) * + !"N ij t 2 () $ ij t 1 () % & ' ( ) * , ? n i - j . / 0 3 4 5 xt 2 t 1 % & ' + "6 i t 2 () $ i t 1 () {} "6 j t 2 () $ j t 1 () - {} ' * (6.63) Spacecraft velocity can be introduced as, !x= t 2 () "xt 1 (6.64) Creating similar derivatives for phase double diference and phase noise, the triple diference of Eq. (6.63) becomes, !"# ij = ! $ ij +"N ij % ? n i & ' j ( ) * , - . /"!x+ 0 i & ' ! j 1 2 3 4 5 6 (6.65) If a system is developed that is able to determine phase measurements over time, a spacecraft velocity measurement could be completed using Eq. (6.65). If the integer cycle velocity term zero, or !"N ij =0 , then the spacecraft velocity can be determined directly from the fractional phase velocity. 220 6.4 Search Space and Cycle Ambiguity Resolution The previous section provided methods to determine the position of a spacecraft with respect to a known location. These methods rely on measuring the phase of an ariving pulse at a detector and comparing this to the phase predicted to arive at the reference location. The predicted phase is determined using a pulse-timing model. However, comparing measured and predicted phase of a single pulse does not determine absolute position unles the number of full pulse cycles betwen these two locations is also known. Since the number of integer phase cycles is not observable in the pulse measurement from a pulsar, or they are ambiguous, additional methods must be developed that resolve these ambiguous cycles so that true absolute position can be determined. This section describes the pulse phase cycle ambiguity resolution proceses. These proceses rely on the fact that for a given fully determined set of phase measurements from separate pulsars, there is one unique position in thre-dimensional space that satisfies al the measurements. Thus, there is only one fully unique set of cycles that satisfies the position and phase measurements. Once this set of cycles is identified, the thre-dimensional position can be determined by adding the fractional portion and integer number of phase cycles that are present betwen the spacecraft and the reference location. A solution for the cycle sets can be generated through direct solution methods. These methods use a linear combination of a subset of measurements. Given enough measurements, solutions can be created for the unique set of cycles and the absolute position. However, since the phase measurements and the position produce an under- 221 determined system (more unknowns than equations), some method of inteligently guesing some of the unknowns may need to be implemented. The solution cycle set may also be selected from a search space, or thre-dimensional geometry that contains an aray of candidate cycle sets. Each set within a chosen search space is procesed and the likelihood of each set being the unique solution is tested. Individual candidates that satisfy procesing tests are retained for further evaluation. Using sufficient measurements from enough pulsars ? or by using multiple measurements from a single pulsar ? alows a unique cycle set within the search space to be chosen as the most likely set for the absolute position of the spacecraft. Testing each candidate set of cycles within a large search space can be computationaly intensive and may require large procesing time. Methods that help reduce the search space, or more quickly remove unlikely candidates from the space, are a benefit to the computations. Additionaly, multiple tests of the candidate sets, which help identify likely candidates, improve the eficiency of the selection proces. In an actual navigation system, erors that are present within the system wil cause the candidate selection proces to be les acurate. Within the direct solution methods, erors may cause incorrect cycle sets to be identified. Within the search space methods, erors cause multiple candidate sets to be retained until the correct solution can be identified. Utilizing aggresive candidate tests may incorrectly label a set of cycles as the chosen solution, since this set may pas al the tests. Often, this set of cycles wil appear to be correct given the measurements, but wil eventualy become obviously incorrect once additional measurement procesing is available. For deep space vehicles, or vehicles orbiting Earth, this incorrect navigation solution may have disastrous efects on the 222 spacecraft?s mision. Al atempts must be made to insure that i) selection methods guarante that the correct solution is a potential solution, i) the true candidate set lies within the chosen search space, ii) test criteria must acount for measurement noise within the system, and iv) any chosen set of cycles must be continualy monitored to insure its validity. The GPS and GLONAS systems utilize similar search space and integer cycle ambiguity resolution techniques as the ones described below [3, 4, 73, 85, 106]. The basis of the techniques used for these human-made systems can be applied to the methods using variable celestial sources. However, due to the variety of types of sources and pulse cycles, the techniques for celestial sources are more complex. The following sections describe methods on seting up the cycle determination proces, generating a valid search space if needed, and resolving phase cycle ambiguities. Various options exist for search space geometry and cycle test characteristics. The methods described below provide a broad overview of these options. 6.4.1 Search Space Resolving the ambiguous cycles that exist from the phase measurements often requires generating a search space of possible integer phase cycle combinations. Each candidate cycle set is then tested for its validity and acuracy. It is asumed that only one unique set of cycles correctly solves the phase measurements and position location, as wel as pases the entire candidate set tests. However, if insufficient measurements are available, or the given measurements have large erors, then a unique set may not be solvable, and only several posible cycle sets may be identified. Creating a sufficient search space is critical for acurate cycle identification and position determination. 223 The search space is typicaly symmetrical about its origin. The origin, or center point, of the search space can be chosen depending on the application and would often be chosen as the model location. Since most pulsar timing models exist at the SB, the barycenter is a potential choice as the search space origin. For spacecraft misions studying the solar system?s planets, especialy inner planets, the SB is an appropriate option for the origin. For spacecraft operating in orbit about Earth or within the Earth- Moon system, the geocenter ? or in some cases the Earth-Moon barycenter ? is a more useful choice for the search space origin. When a spacecraft is known to be orbiting a planetary body, choosing this body as the origin of the search space significantly reduces the size of the search space rather than the choice of the SB as origin. Candidate cycles can exist within the search space on either side of the origin, unles some prior knowledge alows the removal of candidates from one side of the origin. The search space could be shifted with respect to the origin if information regarding its shape can be determined. For spacecraft that have failed for some reason and must implement absolute position navigation in order to solve the vehicle?s lost-in-space problem, a beter choice for the search space origin is the vehicle?s last known position. This position would need to be stored in backup memory onboard the vehicle. This provides the ambiguity resolution proces and its search space definition a much more acurate representation of where the vehicle could be, rather than starting the proces entirely over and using a distant reference location as the origin. In an operational sense, any known location can be utilized as the search space origin, since only known locations are valid for defining the pulse timing model. The choice of 224 the origin should be made in the most prudent manner given the vehicle?s situation and application. Figure 6-12 shows a diagram of a candidate cycle search space in two dimensions. The SB, Earth, and spacecraft positions are shown, and ariving pulse phase planes are diagramed ariving from four diferent pulsars. The spherical geometry search space is shown as centered about Earth. The only candidate set of cycles within the search space that has al phase planes crossing in one location is the true location of the spacecraft. Figure 6-12. Phase cycle candidate search space, centered about Earth. There are thre methods presented below for generating a search space. ? Geometrical Space: A straightforward method of developing a cycle search space is to place a thre dimensional geometrical boundary about the origin. Options for shapes include a sphere of specified radius, a cube of specified 225 dimensions, or an elipsoid, perhaps about the planet?s equatorial plane. The dimensions of this geometry, centered about the origin, define the candidate cycles along the line-of-sight vector to each pulsar. The search space candidate sets are selected such that they lie within this geometrical boundary. ? Phase Cycle Space: A search space can be defined as a fixed number of cycles along the line-of-sight to a pulsar. The number of cycles considered can be specific to each pulsar. For example, a choice of ten cycles on each side of the origin could be selected for a pulsar. If the pulse cycle length from each pulsar is sufficiently diferent, care must be taken in order to ensure that the true cycle set is maintained within the created search space. ? Covariance Space: Given a set of pulsar phase measurements and the corresponding measurement noise asociated with each measurement, a search space can be created that is defined by the covariance matrix of the measurements. The covariance matrix wil skew the search space based on the magnitudes of the erors. This method is similar to the Geometrical Space method, however the Covariance Space shape is elipsoidal oriented along the eigenvectors of the covariance matrix [4]. Once a search space has been generated, it is possible to reduce the number of sets to be searched by removing those sets that are known to exist inside any planetary bodies. The spacecraft could not be physicaly located inside these bodies, so there is no need to test these candidate sets. Sets that define a position within the Sun, Earth, or any planetary body, can be imediately removed from the search space. For applications in 226 planetary orbits, such as low-Earth orbits, this may significantly reduce the number of searchable candidates. 6.4.2 Cycle Candidates The candidate cycle sets within a search space are defined by the single, double, or triple diferences as developed in the Measurement Diferences section. Given a set of phase measurements, from predicted phase arivals at a known model reference location and detected arivals at the spacecraft position, then there is only one set of phase cycles that uniquely defines the combination of this data. The search space esentialy contains an aray of cycles defined to be in the vicinity of this true set. Each possible cycle combination within this search space can be identified in the aray and tested to determine whether acurate spacecraft position has been resolved. As an example, the phase single diference of Eq. (6.35) defines the relationship betwen fractional phase diference, !" i () , phase integer cycle diference, !N i () , and spacecraft position, !x () , for a single pulsar. If the phase diference is measured and the integer cycle diference is known a priori, then the spacecraft position along the line-of- sight to that pulsar, ? n i !" () , is directly known from this equation. However, if is not known a priori, and supposing a search space of ten cycles is chosen, then each of the ten diferent cycles could be selected as the potential cycle value that defines the spacecraft location. By utilizing measurements from additional pulsars, each set of potential cycles from each pulsar can be procesed to establish which set uniquely solves for the combination of phase measurements and spacecraft location. 227 This proces could easily be extended for double or triple diferences by using Eqs. (6.51) and (6.62) respectively. If the phase double diferences are measured, then there exists one set of cycle double diferences that solves for the unique spacecraft location. Appropriately, a search space that contains the entire aray of possible cycle double diferences can be generated, and each combination of cycles within this space can be tested for its validity. Figure 6-13 shows an elementary two-dimensional search space generated from two orthogonaly located pulsars. Several phase cycle single diferences are labeled, such as !N 1 , 2 () =, () and !N 1 , 2 () =",1 () . The true spacecraft position happens to be located at the intersection of phase planes 1 and 2, or !N 1 , 2 () =, () . Figure 6-13. Phase cycle search space, containing candidate cycle sets, centered about Earth. 228 6.4.3 Cycle Ambiguity Resolution Acurate spacecraft absolute position determination requires precise phase measurements at the spacecraft detectors, thorough pulse timing models at the base reference location, and exact knowledge of the ambiguous phase cycles betwen the spacecraft and the reference location. The phase cycle ambiguity resolution proces determines these unknown phase cycles, which match the measured phase data. Thre resolution methods are presented. Each method has advantages for specific applications, and some require les procesing than the others. The Batch, or Least Squares, method directly solves for cycle ambiguities based upon input measurements. Procesing is fairly simple, but requires inteligent pre-procesing, and inacurate measurements can lead to widely eroneous results. The Floating-Point Kalman Filter method generates a floating-point estimate of the integer cycle ambiguity set as produced by the observing Kalman filter (or similar observation filter). Somewhat proces intensive, this method may require large amounts of measurement data, spread over time, in order to resolve the correct ambiguity set. The Search Space Aray method exhaustively tests each potential cycle set that exists within a generated search space. Although proces intensive if large amount of candidate sets exist within a search space, with the use of wel-chosen selection tests this method can typicaly correctly resolve the cycle ambiguities. Further detail on each procesing method is provided below. 6.4.3.1 Batch (Least Squares) Resolution This Batch method asembles a set of phase measurements from separate pulsars to simultaneously and instantly solve for spacecraft position and phase cycle ambiguities. A straightforward Least Squares solution can be implemented, or perhaps enhanced 229 Weighted Least Squares method, which uses weights based upon the phase measurement acuracies. To sufficiently solve for the thre-dimensional position and cycle ambiguities, some inteligent pre-procesing of pulsar data must be implemented. This is required since even with measurements from several pulsars, the linear system of equations is under- determined (more unknowns than available equations). Reducing the number of unknown variables is necesary to create a fully determined system. Any of the single, double, or triple diferences may be implemented into this Batch resolution proces. Additionaly, system erors may also be determined. However, adding the estimation of eror terms increases the number of unknowns. From the phase single diference Eq. (6.35), the equation may be placed in linear form for a single pulsar as, !" i = ? n i # $1 % & ' ( ) * !x N i (6.66) Smal erors that may exist for this equation have been ignored. This single equation has one measurement, !" i , and four unknowns ? thre from the position vector, !x , and one from the single-phase cycle unknown, !N i . Asembling phase measurements from k pulsars, this equation becomes, 230 !" 1 2 # # !" k $ % & & ' ( ) ) = ? n * +0##0 1# # # # #0#+0 ? n k * #1 ' ( ) ) ) !x N 1 2 # !N k $ % & & (6.67) This system has k equations and k+3 unknowns, which is an under-determined system. At least thre unknowns must be estimated prior to atempting to solve this equation. Any prior knowledge that alows an estimate of enough unknowns to reduce the system to be fully determined is useful. The selection of certain pulsars may support reducing the number of cycle unknowns. When trying to determine spacecraft position, the knowledge of the vehicle?s mision may provide insight to estimates of its locations. For example, consider a spacecraft within a geosynchronous orbit of Earth (radius = 42,200 km). If observation pulsars are selected that have a cycle period of greater than 0.28 s (= 2*42,200/c), then these specific pulsars have no known cycle ambiguities within the potential orbit radius. Only one cycle exists within this distance. Since a phase diference measurement may have ambiguous sign, it may also be wise to test at least one single cycle diference !N=1 () for these specific pulsars. Choosing a minimum of thre pulsars with large enough period alows prior estimation of their cycle diferences. With these thre values already known, the system of equation becomes, 231 !" 1 2 # " k$3 ! 2 +N 2 k1k1 % & ' ' ' ( ) * * * = ? n 1 + $0##0 2 # # # 0 ? n k$3 0$1 k2 $ ## ? k1 0##0 n k + ## % & ' ' ' ' ( ) * * * * !x N 1 2 # # !N k$3 % & ' ' ( ) (6.68) This new system of equations now has k equations and k unknowns. This new system can be solved by rewriting the system in full vector form as, !" [] =H x N # $ % & ' ( (6.69) The H matrix, composed of the terms from Eq. (6.69), is refered to as the measurement matrix. This new system can be solved using methods of Least Squares as the following, !x N " # $ % & ' =H T () (1 T ( !) [] (6.70) Additionaly, a weighting matrix, W , representing the covariance estimate of acuracies for each measurement can be implemented as, !" [] =WH x N # $ % & ' ( (6.71) The solution to this weighted equation is then, !x N " # $ % & ' = () T % & (1 ) T ! [] (6.72) 232 Thus, using either Eqs. (6.70) or (6.72), a Batch solution of vehicle position and unknown cycle ambiguities can be determined. This method is relatively simple to generate and limited procesing is required. Instant position and cycle value results are available once sufficient measurements are created. This proces can be extended to use the eror equation for a phase single diference of Eq. (6.41), however, unles methods are provided to estimate these additional erors, more equations (or measurements) are required to solve for the additional unknown variables. Alternatively, this Batch proces can be extended to utilize the phase double or triple diferences. As shown previously, creating double or triple diferences reduce the erors asociated with each phase measurement. However, these additional diferences reduce the number of equations within a system. For a system of k measurements, a double diference system has only k!1 equations with k+2 unknowns, and a triple diference system has only 2 equations with unknowns. Additional methods of estimating unknowns must be created for these higher order diference systems. 6.4.3.2 Floating-Point Kalman Filter Resolution In this Floating-Point Kalman Filter resolution method, an analytical filter is developed that estimates the state variables of spacecraft position and phase cycle using measurements of phase diferences. A Kalman filter is a recursive state estimator that relies on adequate models of the behavior of each state variable over time, the state dynamics, and sufficient representation of the relationship of the state variables with respect to the observed measurements [29, 65]. Proces noise asociated with the state dynamics and measurement noise asociated with each measurement are incorporated into the Kalman filter proces. Estimates of state variables and the eror covariance 233 matrix asociated with the state variables are products of this filter. The eror covariance matrix provides an estimate of the acuracy of the state estimation during the filter procesing. The Floating-Point Kalman Filter is created such that the spacecraft position and the cycle ambiguities are treated as state variables. The phase diferences are provided as measurements to the filter. The dynamics of each state can be represented over time using any prior knowledge of their dynamics, or if the measurements are produced over a sufficiently short amount of time, the state dynamics can be treated as static (not changing due to time). This type of filter could incorporate triple diference measurements using Eq. (6.65) to determine spacecraft velocity as wel as position. This would asist with any unknown vehicle dynamics. Although the phase cycle diferences are integer values, these terms are estimated as floating-point (real) values within the Floating-Point Kalman Filter [3]. Once sufficient measurements have been procesed such that the values remain stable, these floating-point estimates can be rounded to the nearest integer. The Floating-Point Kalman Filter resolution method provides procesing of sequential measurements as they become available, as opposed to the Batch procesing technique, which is implemented al at once. However, since there are many pulsars that can be observed, and coordinating the diferences betwen them al can be a bookkeeping chalenge, this method is proces intensive. The Floating-Point Kalman Filter could be implemented as an eror-state filter, where state variables are the asociated erors of whole states (such as eror in position 234 rather than position). Since some erors may be non-linear, the extended form of the Kalman filter algorithms would be implemented. 6.4.3.3 Search Space Aray Resolution The previous methods solve directly for cycle ambiguities as a consequence of their procesing. The Search Space Aray method selects a candidate set of cycles and determines whether this set provides an acurate position solution. This method must exhaustively test al possible candidates for the most likely set, and is consequently proces intensive. However, testing al possible candidate sets within a generated search space asures that the correct solution set wil be tested, rather than potentialy never being evaluated by the previous methods. As was mentioned previously in the Search Space section, inteligent search space creation wil help reduce the exhaustive procesing by limiting the number of candidate sets, while stil atempting to insure the corect solution lies within the search space. As shown in Figure 6-12 and Figure 6-13, the search space is esentialy a geometric grid of candidate cycles from each observed pulsar. Every possible grid point must be evaluated within the search space in order to determine which point is the most likely candidate cycle set for the combined pulse phase diference measurements and the spacecraft position. In order to evaluate each candidate cycle set, a comprehensive test, or series of tests, of the candidate?s validity and acuracy must be performed. From Eq. (6.35), for a phase single diference from one pulsar, using the measured phase diference, !" i , and a chosen set of cycle diferences, !N i , the spacecraft position along the line-of-sight for the pulsar can be solved for using, 235 ? n i !"x=# i $ i + ! N i () (6.73) Given a set of at least thre pulsars, the measurements can be asembled as, ? n 1 2 3 ! " # $ % & 'x=H! ( 1 ')+ ! N 1 () 22 3 ! 3 () " # $ % & (6.74) The spacecraft position can then be solved for using, !x=H T () "1 # $ % & ' ( ) 1 !*+N 1 () 22 3 ! 3 () # $ % & ' ( (6.75) Using this value for spacecraft position, any additional pulsars j>3 () can have their cycle ambiguities directly solved for by !N j =round ? n j " #!x$% j & ' ( ) * + (6.76) where the round function rounds the floating-point expresion within the parentheses to the nearest integer. A residual test can be determined using these new estimated cycle ambiguities as, j #N (6.77) If more than one additional observed pulsar is available, then a vector of these residual tests can be produced, 236 != j +1 " " k # $ % % & ' ( ( ? n j ) "*!x+, j ! N j j1 " j+1j1 " " ? n k ) *!x+, k ! N & ' ( ( ( (6.78) The magnitude of this residual vector provides an estimate of the quality of the computed spacecraft position, !x , ! " =norm () (6.79) Each candidate set within a search space can be evaluated using this test statistic, ! " . If a chosen set does not match wel with the measured phase diference and spacecraft position, then the value of residual wil be large. Likewise, if the chosen set does match wel, then the diferences for each extra observable pulsar from Eq. (6.78) wil be smal and consequently, the magnitude of the residual vector wil be smal. A threshold for this residual magnitude can be chosen in order to remove many, if not al, of the candidate sets other than the specific candidate set that represents the true spacecraft position. If several candidate sets remain below a chosen threshold, additional measurements from pulsars can help to eliminate wrong candidate sets. Eventualy, after enough measurements have been procesed, the true candidate set wil be identified and the absolute position of the spacecraft wil be determined. For some cases, the vector of residual tests can be computed using al available sources instead of just those with index j>3 , which may give further information about which candidate sets can be discarded. 237 As was shown within the Batch resolution proces, weighting of individual pulsars can be used to help determine an estimated vehicle position. Adding a weighting matrix to Eq. (6.74), the spacecraft position solution of Eq. (6.75) becomes, !x=WH () T " # $ % &1 () T ' 1 !(+N 1 () 22 3 ! 3 () " # ) $ % * (6.80) Weights may also be included in the residual calculation of Eq. (6.78). Incorporating weights into these measurements may be necesary if a subset of pulsars is more acurately measurable than the remaining pulsars. The residual vector defined in Eq. (6.78) can be extended to include double and/or triple phase and cycle diferences. The sections describing these diferences have shown that erors are reduced when using higher order diferences. However, because these higher order diferences are evaluated using diferences of close or similar values, developing a test statistic threshold that sufficiently removes unwanted candidate sets and retains the correct candidate set becomes increasingly dificult. Care must be exercised in choosing a good statistic threshold. In order to augment this isue, combined-order systems, where candidate set evaluation is performed at multiple levels of diferences can asist in selecting the correct cycle set. For example a combined-order system incorporating both first and second diferences may help to identify the correct cycle set. Additional tests may be created that help remove unwanted candidate sets. If any dynamics of the vehicle is known during an observation time, this information can determine how future cycles behave with respect to current cycle estimates. Comparing 238 the Batch method results to the Search Space Aray results, using the asumed correct set of cycles, can be an additional test of cycle and spacecraft position validity. 6.5 Relative Position The preceding sections developed methods to determine a spacecraft?s absolute position within an inertial frame. Choosing a known reference location within this frame, the offset position with respect to this location is determined from these methods. The spacecraft?s absolute position is then the sum of the reference position and the offset position. Some applications, however, may only require knowledge of relative position, or the position relative to a location that may or may not be fixed. This relative, or base station, location may be the position of another vehicle or any object that the spacecraft uses as a relative reference. Since this base station?s relative location may not be known by the spacecraft at any given instance, the location of this relative object must be transmited to the spacecraft when measurements are needed. This requires communication betwen the base station and the spacecraft. If the base station also has a detector, similar to the spacecraft, then direct phase measurement diferences can be implemented instead of using a pulse-timing model. If a pulse-timing model is used, the base station must transmit its location so that the inertial- based timing model can be transfered to the base station?s location. If full detector information can be transmited from the base station, then a model is not required, since direct phase diferences can be calculated. 239 Figure 6-14 provides a diagram of the relative navigation concept with a base station spacecraft and a single remote spacecraft. Communication betwen the remote spacecraft and the base station, as wel as contemporaneously measured pulse arival times, alows relative navigation of the vehicles. This relative navigation system requires more procesing due to the extra communication and because the system is a dynamicaly operating system versus a static base station. Time alignment of measurement date is crucial and often complicated. This type of navigation has similarities to the proceses of diferential or relative GPS navigation, where one receiver station transmits its information to another station in order to determine relative position and velocity information [156]. Relative navigation is useful for applications such as multiple spacecraft formation flying, a spacecraft docking with another vehicle, or a rover operating on a planetary body with respect to its lander's base station. Alternatively, a base station satelite can be placed in Earth orbit and be used to monitor and update pulsar ephemeris information. Ideal locations for these base stations may include geosynchronous orbits, Sun-Earth and Earth-Moon Lagrange points, or solar-system halo orbits. Once new or updated pulsar data is computed, the base station could broadcast this information to al operational spacecraft. Those spacecraft within the base station?s vicinity and within communication contact can use the station?s information to compute a relative position solution. This method may provide improved acuracy over the absolute position method, since the base station can provide real-time updates of pulse models. If acurate base station navigation information is known, then computing a relative navigation solution with respect to the base station also alows the spacecraft to compute its own absolute position. 240 For spacecraft operating in near-vicinity to one another, linear approximations to their relative equations of motions can provide additional simplifications to this relative navigation proces. The Clohesy-Wiltshire-Hil equations describe this motion betwen two orbiting vehicles when their distance apart is smal and they have similar orbit parameters [41]. Using these linear equations in addition to the simultaneous range measurements from the two vehicles can benefit the relative navigation methods. Figure 6-14. Position of remote spacecraft relative to base station spacecraft. 6.5.1 Vehicle Attitude Determination An interesting potential application of relative position determination is the calculation of the position of two pulsar detectors afixed to the same spacecraft. Determining the position of one detector relative to another on the vehicle could alow an alternative method of determining the atitude, or orientation, of the vehicle. A significant advantage of this method is that no integer cycle ambiguity resolution is required, since even the fastest pulsar period is much larger than any previously developed spacecraft (pulse period = 0.00156 s => 467 km), thus the detectors are always within a cycle of each other. Additionaly, the separation betwen the two detectors can be determined 241 when instaled on the vehicle, reducing the unknown relative position in the above ambiguity resolution proceses. Once the phase diference can be determined for the same pulse at each detector, only the angle, ! , along the line-of-sight to the pulsar needs to be determined. Similar to Figure 6-9, Figure 6-15 ilustrates the orientation of the baseline, L AB , betwen two detectors, detectors A and B, mounted on the same spacecraft relative to the incoming pulse planes from a pulsar. The angle is related to the phase diference and the baseline length as, n! () = "# i L AB (6.81) The baseline betwen the two detectors and the eror in determining the relative position determines the potential acuracy of such an atitude system. Asuming the pulse time of arival can be determined to within 1 ns for each detector, then atitude acuracy of 0.5? requires a baseline length of 33 m. Future spacecraft, such as solar sails, may be able to acommodate detectors spaced this far apart. Figure 6-15. Orientation of two detectors on spacecraft relative to pulsar. Unlike GPS and GLONAS, it is dificult to track the carier signal of pulsars. This may be possible at the radio wavelengths, but would be complicated at the visible and X- 242 ray wavelengths since only individual photons are detected. Thus, this atitude determination would only be computed occasionaly when TOA measurements are produced. Blending this data with other onboard atitude sensors, such as gyros, could enhance a spacecraft?s navigation performance. 6.6 Solution Acuracy Upon the computation of a position solution, providing an estimate of its acuracy is important for many operations. This acuracy estimate provides a measure of how close the solution is with regards to the true solution. The Floating-Point Kalman Filter and Search Space Aray methods provide acuracy estimates as part of their procesing. Several additional methods determining position acuracy estimates are discused in this section. These concepts alow an asesment of the quality of the computations. 6.6.1 Position Covariance The covariance of position (the cov function for short) uses the expectation operator, E , as ovaincon ) =ovon ( =E!x" T () (6.82) The relationship of position to the measured range to each pulsar is from Eq. (6.26) as, !" i =# i $ ? n i %!x (6.83) Creating a vector of these measurements from j pulsars, Eq. (6.83) becomes, 243 !"= ? n 1 2 # # ? n j $ % & & ' ( ) ) xH! (6.84) A word of caution, the symbol !" is used here to represent a vector of range measurements, not to become confused with the range diference vector, !" , of Eq. (6.24). Using the pseudo-inverse of the line-of-sight measurement matrix, H , the covariance of position with respect to the range measurements is, covon () =E!x" T () H T () #1 {} E!$ " T % & ' ( H () #1 T {} (6.85) With the relationship betwen the range measurement and the phase measurement as listed in Eq. (6.35), the position covariance can also be expresed from the phase measurement expectations as, ovposon () =H T () !1 T {} E"# ! % T & ' ( ) H () !1 T {} (6.86) where !"# is the vector of phase measurements and their cycle wavelengths. Unlike the GPS system, which asumes the same variance for each range measurement from al the similar satelites, each pulsar is asumed to have specific diference acuracy for its measurement. Hence, each measurement wil have a unique variance. This is primarily due to the unique pulse cycle length and timing model for each pulsar. However, these measurements are asumed to be uncorrelated, with zero mean, 244 such that E!" i # j $ % & ' =0;i(j , or E! i "#$ j % & ' ( =0;i)j . Thus the expectations matrix for the range measurements can be expresed as the diagonal matrix, E!"# T $ % & ' = ( " 1 2 0##0 2 ### ##0 0#( " k 2 $ % ) ) & ' * * (6.87) Similarly, the expectations matrix for phase can be represented as, E!"#$ T % & ' ( = ! 1 2 ) # 0$$0 2 $$$ $ $0 $! j 2 ) # k % & * * ' ( + + (6.88) The values of each variance would be created based upon the acuracy of the measured pulsar pulse arival time. It may also be related to the cycle period and the pulse width. It is expected that each pulsar would typicaly have a unique variance. However, if a system were created such that the variance was the same value for each measurement, then the position covariance would be simplified to either, covpositon () =H T () !1 T {} E"# ! $ T % & ' ( H () !1 T {} # 2 (6.89) or, in terms of phase, covpositon () =H T () !1 T {} E"# ! % T & ' ( ) H () !1 T {} * $ 2 diag 1 2 ,..., j 2 ) !1 (6.90) 245 This simplification relies on the symmetric matrix identity of H T () !1 = T () !1 {} . It is more than likely this asumption of the same acuracy of range measurement for each pulsar is not valid. Pulsars are very unique; no two emit the same signal. Thus, it is expected that specific variances for each range must be considered as in Eq. (6.87) and as phase in Eq. (6.88). 6.6.1.1 Including Spacecraft Clock Eror If spacecraft clock eror, !t SC , is also considered as an eror that is observable from the pulsar range measurements, then this eror can be included in the state vector. The equation for range measurements can be modified for this additional eror as, !"= ? n 1 2 # # ? n j 1 $ % & & ' ( ) ) x c*t s =H'! (6.91) In this equation, H' is the modified measurement matrix, and !x' is new state vector that includes both spacecraft position and spacecraft clock eror. From the eror equations discussed in the Measurement Diferences section, any erors could be included in the state vector, as long the correct modifications to the measurement matrix are implemented and these erors are observable. The analysis for position covariance described above can be implemented using this new model equation of Eq. (6.91). Alternatively, phase measurements could be utilized instead of range measurements, as presented in previous discussions. 246 6.6.2 Geometric Dilution of Precision The Geometric Dilution of Precision (GDOP) is an expresion of the acuracy of the estimated position [156]. GDOP is based upon the covariance matrix of the estimated erors of the position solution. This parameter is often used in GPS position acuracy estimates, and some of the algorithms used for GPS apply to pulsars, although modifications shown above for the position covariance are required. In the GPS system, the range acuracy from each GPS satelite is often asumed constant, thus the range covariance matrix reduces to a constant value multiplied by an identity matrix. The GPS- specific GDOP can then be represented as a scalar quantity. For a pulsar-based system, range measurements to each pulsars are most likely unique to each pulsar, thus the simplification in GPS cannot be realized within a pulsar-based system. Nonetheles, the position acuracy can stil be estimated using the computed variance. The pulsar-based navigation system GDOP is then no longer a scalar value, but rather a direct estimate of position acuracy. The position covariance matrix of Eq. (6.89) or (6.90) are 3x3 matrices, since the state vector is composed of position. This covariance matrix can be represented as, covpositon () =E!x" T () C= # x 2 yx # z y zxzyz 2 $ % & ' ( ) (6.92) The GDOP can be computed from the trace of this matrix. With this representation, a GDOP from a pulsar-based system has units of position, not a simple scalar unitles quantity as in GPS, and is represented as, SR =acC () ! x 2 + yz 2 (6.93) 247 If the eror state covariance matrix is developed to include spacecraft clock eror, as shown in Eq. (6.91), then the covariance matrix is represented as, covpositon () =E!x'" T () =C' # x 2 yx # zxt y y zxzyz 2 zt ttt $ % & ' ( ) (6.94) The GDOP for this system is again based upon the trace of the covariance matrix, but this now includes the variance due to clock eror, GDOP SR =traceC' () ! x 2 + yz 2 t (6.95) The position dilution of precision (PDOP) can be determined from this system by considering only the position related states as, P SR =traceC 3x ' =! x 2 + yz 2 (6.96) The time dilution of precision (TDOP) is directly computed by the time variance in this matrix and also has units of position, T PSR = t (6.97) The measured GDOP provides a description of how wel the set of chosen pulsars wil compute an acurate thre-dimensional position, based upon the covariance matrix of the estimated position erors. If pulsars are chosen from only one portion of the sky, the measurement matrix wil skew the observations towards this direction and wil not produce a good thre-dimensional solution. If pulsars are chosen that are distributed correctly in the sky, then no prefered direction wil be skewed by the measurement matrix and a good thre-dimensional solution wil result. Lower values of GDOP indicate more favorable pulsar distribution. Thus various sets of pulsars can be chosen and their 248 asociated GDOP wil determine which is the more appropriate set for procesing. This GDOP value may prove very useful when choosing pulsars for the Batch resolution proces, since a good distribution of pulsars improves this solution. 6.6.2.1 Example GDOP Values Using the unit direction for position and range measurement acuracy from the Table 3.5 and Table 3.6, after 1000 seconds of observation, the GDOP for the top ten RPSRs and top ten APSRs is 9.22 km for a 1-m 2 detector. Using the top four of each RPSRs and APSRs the GDOP reduces to 1.04 km for this size detector. If only the four pulsars PSR B0531+21, PSR B1937+21, PSR B1617-155, and PSR B1758-250 are considered due to their good geometrical distribution and range variance, the GDOP improves to 0.37 km for 1-m 2 . If the observation time is increased to 5000 seconds for these four pulsars, the GDOP further improves to 0.17 km for a 1-m 2 detector. If the thre top RPSRs of PSR B0531+21, PSR B1821-24, and PSR B1937+21 are utilized, the GDOP for a 500 s observation is 2.0 km and for a 1000 s observation is 1.4 km. Since the value of A!"t obs is constant throughout the SNR expresions of Chapter 3, system design tradeoffs can be considered for detector area versus observation time. For example, the SNR produces the same range variance, and consequently the same GDOP, for a 1-m 2 detector observing for 5000 seconds as a 5-m 2 detector observing for 1000 seconds. However, other mitigating factors, such as power usage, may need to be considered in this type of study. Most of the RPSRs in Table 3.5 al lie in the lower latitudes of the Galactic sphere. Sources above the Galactic equator may be considered for improved geometrical distribution. 249 6.7 Numerical Simulation In order to test the methods presented above for determination of absolute position of a spacecraft, a simulation of the algorithms has been developed. A description of this simulation and results of several test cases are presented. The current implementation of the simulation concentrates on determining the position of vehicles orbiting Earth. However, the simulation is also designed for relative position determination betwen two vehicles and for position determination of spacecraft orbiting diferent bodies. 6.7.1 Simulation Description To study the performance of the absolute position determination methods, the simulation was developed to compute position of vehicles near-Earth. The geocenter was chosen as the reference location, instead of the SB. The choice was made primarily to reduce the size of the search space, since the distance betwen Earth and the spacecraft is much smaler than the distance betwen the SB and the spacecraft and therefore fewer cycle candidates. The intent of the simulation is to determine the unknown integer pulse cycles of the total phase diference from each source betwen the geocenter reference location and the true location of the spacecraft. A search space is created to identify candidate sets of integer cycles that would produce the most likely position of the spacecraft based upon the measured fractional pulse phase diferences betwen geocenter and the spacecraft. The simulation creates a geometrical search space using a reasonable distance from Earth for a specific spacecraft. The search space is in the form of a spherical shel and is centered about the geocenter. The bounds of the shels are defined by a minimum radius, 250 such as the radius of Earth, and a maximum radius, such as several times the expected orbit radius of the vehicle. Only sets of candidate integer cycles that compute position within these bounds are considered aceptable and procesed within the simulation. Since each candidate set within the search space must be investigated, the procesing time becomes significant with a large number of sets. Any technique that can initialy remove incorrect candidates reduces the procesing time, however these techniques must asure that the correct solution set is not discarded. A set of ten variable sources was selected using their geometrical distribution, availability, and range measurement acuracy as reported in Chapter 3. These sources and some of their characteristics are listed in Table 6-2. It was asumed that each source could be observed simultaneously for duration of 1000 s. This asumption would require multiple detectors acting in unison to produce pulse phase measurements from each source at the same time. Otherwise, a separate scheme must be chosen to align the phase measurements to the same epoch and spacecraft position. Since position is unknown to the vehicle procesing, a source?s pulse arival time was computed asuming the detector was located at the geocenter. However, as shown in Section 6.2.3, since the vehicle?s detector is not actualy located at the geocenter, but rather at its true location, the detector wil measure a pulse TOA that is likely diferent in phase from the predicted TOA of a pulse-timing model located at the geocenter. The true phase diference is in terms of both fractional phase cycle and an integer number of cycles, although since the number of cycles is unknown, only the fractional phase portion of the diference can be measured. 251 Table 6-2. Sources Used By Absolute Position Simulation. Source Name Period (s) Cycle Wavelength (km) ! RANGE after 100 s (km) PSR B0531+21 0.0340 1013.1 0.078 PSR B1937+21 0.0156 467.7 0.247 PSR J0218+4232 0.0232 695.5 9.812 B1636-536 0.0345 1034.3 0.216 B1758-250 0.0303 908.4 0.080 PSR B1821?24 0.0305 914.4 0.23 B1820-303 0.0363 108.2 0.214 PSR B1823?13 0.10145 30413.9 6.708 PSR J124-5916 0.13531 40564.9 1.81 PSR B1509?58 0.15023 45037.8 1.294 To simulate the measurement eror within a phase measurement, the magnitude of the contribution of betwen 5% and 10% of fractional phase plus the range measurement acuracy from Table 6-2 divided by cycle wavelength is determined. For each source?s observation, the total eror is multiplied by a normalized random number. This span of eror was selected based upon the Crab Pulsar observation by the USA experiment discussed in section 6.2.3 and Appendix C, where the geocenter is the asumed position. Within the simulation, this measurement eror was added to the true phase value for each source, and was provided to the position determination algorithm for procesing. There are two main procesing loops within the simulation that implements a combined order system. A phase double diference loop and a phase single diference loop are used. Within the double diference loop, the first four sources from Table 6-2 (the shaded rows) are used along with each combination of their integer cycle candidates in the defined search space to compute a position offset from the geocenter as in Eq. (6.54). The sources were selected due to their short cycle wavelengths and their good GDOPs. The computed position from this set of four sources is verified to exist within 252 the search space. This position is then used to compute a residual as in Eq. (6.78) for each of the six remaining sources from the table. The magnitude of this residual is compared to a test statistic threshold value. The set of candidate cycles that pas the residual threshold test are recorded and pased to the single diference loop. The second loop within the simulation computes a position based upon the phase measurements and al the search space candidates that pased the double diference residual test. This new position is first verified to exist within the defined search space. Those positions that pas the search space geometry test are then used along with their phase measurements and candidate cycles to compute a single diference residual vector for al ten sources. Those candidate sets that pas a single diference threshold residual test are recorded. For many runs of the simulation, the set of cycles that computes the smalest single diference residual is the set that computes the correct spacecraft position. For some cases, there are several single diferenced candidate sets that compute residuals that are smaler than the candidate set of the true solution. This is due to the amount of phase eror measured by the system. For some candidate sets, large phase erors can create solutions that although having smal residuals their position solutions are incorrect. In these situations, additional tests must be pursued to determine which solution is the correct one. Otherwise, another complete observation and procesing of the algorithm can be pursued. The new data should expose those incorrect solution sets and help identify the correct solution from both observations. Although geocentric operations are demonstrated here, it is projected that the simulation would work equaly wel for selenocentric, Mars-centered, or other planetary body-centered orbiting spacecraft. The position information of that planetary body is 253 required for correct operation in these instances. For interplanetary misions, where typicaly only SB-centered simulations could be pursued, additional inteligence of the spacecraft?s trajectory must be gathered to asist in reducing the size of the search space. Alternatively, longer cycle wavelength sources could be utilized within the scheme to reduce the number of candidate cycles that could exist over these long distances. 6.7.2 Simulation Results Several test cases have been investigated using this simulation. Presented below are simulations of the absolute position determination of spacecraft in the ARGOS, GPS, and geosynchronous orbits. Each case has a specificaly defined search space. The dimensions of each search space are provided in Table 6-3. For the ARGOS and GPS orbit, spherical shels are created for the search space, since these spacecraft could be anywhere within this thre-dimensional region. For the geosynchronous orbit, the DirecTV 2 spacecraft was chosen to represent satelites in this orbit. Within this geosynchronous orbit, the spherical shel search spaces are truncated along the z-axis, since these vehicles would most likely remain close to the equator. This table also presents the selected threshold values for the double diference and single diference residual tests used in the simulation. Orbit data of each spacecraft?s orbit is provided by the NORAD Two-Line Element (TLE) sets [83, 97]. Appendix C provides a listing of these sets for each vehicle. The chosen epoch that defines the position of the vehicle within its orbit is provided in Table 6-3. Table 6-4 presents example simulation results for determining the correct set of cycle candidates within the ARGOS spacecraft orbit. With 5% of phase measurement eror and using the ARGOS orbit radius of 7218 km, there are initialy 245125 candidates that are 254 investigated. Of these candidates, only 44966 sets remain within the defined search space shel. Using the threshold value from Table 6-3, only 30 candidates remain after the double diference residual test. Using the al sources to define the single diference position solution, only 19 candidates remain within the search space region. After the single diferenced residual test only 4 candidates remain. Of these four candidates, the set with the smalest value from the single diference residual test is the correct solution. With 10% of phase measurement eror similar reduction in candidate sets are evident. However, four potential candidate sets have a single diference residual that is smaler than the set that computes the true position solution. These five sets would need to be monitored or re-evaluated to determine which one is the correct solution. Table 6-3. Simulated Orbit Search Space And Threshold Data. Spacecraft Orbit Epoch (JD) Search Space (km) Double Diference Residual Threshold Single Diferenced Residual Threshold ARGOS 2451538.96769260 R min = R Earth R max = 1320 5% Phs Er: 0.20 10% Phs Er: 0.25 5% Phs Er: 0.20 10% Phs Er: 0.25 GPS BIA-16 PRN-01 245345.82034930 R min = 2025 R max = 3375 5% Phs Er: 0.20 10% Phs Er: 0.20 5% Phs Er: 0.20 10% Phs Er: 0.25 DirecTV 2 (DBS 2) 245372.62423230 R min = 3150 R max = 5250 z max = ?100 5% Phs Er: 0.20 10% Phs Er: 0.25 5% Phs Er: 0.20 10% Phs Er: 0.25 Due to the 5% of phase measurement eror and the phase measurement acuracy, the correct set of pulse candidates produce a position solution that has a magnitude of 118 km of eror with respect to the true position. Although at first this may appear to be a large position eror, since the vehicle was initialy asumed to exist at the center of Earth at the start of this proces, the eror in position has been significantly improved. To improve the position solution even further, several options could be pursued. Using the new estimated position, the simulation could re-run. This new position would improve 255 the acuracy of the pulse time transfer to the SB, and consequently would reduce the pulse phase measurement eror for each source. With reduced phase measurement eror, and selecting sources with short cycle wavelengths and best GDOPs, the updated position estimate should have reduced eror. Methods such as this iterative proces refine the estimated position solution. Techniques such as this could also be used to investigate the remaining five candidate sets for the 10% phase measurement eror case. Table 6-4. Example Simulation Results For ARGOS Spacecraft. Integer Cycle Candidate Set Characteristics 5% Phase Measurement Eror 10% Phase Measurement Eror # Initial Total Candidates 245125 245125 # Found Within Search Space Shel 496 4974 # Pas Double Diference Residual Test 30 90 # Found Within Search Space Shel 19 60 # Pas Single Diference Residual Test 4 12 # Candidates with Single Diference Residual Les than True Candidate Set 0 4 Magnitude of Position Eror for Corect Candidate Set (km) 18 235 Table 6-5 presents the simulation results for the GPS orbit. Since the search space region is much larger than in the ARGO orbit case, there are many more initial candidate sets that must be investigated. However, this large number of candidates is quickly reduced when tested to exist within the search space region and tested against the double diference residual threshold. For this specific run, with the 5% phase eror the correct solution is identified with the smalest single diference residual. For the 10% phase eror case, although al ten remaining candidates other than the true solution have residuals les than the true set, only two other solutions compute an orbit radius within 500 km of the true GPS orbit. Table 6-6 presents the simulation results for the DirecTV 2 orbit. There 256 are a significant number of potential candidates at the start of the simulation, however, only a few percent of these exist within the search space shel. For the 10% phase eror case, although 14 candidates remain after the single diference case, only one other candidate than the true candidate set has an orbit radius within 500 km of the actual radius. Table 6-5. Example Simulation Results For GPS Spacecraft. Integer Cycle Candidate Set Characteristics 5% Phase Measurement Eror 10% Phase Measurement Eror # Initial Total Candidates 3429153 3429153 # Found Within Search Space Shel 758025 757894 # Pas Double Diference Residual Test 40 475 # Found Within Search Space Shel 290 343 # Pas Single Diference Residual Test 10 1 # Candidates with Single Diference Residual Les than True Candidate Set 0 10 Magnitude of Position Eror for Corect Candidate Set (km) 158 313 Table 6-6. Example Simulation Results For DirecTV 2 Spacecraft. Integer Cycle Candidate Set Characteristics 5% Phase Measurement Eror 10% Phase Measurement Eror # Initial Total Candidates 2032619 2032619 # Found Within Search Space Shel 184081 183802 # Pas Double Diference Residual Test 407 126 # Found Within Search Space Shel 182 507 # Pas Single Diference Residual Test 1 34 # Candidates with Single Diference Residual Les than True Candidate Set 0 14 Magnitude of Position Eror for Corect Candidate Set (km) 176 352 The algorithms and results presented in this chapter demonstrate the potential of using diferenced phase measurements to compute spacecraft absolute position. By determining 257 the correct phase cycle set for the observed pulses from a set of pulsars, the range estimates betwen a reference location and the spacecraft can be computed for each observation. The several techniques discussed select the correct cycle set from a group of candidate sets. Combining the range estimates and the line-of-sight direction to each pulsar provides an approach to determine the ful thre-dimensional absolute position within an inertial coordinate system. The acuracy of the position solution depends on the eror of each phase measurement. As the simulation results show, choosing a search space origin close to the estimated position reduces the number of candidates that must be investigated, and may also help reduce the amount of phase measurement eror. The set of sources chosen for this simulation were primarily selected based upon their geometrical distribution and range measurement acuracy. Other sources could also be selected to either include additional measurements within the procesing or replace any of those sources that do not achieve their predicted performance. Future investigations of the simulation would choose alternative sets of sources to analyze their absolute position determination performance. For various applications, the position solution produced by this method may be sufficient for the vehicle to complete its mision. For those applications that require additional acuracy, this method can be used in an iterative proces to yield improved solutions. Once the initial correct cycle set is determined, the proces of creating pulse profiles from photons and determining the pulse arival times could be recomputed using the new position solution. This would reduce the phase measurement erors further and would produce improved range estimates. These new range estimates would consequently produce a position solution with greater acuracy. Iterative proceses such 258 as these would help produce solutions with sufficient acuracy for most applications. Alternatively, the solution produced by this absolute position determination proces could be utilized as the initial conditions for a numerical orbit propagation routine, which could then be corrected over time using the concepts that are presented in Chapters 7 and 8. Determining absolute position with no a priori information using the signals emited by these variable celestial sources wil prove to be a significant resource for future spacecraft navigation systems. As new detector systems are developed that can view multiple sources at once, the results demonstrated show that this technique would benefit a wide variety of spacecraft operations. 259 Chapter 7 Delta-Corection of Position Estimate ?An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem.? ? John Tukey Determining absolute position with no prior knowledge of vehicle position or velocity information is useful for many situations. However, navigation can often be interpreted as the proces of improving an estimate of the current state information of a vehicle. If an estimate is sufficiently acurate and provides enough information to safely guide and control the vehicle, then the navigation system?s role is to maintain this acuracy, or continualy improve the solution over time. This Chapter describes the methods used to improve an estimate of the position and velocity state information using the measured pulse arival times from variable celestial sources. 7.1 Concept Description 7.1.1 Estimated Position Given a navigation solution of time, position, and velocity, a spacecraft can predict this state information using its known dynamics through the proces of onboard orbit 260 propagation. External forces acting on the spacecraft, such as gravity, atmospheric drag, and solar presure, as wel as thrusting forces due to the vehicle?s own engines, can be used as models to propagate the state dynamics. If these force and perturbation models are sufficiently acurate, forward propagation of the state dynamics can correctly predict the navigation state of the vehicle at a future time. However, smal model erors or unmodeled disturbances can significantly afect the state prediction. Higher order gravitational potential, fluctuating drag, and varying solar radiation presure efects that are not acounted for in the dynamics models can alter the known state of the vehicle such that large prediction erors can result. Especialy with the periodic nature of spacecraft orbits, any incorrectly modeled efects can cause erors to grow without bounds, such that predicted orbits wil not match the true orbit of the vehicle. Variable celestial sources provide the necesary signal to create updates to the estimates of onboard navigation solutions. Since these sources are significantly distant from the solar system, they provide signal coverage for much greater regions than the near-Earth designed systems of GPS and GLONAS. The procesing concepts rely on measuring of pulse time arivals from the sources and comparing the measured times to the predicted arival times from pulse timing models. Although this comparison proces is similar to those completed in the algorithms of Chapter 6 for absolute position determination, in this concept reasonable estimates of position and velocity are utilized within the procesing algorithms and updates to these estimates are generated. This method of creating an update to an estimated navigation solution is refered to as the delta-correction method, as the product of this method is a delta, or smal ofset, 261 correction to an estimated solution. Some authors refer to this technique as a diferential- correction method [16, 17, 55, 160, 213]. However, due to the current popularity of diferential corrections for GPS systems [156], it was chosen to avoid the confusion betwen these disimilar concepts. In diferential GPS, it is asumed a receiver and its antenna are located at some known location and GPS satelite and atmospheric corrections are broadcast from this receiver to local users. In the delta-correction variable celestial source method only algorithmic models are provided at a known location and stored within the spacecraft?s database. There is no detector located at the model?s location that broadcasts its model information. However, refering to this described method as a diferential correction from pulsars concept is not entirely incorrect. 7.1.2 Algorithms Pulsar signals received at a spacecraft are offset from those ariving at the SB primarily by the distance betwen the SB and the spacecraft. If acurate detector position is known, then the time offset of the ariving pulses betwen the detector and the SB can be calculated. Conversely, if acurate time is known such that pulses are acurately measured at the detector, then the position offset of the detector and the SB can be computed by comparing the pulse measurement with that predicted by the pulsar- timing model. The pulse timing models defined in Chapter 3 predict the arival of individual pulses at the SB. As it moves away from the SB, a spacecraft sensor wil detect a pulse at a time relative to the predicted arival time based upon the pulse-timing model. A direct comparison of the arival time at the spacecraft to the same pulse?s arival time at the SB is acomplished using the time transfer equations of Chapter 4. These equations 262 require acurate knowledge of the spacecraft?s position and velocity in order to be implemented correctly. If, however, the spacecraft position is in eror by some amount, using the time transfer equations to transform the detected pulse time from the spacecraft to the SB wil result in some offset in the comparison of pulse arival times. If the spacecraft position is not known whatsoever, then the time transfer equations cannot be utilized. Pulses can stil be detected and timed at the spacecraft?s detector, but timing can only be made relative to the spacecraft itself. In the delta-correction scheme, estimated values of spacecraft position and velocity are utilized within the time transfer equation to create the best estimates of pulse arival times at the SB. The estimated values can come from a variety of potential methods. Other external navigation sensors onboard the spacecraft could provide these estimates, Sensors such as GPS or GLONAS could directly provide periodic position and velocity values when those system?s satelites are visible to the spacecraft?s receiving antenna. Star camera and trackers could also be utilized to provide estimated position values. Data telemetry from ground stations using the DSN could also provide position and velocity estimates. Any complementing external method that provides estimated values could be used within this scheme. However, additional spacecraft operations autonomy is provided if a high fidelity onboard orbit propagator is implemented within the vehicle?s navigation system in order to provide a continuous estimate of the vehicle?s dynamics during a pulsar observation. The implementation of onboard orbit propagators wil be presented in more detail in Chapter 8. Using an approximate set of starting values for position and velocity, orbit 263 propagators can provide the necesary information to transfer spacecraft pulse time of arival to the SB. From an estimated position, !r , the detected pulse arival times at the spacecraft are transfered to the SB origin via the time transfer equations. A range comparison along the line-of-sight to the pulsar is created by diferencing the measured arival time to the predicted arival time from the pulse-timing model. The discrepancy in these values provides a contribution to the estimate of the offset position, !r , betwen the true position of the vehicle and the estimated position. Refering to Figure 7-1, the eror in position wil relate to the computed time offset of a pulse along the line-of-sight to the pulsar. Using pulsars at diferent locations provides line-of-sight measurements in each pulsar?s direction. Combining measurements from diferent pulsars solves for the full position offset in thre dimensions. The following sections provide details on methods to compute the range diferences for varying degres of complexity in the time transfer equations. Figure 7-1. Estimated position eror relative to the signal received from two pulsars. 264 7.1.2.1 First Order Measurement The position eror, or offset, !r , can be defined as the diference of true and estimated position as, ="! (7.1) The eror in spacecraft observation time of the pulse is the diference betwen the true and estimated arival time at the spacecraft and can be represented as, !t SC =" ! t SC (7.2) The eror in the pulse arival time at the SB is the diference betwen the true and estimated arival times, and can be represented as, !t SSB =" ! t SSB (7.3) The pulse TOA measured at the spacecraft, SC , can be transfered to its arival time at the SB, t SSB . To first order from Chapter 4, this transfer has been shown to be the following for the i th pulsar, SSB =t SC + ? !r (7.4) Eq. (7.4) asumes perfect TOA measurement at the spacecraft, as wel as absolute knowledge of the direction to the pulsar and the spacecraft position. If position is only an estimated value, and potentialy some uncertainty in the spacecraft measured TOA, then this equation becomes an estimated value as, ! t SSB = SC + ? n i !r c (7.5) The true pulse TOA at its arival at the SB can be predicted via the pulse-timing model. Using SSB to represent the true predicted TOA at the SB, then the two representations of TOA from the model and TOA from the spacecraft measurement in 265 Eqs. (7.4) and (7.5), respectively, can be diferenced to produce the offset in TOA arival. Using Eqs. (7.3) through (7.5) this offset is expresed as, !t SSB =" ! t SSBSC + ? n i #r c $ % & ' ( ) " ! t SC + ? n i #r c $ % & ' ( ) (7.6) From the eror expresions for position and spacecraft observation TOA of Eqs. (7.1) and (7.2) respectively, the eror in position can be expresed as a function of SB pulse TOA offset and spacecraft observation eror as, c!t SSB "t SC = ? n i #!r (7.7) Asuming there is no measurable eror within the spacecraft?s direct observation of the photons used to create the pulse profile then t SC can be asumed negligible. Thus, any determined diference betwen he predicted TOA from the timing model and the measured pulse TOA can be expresed as range offset of the spacecraft along the unit direction to the pulsar, or, c!t SSB = ? n i "r (7.8) This is the fundamental observable within the delta-correction scheme. This equation is used to correct the estimated position of the spacecraft due to the observed measured pulse TOA. 7.1.2.1.1 Position Ofset Relative to Earth The position offset computed above pertains to the position relative to the inertial location of the defined pulse model, typicaly taken as the SB origin. Most operational spacecraft utilize position relative to Earth in thei navigation systems. The time transfer expresion from Eq. (7.4) can be expresed in terms of Earth position and the spacecraft relative position to Earth as, 266 t SSB ! SC = ? n i "r c i " E +r SC/ () (7.9) Using the estimated value of this relative position, !r SC/E , the eror in this value, !r SC/E , is related to the true value as, r SC/E =! / +r SC/E (7.10) The eror expresion of Eq. (7.7) can be expanded using Eqs. (7.9) and (7.10) such that, c!t SSB "t SC ? n i #r E ? i #! SC/E (7.11) The known Earth position could be provided by standard ephemeris tables (ex. JPL ephemeris data). If planetary ephemeris data is asumed without eror, such that !r E =0 , then !r= SC/E , and Eq. (7.11) reverts to Eq. (7.7). 7.1.2.1.2 Simple One-Dimensional Example Figure 12 ilustrates how delta-correction scheme is visualized along a one- dimensional pulse train from a pulsar. This simple example uses the first order terms of the pulse timing model and Eqs. (7.5), and (7.7) to demonstrate how a new estimate of position is computed based upon the predicted and actual arival times of a detected pulse. 267 Figure 7-2. One-dimensional position estimate eror example. Although the SB origin is used as the model location within these equations, the methods works equaly wel for any reference model location. Thus if pulse timing models were provided at the geocenter, then time transfer could be implemented betwen the spacecraft and the geocenter, and the delta-correction scheme could produce position offsets directly for the vehicle?s estimated position relative to Earth?s center. If the pulse model was defined at the location of another spacecraft, then this scheme could also produce the relative position offset betwen the two spacecrafts. 7.1.2.2 Higher Order Measurement The previous section presents methods to determine the eror in an estimate of position based upon the first order expresions of time transfer. However, as was discussed in Chapter 4, higher order relativistic terms should be included in order to acurately transfer time from a spacecraft to the SB. Although the previous section demonstrates the basic correction methods of this scheme, an actual navigation system 268 would need to use the full time transfer equations for high acuracy. Additional considerations for improving the acuracy of the delta-correction measurement include numbering the individual pulses received at the detector from a reference value to correctly identify pulses for comparison, and acounting for any modeling uncertainties and measurement noise within the entire system. A high acuracy time transfer equation betwen the spacecraft coordinate time and the SB coordinate time is provided in Chapter 4. Slight modification of this expresion by asuming the Sun is the primary gravitational efect in the Shapiro delay term produces the following time transfer equation, t SSB = SC + 1 c ? n!r" 2 D 0 + ? !r () 2 0 !V#t N 0 V#t N () ! 0 b! 0 + ? n! () r D 0 $ % & ' ( ) + 2? S c 3 ln ? !r b +1 (7.12) Using an estimated position and its eror from Eq. (7.1) this time transfer equation becomes, ct SSB ! SC () = ? n"!r+# () 1 D 0 2 ? n"!r+# () $ % & ' 21 !r# 2 Vt N ? n"(t N () ? "!r+ () $ % & ' b"! () b % ) * * 2? S c ln ? "r$& ' +#r 1 (7.13) The terms involving the position eror can be linearized such that, ? !+" () # $ % & 2 = ? ! () 2 + ? ! () n"+ ? ! () 2 (7.14) "2" (7.15) 269 ln ? !r+" () # $ % & !r b +1=ln ? !r b +1 ? !" r ! () nb () # $ ' % & ( +H.OT (7.16) In Eq. (7.16), the higher-order terms H.OT () are functions of !r () 2 and higher. Asuming second-order and higher terms are negligible in Eqs. (7.14)-(7.16), the linearized expresion of Eq. (7.13) becomes, ct SSB ! SC () ? n"!r ( 1 D 0 2 ? "!r () 1 2 +V#t N () ? n"t N () ? "!r ( b"! $ % & ' ( ) 2? S c ln ? "!r+ b 1 = ? n"*r+ 1 0 ? "! () *r" t N () " ? nt N () ? "*r b+" $ % & ' ) + 2? S c ? "*r+ ! " n () b () $ % & ' ( ) (7.17) The LHS of Eq. (7.17) can be further simplified by noting that the terms with estimated position produce the estimated arival time at the SB, ! t SSB . The diference betwen this estimated value and the predicted arival time is expresed as in Eq. (7.3). Including the potential eror in spacecraft timing, Eq. (7.17) can be writen as, c!t SSB " SC () = ? n#!r+ 1 D 0 ? #!r () n"!#r V$t N # ? t N () ? n#! ( b+# % & ' ( * 2? S c ? #r ! # () n () % & '* (7.18) It is noted that the RHS of Eq. (7.18) is a linear expresion with respect to the position offset, !r . This representation asumes a straightforward measurement from a 270 recognizable singular source. Additional complexity is added if binary pulsar observations are incorporated, and these extra terms must be added through the time transfer equations [28]. 7.1.2.2.1 Spacecraft Proper Time The coordinate time used for the spacecraft observation time in the above equations is composed of the spacecraft?s acurate clock time, or proper time, ! SC , and the standard corrections from this proper time to standard coordinate time. As discussed in Chapter 4, spacecraft clocks must also be corrected for their motion within the inertial frame. Using StdCorr E to represent the standard corrections for terestrial bound clocks, the coordinate time of spacecraft orbiting Earth can be represented as, SC =!+StdCor E 1 2 " SC/E () (7.19) For spacecraft using an estimated position, then the spacecraft?s position relative to Earth can be represented by this estimate and its eror as in Eq. (7.10). The coordinate time equation from Eq. (7.19) then becomes, t SC =!+StdCor E 1 2 v"! SC/E () + 1 2 v E "#r SC/ () (7.20) Utilizing estimated values for spacecraft proper time, this expresion can be rewriten as, !t SC ="+ 1 2 v E #!r SC/ () (7.21) Eq. (7.21) asumes no erors in the coordinate time standard corrections, or Earth ephemeris data; however, these erors could also be included if considered relevant. This equation could be added to Eq. (7.18) if spacecraft proper time is necesary to use in this expresion instead of spacecraft coordinate time. 271 7.1.2.3 Multiple Measurements The measurement equations presented in the previous sections provide estimates of range eror along the unit direction to an observed pulsar. If the full thre-dimensional position offset is desired, then measurements from multiple pulsars located in diferent directions must be blended together. Since Eq. (7.18) is a linear function of the offset position, it can be rewriten in vector form as, c!t SSB " SC () =A#!r (7.22) The vector A=!r, ? nD 0 V,b N ,? S () is composed of the terms from Eq. (7.18). This linear expresion in Eq. (7.22) can be asembled for k diferent pulsars to create a matrix of observations, c!t SSB " SC () 1 2 # # c!t SSB " SC () k $ % & & ' ( ) ) = A T 2 # # k T $ % & & !r (7.23) The LHS of Eq. (7.23) is computed using the models presented above. The diference in SB pulse arival times is computed using the predicted arival time from the pulse- timing model and the measured time computed using the estimated position to transfer the arival time at the spacecraft. The diference in spacecraft time is determined through any known erors in the spacecraft clock, proper time conversion, and photon timing. Eq. (7.23) can be solved directly through a batch method such at Least Squares, where the inverse of the A matrix multiplied by the time diferences computes the position offset. Repeating this measurement proces refines the position estimate over 272 time. However, creating these time diferences for multiple pulsars requires the observations to be detected simultaneously such that the same position eror is valid for al the observations. This requires detectors, or multiple detectors, that can track multiple pulsars. Although this type of system would be beneficial for navigation, many vehicles may only be able to acommodate one detector. With only one detector producing one measurement per pulsar, vehicle motion that is significant during the time span betwen the measurements must be addresed in an implementation of this delta-correction method for full thre-dimensional position offset determination. A Kalman filter that incorporates vehicle dynamics and a measurement model from Eq. (7.18) can be used to blend sequential observations with vehicle motion to succesfully update the estimate of vehicle position. Chapter 8 describes this type of implementation using an extended Kalman filter, along with providing examples of various orbits. 7.1.2.4 Expected Performance To ases the potential performance of a pulsar-based navigation system, it is necesary to understand the eror sources inherent to the system. If no erors in modeling or measurement are present, then Eq. (7.23) solves directly for acurate position offsets. However, erors do remain which limit the performance of this system. The magnitude of these erors must be considered when evaluating the determined position offset. Erors within each of the terms in this equation include the following; ? ! SSB : The SB time diference contains erors due to pulsar timing models and time transfer. ? SC : The spacecraft time diference contains system level timing erors and pulse signal timing erors. 273 ? A : The observation matrix contains erors in the approximations to the relativistic time transfer efects, as wel as pulsar position uncertainty and planetary ephemeris acuracy. A phase cycle ambiguity may stil be present in these equations if the estimate of position has large eror. The delta-correction scheme equations relate the fraction of a cycle to the diference in predicted and measured time. This method does not identify which specific cycle is being detected. It is important to have an initial estimate of the acuracy of the estimated position prior to using this scheme so that it can be determined if more than a fraction of phase cycle could exist. In deriving the observations used within the delta-correction method, the time equations were linearized with respect to position eror, clock eror, and pulsar timing eror. This linearization did not include al eror sources, namely erors in pulsar position and proper?motion. Adding pulsar position eror and considering only first order efects from Eq. (7.7), the position eror equation becomes, c!t SSB " SC () ! ? n i #r=! i # (7.24) Using only the first order terms is valid in this analysis since the remaining terms are several orders of magnitude smaler [note the division by either pulsar distance or multiples of speed of light in Eq. (7.18)]. Navigation system performance with respect to the SB can be established using Eq. (7.24) based upon projected estimates of eror sources. The second term of the LHS of Eq. (7.24) shows that if pulsar position is not determined to high acuracy, then this system?s performance degrades as distance increases away from the SB. For pulsars with poorly determined position, this eror growth due to distance is similar to those of 274 Earth-based radar range systems. Table 7-1 provides theoretical estimates of position performance using Eq. (7.24) for a pulsar-based navigation system centered at the SB origin using the delta-correction scheme. The Total Timing Eror column includes the sum of the SB diferenced pulse arival time erors, system clock erors and pulsar timing erors. The first and second rows of Table 7-1 represent the current technology from today?s sensors and measured pulsar positions and timing models. If the goal of this system were to provide meter-level position acuracy of spacecraft, pulsar position knowledge to les than 0.0001 arcseconds and pulse timing to les than 0.1 microseconds would be required for misions near Earth. If improvements can be made to current day values, the performance of the method could reach the levels of GPS performance for near-Earth applications, and any continued improvements would generate this type of performance for operations throughout the solar system. The expresion of Eq. (7.24) and values in Table 7-1 are appropriate for solar system misions. Inertial frames at the barycenter of other star systems, or the galactic center, would be appropriate for interstelar misions. However, the same performance degradation would exist as vehicles travel further from the frame?s origin. Table 7-1. Delta-Correction Method Performance Within Solar System. Detector Position Total Timing Eror (10 -6 s) Pulsar Position Eror (arcsec) Position Acuracy From SB 1 AU 10 0.01 < 10 km 1 AU 1 0.01 < 1 km 1 AU 0.1 0.001 < 0.1 km 10 AU 10 0.01 < 10 km 10 AU 1 0.001 < 1 km 10 AU 0.1 0.001 < 0.1 km 275 7.2 Experimental Validation of Method The preceding sections describe the delta-correction scheme for updating an estimate of a navigation system?s position solution. These finite corrections can be used to improve the overal navigation solution, and maintain a level of acuracy that can ensure mision suces. This section presents empirical data used to validate this concept, as wel as descriptions of the acuracy of the data and the position solution. 7.2.1 USA Experiment Description Most of the X-ray survey misions presented in Chapter 2 did not provide enhanced photon arival timing resolution as wel as precise spacecraft position and velocity information in order to thoroughly test the delta-correction method with actual data. However, the NRL USA experiment onboard the ARGOS spacecraft was partialy designed to investigate the use of pulsars for navigation. Thus the data it provides can be used to begin to investigate the capability of the delta-correction methods. The USA experiment was a collimated proportional counter telescope comprised of two detectors mounted on the aft section of the ARGOS vehicle [166, 229, 231, 232, 234, 235]. The experiment?s parameters are provided in Table 7-2. The ARGOS vehicle was thre-axis stabilized and nadir-pointing. The vehicle was placed in a sun synchronous, circular orbit of 840 km altitude. Although the experiment was comprised of two detectors, only one detector was used during a given observation. The experiment operated from May 1, 1999 through November 16, 2000, when its gas for the detector was depleted due to a leak, suspected to be produced by a micrometeorite strike. Figure 7-3 provides an image of the USA experiment, with its X-ray detector mounted on the ARGOS satelite. 276 Table 7-2. USA Experiment Parameters [72, 166, 232]. Two Detectors: 100 cm 2 each, efective area Field Of View: 1.2? x 1.2? (colimated) (FWHM) Mas: 245.2 kg Power: ~50 W Energy Range: 1 ? 15 keV Energy Resolution: 0.17 (1 keV @ 5.9 keV) Background Rejection: Five-sided cosmic ray veto Field Of Regard: 2? sr Two-Axis Gimbaled System: ~3.6?/min (track), ~20?/min (slew) Data Time Taging: 32 ?s timing resolution, GPS receiver provided time Figure 7-3. NRL's USA experiment onboard ARGOS spacecraft [Courtesy of NRL]. 7.2.2 USA Detector Crab Pulsar Observations The USA experiment?s detector was pointed to observe the Crab Pulsar for multiple observations during December 1999. Table 7-3 provides the Crab Pulsar ephemeris values used for this experiment as provided by the Jodrel Band Observatory, through X-ray Detectors USA Experiment ARGOS Main Bus 277 their monthly ephemeris updates [115]. The observation data were recorded, including time-tagged X-ray photon detection events and ARGOS satelite one-second navigation values. Using the Crab Pulsar pulse period, the recorded observation data were folded to produce an observed profile. Table 7-3. Crab Pulsar (PSR B0531+21) Ephemeris Data [115]. Parameter Value Right Ascension (J200) 05 h 34 m 31.972 s Declination (J200) 2?0'52.069" Galactic Longitude 184.575? Galactic Latitude -5.7843? Distance (kpc) 2.0 Frequency (Hz) 29.8467040932 Period (s) 0.035045369458 Frequency Derivative (Hz/s) -3.7461268?10 -10 Period Derivative (s/s) 4.205296?10 -13 Epoch of Ephemeris (MJD) 51527.0001373958 Prior to these specific observations, several separate observations of the Crab Pulsar were folded to produce a standard template profile with a high SNR. The observed profiles and the template profile were then compared as described in Chapter 3 to produce observation TOAs. The measured pulse TOA represents the arival time of the peak of the first pulse within the observation window. The eror in the TOA was also computed, and represents the uncertainty in aligning the observed and template profiles [204]. In the proces of computing the pulse TOA, an analysis tool was used to transfer the spacecraft?s recorded photon arival time to their arival time at the SB using an expresion similar to Eq. (7.12), expect the pulsar distance, D 0 , and proper-motion, V! N , as wel as the barycenter position, b , are ignored in this tool. Since the photon timing resolution was on the order of microseconds, interpolation of the 1 Hz navigation 278 data was used to produce spacecraft positions at each photon arival time. Thus, the computed TOA is the arival time at the SB of the measured pulse detected at the USA detector using the ARGOS navigation data to complete the time transfer. Computed offsets from estimated spacecraft position can now be derived from the diference betwen the predicted and measured pulse arival times. If the asumption is made that any time diference is based solely upon vehicle position offset in the direction of the pulsar, the eror in position can be deduced from this pulsar pulse comparison as in Eq. (7.18). The computed offset is the delta-correction for range along the unit direction to the Crab Pulsar. Table 7-4 provides a list of recorded observations; their corresponding position offset determination, and estimated acuracies. Position corrections of several kilometers along the line-of-sight to the Crab Pulsar are produced, with estimated acuracies on the order of two kilometers. Table 7-4. Computed Position Ofsets from Crab Pulsar Observations. Observation Date (Dec. 199) Duration (s) Observed Pulse Cycles TOA Diference (10 -6 s) TOA Estimated Eror (10 -6 s) Position Ofset (km) Estimated Ofset Eror (km) 21 st 46.7 1332 53.75 5.8 16.1 1.8 24 th 695.9 2070 -31.02 5.2 -9.3 1.6 26 th 421.7 12586 -37.16 6.3 -1.1 1.9 7.2.3 Delta-Position Truth Comparisons To ases the validity of the computed position offsets in Table 7-4, it is necesary to know the exact position of the ARGOS vehicle. This truth information can then be compared to the solutions created by correcting the estimated position of the navigation system. Unfortunately, a reference truth position of ARGOS was not available at the time of these 1999 observations. However, an external estimation of vehicle position was 279 studied during January 2000. This paralel study conducted by NRL using a ground-based navigation system concluded that the navigation system onboard ARGOS had erors betwen 5 and 15 km. It has been speculated that much of this position eror is due to erors within the navigation system software, as during the ARGOS mision it was determined that the spacecraft?s GPS receiver and clock were faulty. Correction solutions were required every four hours to update the spacecraft?s onboard orbit propagation algorithm. Further investigation is being conducted to determine why this navigation position eror existed. With these magnitudes of position eror discovered for January 2000, it is likely that they existed for the observations completed during late December 1999, which could acount for much of the position offset determined from the measured TOAs. Future studies are planned to simulate pulsar measurements and ARGOS orbit propagation, in order to help investigate the ARGOS navigation isues. Although the lack of absolute truth data does not alow direct evaluation of the measurements, basic asesments of the computed position offsets can be provided. The two main computations in this experiment include the position offset calculation and its estimated acuracy. Factors that limit the position offset calculation include pulsar timing model inacuracies, calibration erors in the USA experiment timing system, photon time binning of 32 ?s in the USA data collection mode, and pulsar position erors. The reported acuracy of the Crab Pulsar timing model parameters is 60 ?s for the month of December 1999 and is likely a large contributor to the measured position offset [115]. Although the USA experiment was designed to maintain a 32-?s photon bin timing acuracy, fractions of the bin size were used to improve the time resolution of ariving 280 photons. From the range measurement acuracies reported in Chapter 3, for a 0.1 m 2 detector, ! RANGE = 0.1 km for the Crab Pulsar after 500 seconds of observation. Although this ideal computation of position acuracy is a few times les than the calculated values in Table 7-4, several of the above mentioned isues likely contribute to the measured eror. Future studies on ARGOS navigation data wil also atempt to understand this discrepancy betwen theoretical acuracy and recorded data acuracy to determine whether system erors or pulsar model erors dominate. 281 Chapter 8 Recursive Estimation of Position and Velocity ?Big results require big ambitions.? ? Heraclitus A range measurement of a spacecraft relative to an inertial reference location can be computed based upon a pulse TOA from a single celestial source, as demonstrated in Chapter 7. However, the portion of range measured along the line-of-sight to the source does not compute full thre-dimensional position of the vehicle. Nonetheles, in a manner similar to orbit determination, which uses sequential measurements of range and/or range-rate by ground stations of a spacecraft to compute its orbit solution, the dynamics of the vehicle can be blended with the pulsar-based range measurements to alow an onboard navigation system to systematicaly compute a full position and velocity solution. The blending of spacecraft state dynamics and pulse range measurement has been implemented within a Kalman filter technique [65, 91]. This filter, refered to as the Navigation Kalman filter (NKF), recursively incorporates pulse TOA measurements with an estimate of the orbit state. These estimated states are based upon a numericaly propagated position and velocity solution [42, 55, 71, 93, 136, 190, 191, 195, 212, 213, 282 224]. A discussion is provided on the dynamics of the filter states, as wel as how the dynamics are used within the filter. Methods to implement various measurement models within the filter are also provided. A simulation of the NKF and pulsar-based TOA measurements is presented, along with performance results of spacecraft position determination using these techniques. Appendix D describes the fundamentals of procesing navigation information through the dynamics and observations within a Kalman filter, and should be refered to as a supplement to the descriptions within this chapter. 8.1 Kalman Filter Dynamics 8.1.1 Spacecraft Orbit Navigation States The specific dynamics of the NKF used to integrate pulsar-based range measurements along a spacecraft?s flight path is described in detail within this section [189, 191]. A spacecraft in orbit about a central body wil follow a stable, often predictable, path if left unperturbed from its motion. The dynamics of the spacecraft can be expresed in analytical form, which in turn can be used within the filter?s time propagation routines. 8.1.1.1 State Dynamics The states used by the NKF to describe the spacecraft dynamics are thre-dimensional inertial frame position and velocity. These primary states are the absolute values, or whole-values, of each parameter. The state vector, x , has six states, and is composed of the thre element position vector, = SC r x , yz {} , and the thre element velocity vector, v= SCx ,v yz {} . The states are represented in vector form as, 283 x= r v ! " # $ % & x y z x y z (8.1) In a general form, the dynamics of the state variables can be presented as !xt () = " ft () ,ut () +! () (8.2) In this equation, ! f is a function that describes the dynamics of each state in terms of the state vector, xt () , any control inputs, , and the noise asociated with the state dynamics, . The dynamics may be non-linear with respect to the states with this expresion. To determine the natural dynamics of a spacecraft, noise can be initialy ignored !t () "0 () and no control inputs are commanded ut () !0 () . With vehicle aceleration, a , being the time derivative of velocity and velocity, v , being the time derivative of position, the time derivative of the state vector from Eq. (8.1) is therefore represented as, !x= " ft () , !r v " # $ % & = a v x y z x y z ! " # # $ % & & (8.3) This may also be writen as, !rt () =v at () (8.4) 284 The dynamics of Eq. (8.3) represents a first-order system. From Newton?s second law of dynamics [150], the relationship betwen the vehicle?s dynamics and the external forces acting on the vehicle is the following, a= 1 m F ext! (8.5) where a is the aceleration of the vehicle, m is the mas of the vehicle, and F ext! is the sum of al external forces applied to the vehicle [this should not be confused with the Jacobian matrix Ft () for the eror-state dynamics later in this chapter and Appendix D]. Once an initial condition is known, such as, xt 0 () = 0 v ! " # $ % & (8.6) and the aceleration on the vehicle is determined from Eq. (8.5), the state dynamics of Eqs. (8.3) and (8.6) completely defines the motion of the spacecraft. If an analytical expresion for the integral of Eq. (8.3) can be determined, then the vehicle state can be directly computed for any future time, t . However, the full dynamics of a spacecraft is a complex expresion due to the multiple high order efects, and it is dificult to determine an acurate analytical solution. Thus, the dynamics of the spacecraft, along with its initial condition, are typicaly numericaly integrated in order to determine the vehicle?s state at some future time. The six translational state elements of position and velocity of a spacecraft expresed as Eq. (8.3) is one posible representation for the dynamics. An alternative method is the utilization of Keplerian elements that describe a specific orbit of a spacecraft [117]. An advantage of this representation is that except for the element of time the remaining five clasical Keplerian elements are nearly constant, and once determined to high acuracy 285 can define a vehicle?s orbit with high performance. However, a significant disadvantage of using these Keplerian elements as state variables is that these elements are only valid for one specific orbit. This may be useful for a spacecraft that is launched and placed in a set orbit, with no mision operations deviating from that orbit. However, if a spacecraft?s mision requires it to maneuver at some point, such as merely changing its location along the orbit track or possibly altering its entire orbit shape, the six inertial states of position and velocity are much more suitable for these types of mision operations. Also, if a vehicle does not operate along a definable Keplerian orbit, the position and velocity states are more appropriate for this motion. An example of this motion is a group of spacecraft flying in formation, where the leader is in a Keplerian orbit, but its followers must maintain non-Keplerian orbits to remain in the desired formation. To adequately represent a spacecraft?s orbit about a central body, the following aceleration efects are considered for the suceding analysis: central two-body aceleration efects; non-spherical gravitational potential efects from the central body; atmospheric drag efects if the spacecraft is close enough to the central body?s atmosphere; and any appreciable third-body gravitational potential efects. The total aceleration on a spacecraft is the sum of these efects as, total =! wobody + non!sphealdrag + third!bodyH.O (8.7) These contributing efects are presented in further detail below. In this equation, H.O represents al higher-order terms that may afect aceleration (such as solar radiation presure, albedo, Earth tidal, etc.) but are nominaly considered negligible compared to the remaining efects. 286 8.1.1.1.1 Two-Body The efect of the aceleration of a spacecraft about a central masive body, where the mas of the body is much greater than the spacecraft, m body ! SC , is the standard expresion of, a two!body = ? r 3 ! 2 ? (8.8) In this equation, ? is the gravitational parameter of the central body, where ?=Gm body and G is the universal gravitational constant. 8.1.1.1.2 Non-Spherical Gravitational Potential The gravitational aceleration of Eq. (8.8) asumes a uniformly spherical gravitational field emanating from the point-mas central body. Many planets, moons, as wel as the Sun, actualy do not have uniformly distributed material within their body?s spheres. Thus, the true gravitational field is not spherical for these objects. Additional terms must be added to the simple two-body spherical approximation in order to more acurately represent these gravity fields. These terms often are presented as Legendre polynomials whose coeficients define the spherical harmonics of the field, whose degre and order define the resolution of the field. These polynomials can be categorized as zonal terms (only terms paralel to a body?s equator, and reflect a body?s oblatenes), sectorial terms (for lumps of mas distributed in a body?s longitudinal direction), and teseral terms (for mas lumps distributed in various sections of the body?s sphere) [213]. These non- spherical gravity efects on a body are a function of the spacecraft?s position within the field, and can be represented as, non!sphe =gNon-sphel grvity, ) (8.9) 287 The specific non-spherical gravity model used in the NKF for Earth-orbiting spacecraft uses the J 2 through J 6 zonal terms of Earth?s gravity. Although many higher- order harmonic representations exist for Earth, this simple zonal model has been shown to be sufficient for most of the NKF?s analysis. These gravitational potential terms only depend on the z-axis position, which does not require the computation to be afected by the rotation of Earth fixed axes relative to inertial axes. Using sind=r z and the radius of Earth, R E , the aceleration can be represented as the following, [55, 213, 221] a non!spherical x = ? 3 r x 1+J 2 R E r " # $ % & ' 3 1!5sin 2 d () 3 7i 2 !J 4 E " # $ % & ' 5 8 !42sin 2 d+63si 4 () 5 R 35210i 2 231in 4 ds +J 6 E r " # $ % & ' 1 16 945s +3465i 4 !3003i 6 % & ' ( ) * * * + , - - - (8.10) a non!spherical y = x a non!spherical x (8.11) 288 a non!spherical z = ? 3 r z 1+J 2 R E r " # $ % & ' 3 !5sin 2 d () 3 67i 2 !J 4 E " # $ % & ' 5 8 15!70sin 2 d+63si 4 () 5 R 105315i 2 231in 4 d +J 6 E r " # $ % & ' 1 16 2452205s +4851in 4 d!3003i 6 % & ' ( ) * * * + , - - - ? 23 R !J 5 E r " # $ % & ' 15 8 ( * + , - (8.12) 8.1.1.1.3 Drag As a spacecraft orbits about a central body, the atmosphere that extends above the body?s surface can produce drag upon the vehicle. This drag retards the motion of the vehicle. This efect, acting tangentialy to the vehicle?s orbit along the negative velocity direction, reduces the velocity of the spacecraft. With prolonged exposure to this drag efect, enough speed can be reduced such that the spacecraft wil no longer be able to maintain its orbit, and the gravitational forces wil dominate the vehicle?s motion such that it eventualy drops out of orbit onto the body?s surface. The aceleration efect due to drag can be writen as a drag =! 1 2 C D A SC m " TM v r =! 1 2 C D A SC m " TM v r 2 ? (8.13) In this expresion, C D is the coeficient of drag due to the shape of the vehicle, A SC is the cross-sectional area of the spacecraft that impinges on the oncoming atmosphere, and m SC is the mas of the spacecraft. Together, these terms can be grouped as 289 B=m SC C D A , which is refered to as the balistic coeficient of the vehicle. The density of the atmosphere is represented as ! ATM . This term is often expresed as either an exponential function with respect to altitude of the spacecraft above the body?s surface, or a table of values dependent on altitude. For Earth-orbiting spacecraft, the NKF utilizes the Haris-Priester Earth atmosphere model [136]. The velocity used in Eq. (8.13) is the velocity of the spacecraft relative to the atmosphere. Since the atmosphere typicaly rotates along with the body?s surface, this relative velocity is the spacecraft?s velocity corrected for the atmosphere?s rotation rate as [136], v r =!" E #r (8.14) 8.1.1.1.4 Third-Body Gravitational Efects Spacecraft orbiting a central body are dominated by the gravitational efect of this body upon the vehicle. However, al gravitational efects from any nearby body, no mater how smal, are actualy acting upon the vehicle. Over time, these third-body gravitational efects can alter the motion of the vehicle, and if ignored, can cause the estimated vehicle state to acumulate significant erors. Thus, any body that could potentialy act upon a spacecraft?s orbit should be considered within the vehicle dynamics. The aceleration efects acting on the vehicle due to a third-body can be represented as [136], a third!body =? 3 rd body SC3 rd body + 3 rd bodyMain!body " # $ % & ' (8.15) 290 In this equation, ? 3 rd body is the gravitational parameter of the third-body acting on the vehicle, SC rd body is the inertial frame position of the spacecraft with respect to the third- body, and 3 rd Main! is the position of the third-body with respect to the central main body that the vehicle is orbiting. For spacecraft orbiting Earth, the two primary additional perturbing third-bodies are the Moon and the Sun. The third-body efect from the Moon can be represented from Eq. (8.15) as, a Moon =!? oon r SCMoon 3 + Earth 3 " # $ % & ' (8.16) Since the position of the spacecraft with respect to the Moon is not typicaly directly computed, the vectorial representation of this vector can be expanded using the known state position of the spacecraft with respect to Earth and the wel known position of the Moon with respect to Earth, such that, r SC/Moon = SC/Earth !r Moon/Earth (8.17) The third body gravitational efect due the Moon can thus be represented using Eq. (8.17) as, a Moon =!? oon r SCEarth ! MoonEarth () tt 3 + r oonEarth " # $ % & ' (8.18) Although the Sun is much further away from Earth than the Moon, its gravity field is masive enough such that it should be considered as a third-body efect for Earth-orbiting spacecraft. Due to the Sun, the third-body aceleration expresions are represented as, 291 a Sun =!? Sun r SC 3 + SunEarth 3 " # $ % & ' (8.19) a Sun =!? Sun r SCEarth ! SunEarth () tt 3 + r SunEarth " # $ % & ' (8.20) To asure numerical stability of these third-body expresions the magnitude term of r SCEarth ! 3 rd bodyEarth 3 is often expanded in Taylor series form. The magnitude of the third-body position is often significantly greater than the magnitude of the spacecraft?s position with respect to Earth, such that r 3 d bodyEarth !r SCEarth . Expanding this diference in Taylor series doesn?t require the computation of the potentialy eroneous diference of a smal value minus a large value [136]. The NKF uses the direct forms of these equations as in Eqs. (8.18) and (8.20) since double precision calculations are used throughout the analysis. If les precision is used for these computations, Taylor series expansion should be considered. 8.1.2 Orbit State Transition Matrix The NKF is implemented as an extended Kalman filter, due to the non-linear state dynamics as shown above. Although the navigation states are the ultimate product of this filter, the terms procesed within the NKF filter are the erors asociated with each element of the state vector. These eror-states, ! , can be represented based upon the true states, x , and the estimated states, !x , as, =!+ (8.21) Necesary for eror-state and eror-covariance procesing within the NKF is the proper representation of the state transition matrix, . The primary definition of this 292 matrix is from the following expresion, where it is used to determine the values of the eror-state, !x , at a future time, t . !x="t, 0 () (8.22) The state transition matrix is found by solving the integral of the following expresions, ! t, 0 () =F () , 0 () I (8.23) 8.1.2.1 State Jacobian Matrix The Jacobian matrix, Ft () , is defined as the derivative of the dynamics of the states with respect to it states, as in, Ft= !f"x (8.24) Determining the Jacobian matrix is necesary in order to solve for the state transition matrix in Eq. (8.23). Thus, the dynamics of the states from Eq. (8.2) must be known or estimated in order to complete this diferentiation. The dynamics of the navigation states from Eq. (8.3) are the following, ! fxt () ,ut= "r v ! # $ % & a (8.25) From Eq. (8.24), to determine the dynamics of the erors of these states, the Jacobian matrix can be determined as, Ft () = !f"x v a # $ % & ' = ! r "% & ' (8.26) 293 From the known definition of the states from Eqs. (8.1) and (8.4), the first row elements of Eq. (8.26) can be simplified as, !v r =0 3x ;I 3x (8.27) The second row elements depend entirely upon the aceleration of the spacecraft, and cannot be imediately simplified. Thus, using Eq. (8.27), the Jacobian matrix for spacecraft dynamics can be expresed as, Ft () = 0 3x I !a rv " # $ % & ' (8.28) 8.1.2.1.1 Aceleration Derivatives Using the aceleration expresions from Eqs. (8.7)-(8.20), the derivatives with respect to position and velocity can be determined for each of the gravitational, drag, and third- body efects. Since position, velocity, and aceleration are al thre-element vectors, taking their derivative requires the derivative to be determined from each vector element. In matrix form, this is determined as, !a r = x r y !a x z xyz z x r y !a z " # $ $ % & ' ' ; v = !a x v y x z xyz !a z x z v yz " # $ $ % & ' ' (8.29) where = x , yz {} , r= x , yz {} , and v= x , yz {} . The following vector diferential identities are useful when deriving these aceleration derivatives, 294 !r = ? (8.30) n () nr "2T (8.31) !r =I 3x (8.32) T v () (8.33) In these equations, r= , ? r is the unit direction of r such that ? r= , and r T v is the scalar value inner product of vectors r and v r T v=!r x v+ y r z v ( ) . 8.1.2.1.2 Two-Body For the two-body aceleration efect from Eq. (8.8), the position derivative is straightforward to determine using the identities of Eqs. (8.30)-(8.33) [120, 213], !a two"body r = ? 3 ? r T "I 3x ( (8.34) In this equation, ? r T is the outer-product of this vector and produces a 3x3 matrix. Since the two-body aceleration is independent of spacecraft velocity, this derivative is zero, or, !a two"body v =0 3x (8.35) 8.1.2.1.3 Non-Spherical Gravitational Potential For higher-order non-spherical gravitational potential efects, the derivative of the spacecraft aceleration due to position from Eq. (8.9) is, !a non"spherical # = ! g () (8.36) 295 Due to the recursive nature of the typical gravity field harmonics for higher-order representations, various analytical methods exist to represent the derivative of Eq. (8.36) [46, 130, 236]. For the most acurate representation of the efects due to the non-spherical gravity, the derivatives of al terms used in the dynamics should be computed. However, contributions to the derivative of total aceleration with respect to the highest-order terms are usualy not significant. Instead, it is often sufficient to only consider the primary contributors and ignore the remaining terms. This is often a trade-off when considering algorithm computation time versus precision. In the NKF used for pulsar-based navigation, only the zonal terms of Earth?s gravity are considered in the dynamics of Earth-orbiting spacecraft. Up to zonal degre six, J 6 , is considered, with zero order. However, for the Jacobian matrix, currently only degre two, J 2 , is considered in the aceleration derivative since the higher order terms compute only smal efects. This can be expresed as [120], !a non"spherical = ? 3 2 J R Earth r # $ % & ' ( 2 ) * + , - . 5 ? T 1"7 ? n T r () 2 ) * , - 1"5 ? n T r () 2 ) * , - I 3x +10+ / 0 4 1 5 (8.37) If degre thre or higher, or order greater than zero, should be incorporated into the harmonics for improved acuracy, then the derivatives of these terms should also be included in Eq. (8.36). Since the gravity field from Eq. (8.36) is independent of velocity, this derivative is zero, or, !a non"spherical v =0 3x (8.38) 296 8.1.2.1.4 Drag The expresion for drag aceleration efects on a spacecraft is complex, as Eq. (8.13) suggests. It is a function of position and velocity, since the intermediate term of density is a function of position, and relative velocity a function of both. The derivatives must use the chain-rule for diferentiation to determine the complete formulas [136]. These can be expresed initialy as, ! drag r =" 1 2B !# ATM r v r " AT 2B ! v r () (8.39) ! drag v = drag r ! v " # ATM 2B ! v r () $ % & ' ( ) r (8.40) The derivative of density with respect to position can be approximated using the diferences of the table values for density, or !" ATM # T ! $ %" ATM r ? (8.41) The ! terms can be computed using values close to the computed altitude, h , of the specified position r=R E +h () , as, !" ATM r = 2 #" ATM 1 r (8.42) The derivative of relative velocity with respect to position magnitude can be expresed from Eq. (8.14) as, !v r = E $ () v !r E {} ( = E I 3x (8.43) In Eq. (8.43), E {} represents the skew-symmetric representation of the Earth rotation matrix as, 297 ! E {} = 0" z ! y zx yx # $ % & ' ( (8.44) The derivative of the relative velocity terms in Eq. (8.39) with respect to position can be rewriten as, ! r v () = r v () ! r = ? r +vI 3x () ! r (8.45) Using the representation in Eq. (8.43), this expresion becomes, " r3x # E {} (8.46) Thus, using Eqs. (8.41) and (8.45), the derivative of aceleration with respect to position from Eq. (8.39) is, !a drag r =" 1 2B #$ ATM r v ? r + ATM 2B v r r I 3x % & ' ( ) * + E {} (8.47) The derivative of relative velocity with respect to velocity can be represented as, !v r ="# E $= !v "# {} () =I 3x "0 3x (8.48) The derivative of aceleration with respect to relative velocity using Eq. (8.40) is expresed as, !a drag v r =" # ATM 2B ! v r () $ % & ' ( ) =" # ATM 2B v r + r I 3x $ % & ' ( ) (8.49) Thus, the derivative of aceleration with respect to velocity is the combination of Eqs. (8.48) and (8.49) as, a drag !v " # ATM 2B v r + r I 3x % & ( ) (8.50) 298 8.1.2.1.5 Third-Body The derivative of aceleration due to third-body aceleration efects can be computed using the following notational simplifications of r= SC/Main!body and s=r 3 d bodyMain!body from Eq. (8.15) such that [136], third!body =? 3 rd body !s 3 + " # $ % & ' (8.51) The derivation with respect to position yields, !a third"body =? 3 rd body !r "s 3 # $ % & ' ( !s r" 3 # $ % & ' ( + !s 3 # $ % & ' ( ) * + , - . 3 rd body 1 3 I x5 s () T + . (8.52) This partial derivative must be computed for each of the third-body perturbations that are considered within the dynamics. Since this aceleration efect is independent of velocity, the derivative with respect to velocity is zero, or, a thirdbody v 0 x (8.53) 8.1.2.2 State Transition Matrix Integration Using the above representations for the partial derivatives of aceleration the terms for the Jacobian matrix in Eq. (8.28) can be asembled as, !a r = two"body + !a non"spherical # !a drag + i th hird"body ! i PB S $ (8.54) !a v = drag (8.55) 299 In Eq. (8.54), the third-body gravitational potential efects are summed over al the bodies within the solar system (PB S ). In the NKF, only the Moon and Sun are currently considered for Earth-orbiting spacecraft. Drag is the only perturbing force that is a function of velocity, thus the only term in Eq. (8.5). The partial derivatives of aceleration can then be placed in the Jacobian matrix in Eq. (8.28). The best estimated values of the navigation states are considered in this matrix, such that F=!r,v () . This matrix can then be used in the numerical integration of Eq. (8.23) in order to determine the current state transition matrix used for time propagation of the eror-states and eror-covariances. 8.1.3 Covariance Matrix Dynamics The expectations of the eror-states and the noise of the k th step in a discrete system are represented as, P k =E!x k T " # $ % (8.56) Q (8.57) The covariance matrix, P , is symmetric and provides a representation of the statistical uncertainty in the eror-states, !x [65]. The Q matrix is refered to as the proces noise matrix for the system, and is related to how wel the dynamics of the state variables are known. A Kalman filter interprets high proces noise as poor knowledge of the dynamics by maintaining a high estimate of the state covariances. The noise of the individual eror states, ! , is asumed to be uncorrelated with respect to time (white noise), and asumed to be uncorrelated with respect to the states such that !x k " T # $ % & =0 . (Note that the proces noise, ! k , should not be confused with the symbol for Earth rotation rate, ! E , 300 above). The discrete form of the dynamics of the covariance matrix can be represented as [65], P k+1 ! =" k T # k Q T (8.58) From the dynamics of Eq. (8.2), the matrix ! is identity. Eqs. (8.21) and (8.58) represent the time update (a priori) of the NKF. 8.2 Kalman Filter Measurement Models The time propagation of the NKF eror-states provides predicted estimates of the erors as the spacecraft progreses through its motion. The dynamics defined in the previous section asures this prediction is produced in its most acurate manner. However, any erors that exist within the system, such as initial erors in the estimated states, dynamic modeling erors, or unforesen disturbances, wil cause the estimated dynamics solution to remain in eror with respect to the true solution. In order to correct any erors in these states, it is necesary to utilize external observations and proces these through the filter. Thus, with high-quality time propagation and correcting measurement updates, over time the filter produces the most acurate state solution possible. The NKF utilizes range measurements produced by the observation of pulses from pulsars. These range measurements are blended with eror-state dynamics of position and velocity such that any erors in these states are determined. This section describes the methods used to incorporate the range measurement from pulsars into the NKF elements so that the measurement updates can proced in an optimal manner. Both first order and higher-order measurement methods are presented for pulsars based upon the fidelity of the pulsar knowledge and pulse timing acuracy. 301 Similar to the state dynamics, the observations may also have a non-linear relationship with respect to the whole-value states. Thus the measurement, y , has the following representation, yt () = ! hxt () , () +t () (8.59) In this expresion, ! h is a non-linear function of the state vector, and perhaps time. The measurement noise asociated with each observation is represented as ! . In order to asemble the observations in terms of the eror-states of the NKF, a measurement diference, z , betwen the measurement and its estimate from Eq. (8.59) is computed [65]. To first order, this diference is computed as, zt () =y!h"x () () #+$t () H#$t (8.60) This measurement diference, zt () , is refered to as the measurement residual, and H=!hx is the measurement matrix of measurement partial derivatives with respect to the states [65]. This can be represented in discrete form as, z k+1 =H!x k+1 " (8.61) A measurement update (a posteriori) of the state vector estimates and the covariance matrix is produced using [29, 65], !x k+1 =K k+1 opt z (8.62) P k+1 =I!K k+1 opt H " # $ % P k+1 ! (8.63) This update proces uses the optimal Kalman gain, opt , which can be computed based upon the time update of the covariance matrix, the measurement matrix, and the 302 expectations of the measurement noise, R=E!! " # $ % & [91]. In discrete form this optimal gain is writen as, K k+1 opt =P k ! H +1 T k1 ! k+ T R 1 () ! (8.64) Within the NKF, individual measurements are evaluated prior to a measurement update to remove those out-lying measurements that may potentialy corrupt the filter?s solution. Using a measurement residual test (Appendix D), the NKF verifies each measurement is five times les than the innovations as computed by the filter. 8.2.1 Pulsar Range Measurement The range measurement for a spacecraft with respect to a reference location is produced by comparing the measured pulse TOA at the spacecraft to its predicted TOA at the reference location. Any diference in the measured and predicted TOA values is asumed to be a result of erors in the estimated vehicle position, as it is asumed that any additional erors within the system (ex. photon arival time tagging, spacecraft clock erors, proces delays) have already been acounted for in the measurement TOA, and the pulse model is as acurate as possible. A direct comparison of the arival time at the spacecraft to the same pulse?s arival time at the SB is acomplished using time transfer equations. These equations require knowledge of the spacecraft?s position and velocity in order to be implemented correctly. In the NKF?s measurement scheme, estimated values of spacecraft position and velocity are utilized within the time transfer equation to create the best estimates of pulse arival times at the SB. These state estimates are provided by the onboard orbit propagator 303 using Eqs. (8.3) and (8.6) implemented within the vehicle?s navigation system, which provides a continuous estimate of the vehicle?s dynamics during a pulsar observation. Figure 8-1 presents a diagram of an Earth-orbiting spacecraft and two pulsars. Unit directions to the pulsars, ? n i and j , as wel as the position of the spacecraft with respect to the SB, r SC , the position of Earth with respect to the SB, r E , and the position of the spacecraft with respect to Earth, r SC/E are shown. Figure 8-1. Multiple pulsars viewed by Earth-orbiting spacecraft. 8.2.1.1 First Order Measurement From Chapter 7, to first order, the pulse TOA measured at the spacecraft, t SC , compared to its predicted arival time at the SB, t SSB , is shown for the i th pulsar to be, 304 t SSB = SC + ? n i !r SC c t ? i c !r E + SC/ () (8.65) This expresion can be writen in terms of spacecraft Earth-relative position, r SC/E , as, ct SSB ! SC ? n i "r E = i " SC/E (8.66) Eq. (8.66) give a method to represent the desired position of the spacecraft relative to Earth based upon the measured diference in pulse TOA and the known position of Earth within the solar system. The known Earth position could be provided by standard ephemeris tables (ex. JPL ephemeris data [198]). Using the estimated value of this position, !r SC/E , the eror in this value, !r SC/E , is related to the true value as, r SC/E =! / +r SC/E (8.67) The NKF is used to determine the erors of the spacecraft position. Therefore, the measurement in Eq. (8.66) can be writen in terms of the position eror as, ct i " E/ () =n i "# / (8.68) The form of Eq. (8.68) is the form of the Kalman filter measurement equation of Eq. (8.60), where, yt () =c SSB ! h"x SC + ? n i !r E " SC/ () zthx ) ct b + ? n i !r E " SC/ () # $ % & H" () ' ? i ! SC/E ? i x i y i z 0' /E x y r SC/ z v E x ' / y SC/ z # $ ( & ) (8.69) 305 The measurement noise, !t () , asociated with Eq. (8.69) must be added to asure acurate modeling. This noise would be a function of al unknown measurement erors. For example, this could be chosen as ! = 300 m or ! = 30 m depending on pulse timing resolution of 1 ?s or 100 ns, respectively, or chosen as the range measurement acuracy values for each pulsar in Chapter 3. Thus, using the terms from Eq. (8.69), the first order relationship for a pulsar range measurement would be, zt () =y!h"x () ytH"x () =" () +#t () (8.70) From Eq. (8.69), it can be sen that z in Eq. (8.70) is actualy a scalar value. However, an ensemble of pulsar measurements could be collected together to create a vector of measurements. This measurement relationship is presented in Figure 8-2. The concept has similarities to methods used by ground-based orbit determination. In this figure, the orbit can be determined via at least thre observations by a ground radio telescope from range, ! i , and range-rate, ! i , of the vehicle. Combining these separate observations provides a method to measure the orbital elements, or state, information of the vehicle [16, 17, 55]. The pulsar-based method can also produce range measurements relative to the vehicle?s primary gravitational body, in this case Earth. These first-order range measurements, ! i = SC i , are generated using the expresion of Eq. (8.68) and can be blended with the state dynamics and its erors using the Kalman filter measurement model of Eq. (8.69) to recursively update the estimate of the state erors. Multiple measurements from a single pulsar, or multiple pulsars from diferent line-of-sight directions, alow the filter to compute the best overal continuous, state solution. 306 Figure 8-2. Pulsar-based measurement and radar-range measurement comparison. 8.2.1.2 Higher-Order Measurement The expresion of the measurement from Eq. (8.65) is a first order only representation of the pulsar timing measurement and spacecraft position. Increased acuracy can be pursued by including the relativistic efects on the time transfer equation as presented in Chapter 4 and 7. The proper time to coordinate time correction must acount for the clock?s time measurement due to its motion and efects from nearby gravitational bodies. Additionaly, the relativistic efects of path bending and time transfer within the solar system must be included to adjust the pulse arival time calculation for these efects. From the higher order measurement equations presented in Chapter 7, the full equation can be writen using spacecraft proper time, ! SC , as, 307 ct SSB !" SC StdCorr E () ! 1 c v#!r E () $ % & ' ? n#!r () 1 D 0 2 ? n# ) 2 +!rV(t N () ? #t N () ? #!r b# $ % ) ' * 2? Sun c l ? #!+r b 1 = ? n#+r 1 0 ? #!n+!# t N () #r ? Vt N () ? n#+r () b# $ % ) & ' * 2? Sun c ? #+ ! r # nb $ % & ' * 1 c v E # () (8.71) This expresion can be put into the Kalman filter measurement form as, yt () =c SSB ! h"x SC +StdCorr E () 1 c v"r# E () $ % & ' + ? n"r () 1 D 0 2 ? n" 2 rVt N () ? "t N () ? "r #b"+ $ % ) ' * 2? Sun c l ? "+r b 1 zt () =y ! hx H"x () + ? n 1 D 0 ? "r () n#" +Vt N ? t N () ? n ( b" $ % & ' * 2? Sun c ? r "+ () "b () $ % & ' * + 1 c v E T 0 & ' * * +r v $ % ) (8.72) Using this form, along with its asociated measurement erors, alows the NKF to proces pulsar-based range measurements with high acuracy. 308 8.2.2 Pulsar Phase Measurement As presented in Chapter 6, there is a relationship betwen the range measurement and the total phase measurement of the pulse cycles for the spacecraft. This total phase is related to range, or distance, by the cycle wavelength. If the estimate of spacecraft position used in the measurement equations of (8.69) or (8.72) is sufficiently acurate that the number of integer phase cycles can be imediately determined betwen the spacecraft and the inertial reference location, a phase measurement can be used instead of a range value with each of these measurement equations. The fractional phase diference betwen the phase of the pulse timing model and the measured value at the spacecraft can be added to the diference in full cycle counts to create a measurement of the phase diference that can be implemented within the NKF measurement models. The approach may be directly useful for systems where phase is the chosen as the communicated unit of pulse measurement throughout the system. 8.3 Spacecraft Clock Erors and Measurement The states chosen for the NKF, as presented previously, are spacecraft position and velocity. Updates to these states provide improved overal navigation information. Measurements of pulsar pulse arival times are the primary observation used within the system. Since the measured time is critical for improved performance, erors within the spacecraft clock, or pulse timing system, would contribute to any degraded performance of the navigation system. Thus, for many practical applications it may be prudent to ad clock states and erors to the state vector, so that any measured pulse arival time offset 309 that is atributable to the clock time measurement, and not position eror, can be determined. The spacecraft clock?s state variable can be represented as ! SC . Consequently, its estimated value can be listed as ! SC and its erors as " SC such that the true clock time can be determined to be, ! SC =+! SC (8.73) The eror !" SC is the clock bias state. If the bias is not a fixed value, it wil depend on clock drift rate , whose estimate and eror follow as, ! SC =+"! SC (8.74) Including these two new states, the new estimated state and eror-state vectors for the NKF become, !x= r SC v " SC # $ % & ' ( ;)x= r SC v ! " SC # $ % & ' ( (8.75) 8.3.1 Clock State Dynamics The dynamics of these two new clock eror states can be represented as the following since the bias term is directly related to the drift rate, !" SC =#+$ " f (8.76) The Jacobian matrix for these new states can be computed directly from Eq. (8.76) as, 310 Ft () clock = !" # $ % & ' ( ) 01 $ % & (8.77) The proces noise matrix comes from the white noise from each state as, Qt () clock = ! "# 2 0 $ % & ' ( ) * (8.78) The covariance matrix can be writen using the eror estimate of each state such that, P clock = ! "# 2 0 $ % & ' ( ) * (8.79) 8.3.2 Clock Measurement The clock erors can be measured using the pulsar range equations and the clock eror model of Eq. (8.73). Using the first order range equation from Eq. (8.68) ct SSB ! SC ? n i "r E +! SC/ () = ? n i "#r SC/E +c$ SC (8.80) This expresion can be represented in Kalman filter measurement form as, yt () =c SSB ! h"x SC + ? n i !r E " SC/ () zthx ) ct SSB t+ ? n i !r E " SC/ () # $ % & H" () ' ? i ! SC/E ' SC = i x i y i z 0!!!c0'r SC/E x y / z v SCE x ' / y / z ( SC ) # $ * * * % & + + + (8.81) 311 If additional acuracy is required using the relativistic corrections presented in Chapter 7 and the previous Higher-Order Measurement section, the measurement models from Eq. (8.72) can include the spacecraft clock eror as needed. Other higher-order efects could also be considered. Erors due to coordinate time standard corrections, Earth inertial velocity, v E , or solar system ephemeris data may also contribute to the navigation erors. If these erors are significant compared to the other erors and if they are observable within the measurement system, they could be added as needed to the state vector. 8.4 Visibility Obstruction By Celestial Body Even though sources are very distant from the solar system, any body that pases betwen the spacecraft and the source may obstruct a spacecraft detector?s view of the source. To avoid this obstruction occurring during a planned source observation, it is necesary to determine the location within an orbit where the detector?s visibility of a source is obstructed. For Earth-orbiting spacecraft it is apparent that any source that is not perpendicular to the vehicle?s orbit plane may potentialy pas behind Earth?s limb for some portion of the orbit. Figure 8-3 provides a diagram of a spacecraft in Earth orbit, as wel as the shadow cast by Earth from a pulsar. Earth wil block the view of the source while the vehicle is in Earth?s shadow. Any celestial body, other spacecraft, or components on the vehicle itself could obscure the view of a source. The size of an object and its distance form the spacecraft?s detector afect the amount of obscuration. If a celestial body has an 312 appreciable atmosphere that may absorb X-ray photons, the height of the atmosphere must be added to the diameter of the body when determining source visibility. To determine whether a body obscures the view of a source, it is necesary to determine the size of the shadow cast by the body and whether the spacecraft?s path intersects this shadow [55]. Figure 8-4 provides a diagram of a body and the orbit of a vehicle about this body and the geometry asociated with the shadow cast by the body. The angle, ! , betwen the vehicle?s position relative to the body, r SCB , and the unit direction to the source, ? n , can be determined from, cos! () = ? n"r SCB (8.82) The vehicle is within the body?s shadow when this angle is within the entrance and exit angles, ! ENT and EXIT respectively, of the shadow, ENTEXIT (8.83) The offset distance, d , is related to the position and body radius, R B , as, r SCB =R+d (8.84) Thus the magnitude of this offset is, d= SCB 2 !R (8.85) Since the shadow can only exist for the angles betwen !2 and 3 , Figure 8-4 shows that the entrance and exit angles relate to this distance as, cos!"# ENT () = d r SCB (8.86) EXIT () SCB (8.87) Therefore the test from Eq. (8.83) can be rewriten as, 313 !"arcos SCB 2 "R # $ % & ' ( )arcos ? n* SCB () )!+arcos SCB 2 "R # $ % & ' ( (8.88) If the computed angle is betwen these bounds, then the vehicle is within the body?s shadow. For Earth, the planetary radius should include Earth?s atmosphere height, h ATM , such that R B = E +h ATM . Using the Crab Pulsar and the orbit of the ARGOS vehicle on December 26, 1999, Figure 8-5 plots the visibility of the pulsar due to Earth?s shadow during four orbits. This plot shows that the Crab Pulsar is visible for approximately 4317 s during the 6102 s orbit. Figure 8-6 plots the visibility of two other pulsars, PSR B1937+21, and PSR B1821+24, during the orbit of ARGOS due to Earth?s shadow and these two pulsars are obscured from view for some portion of the vehicle?s orbit. Figure 8-7 plots the visibility of al thre of these pulsars during four ARGOS orbits due to the combined efects of the shadows of Earth, the Sun, and the Moon. This figure shows that during each of these orbits at least one pulsar is visible. Figure 8-8 provides a visibility plot for these thre pulsars within the GPS system orbit. Although the GPS spacecraft nearly enters Earth?s shadow of the Crab Pulsar, al thre pulsars a visible for the entire orbit of this spacecraft. Although visibility durations for a specific source can be determined along a spacecraft orbit, additional visibility limitations such as vehicle component obstruction or detector gimbaled axis limitations may reduce these durations and would require further analysis for a specific implementation. 314 Figure 8-3. Shadow cast by Earth on spacecraft orbit. Figure 8-4. Geometry of body shadow with respect to spacecraft orbit. 315 Figure 8-5. Visibility of Crab Pulsar in ARGOS orbits about Earth. Figure 8-6. Visibility of two pulsars in ARGOS orbits about Earth. 316 Figure 8-7. Visibility of thre pulsars due to shadows from Earth, Sun, and Moon in ARGOS orbit. Figure 8-8. Visibility of thre pulsars due to shadows from Earth, Sun, and Moon in GPS orbit. 317 8.5 Simulation And Results 8.5.1 Simulation Description To test the performance of the NKF, a computer simulation was developed that incorporates vehicle dynamics and pulsar-based range measurements. The simulation esentialy contains two main components, a numerical orbit propagation routine and the NKF used to correct a navigation solution from the propagator. The numerical orbit propagation routine integrates the vehicle state dynamics in order to provide a continuous position and velocity solution. The NKF then proceses simulated range measurements to update the vehicle state dynamics and provide an improved navigation solution. The simulation was coded in the MATLAB ? development environment produced by The MathWorks, Inc. Four existing satelite orbits of ARGOS, Laser Geodynamics (LAGEOS-1), GPS Block IA-16 PRN-01 and DirecTV 2 (DBS 2) were investigated. Initial truth state conditions were chosen from the two-line element sets (TLE) of orbit data provided by NORAD [97]. These TLE sets are read by analytical perturbation orbit propagators, such as the Simplified General Perturbations Number 4 (SGP4) propagator and the Simplified Dep Space Perturbations Number 4 (SDP4) [83, 84]. The TLE data also provided the balistic coeficients of the spacecraft used in the atmospheric drag computations. A proposed orbit of the NASA Lunar Reconnaisance Orbiter (LRO) was also investigated. This planned mision wil orbit the Moon at an altitude of 50 km beginning in 2008 [21]. Table 8-1 lists several orbit parameters for each of the selected spacecraft orbits. 318 Table 8-1. Spacecraft Orbit Information. Orbit Semi- Major Axis (km) Ecentricity Period (s) Inclination (deg) ARGOS 7217 0.021 6102 98.8 LAGEOS-1 1275 0.038 13534 109.8 GPS Block IA-16 PRN-01 26561 0.058 43081 56.3 DirecTV 2 (DBS 2) 4216 0.0018 86169 0.027 LRO 1870 0.036 7256 13 The vehicle state dynamics was implemented as Eqs. (8.3) and (8.6). The non- spherical Earth gravitational zonal terms of J 2 through J 6 were implemented [213], and a Haris-Priester model of Earth?s atmosphere was utilized [136]. The Moon and Sun were the two third-body efects considered. The solar system position and velocity information was provided by the JPL ephemeris data [198]. A truth orbit model was created by integrating the numerical propagator with the initial conditions set from the TLE data values. Two other orbit solutions were created. One of these propagators was used by the NKF and was updated based upon measurement procesing within the NKF. The second solution was alowed to run frely and was not corrected at al during the simulation. Each of these two solutions was initialized with state data that included simulated position and velocity eror. The simulated state dynamics for these orbits was integrated using a fourth-order Runge-Kutta method with a fixed time step of 10 s. The numerical solution was validated for each of the Earth orbiting cases using both the SDP4 and the Navy?s Position and Partials as functions of Time Version 3 (PT3) [84, 182] analytical orbit propagators. Although diferences betwen the numerical solution and the analytical solutions for each 319 orbit were smal, the analytical model for orbit propagation cannot match the simulation?s results exactly due to the higher order perturbation efects considered within the numerical simulation. To demonstrate the acuracy of the numerical solution compared to the analytical solutions, within the LAGEOS-1 orbit Figure 8-9 and Figure 8-10 present the diference betwen the SDP4 and NKF state dynamics of position and velocity, respectively, for two orbits. Both solutions were begun with the same initial conditions for this test. Comparisons to the PT3 solution are similar. These plots show that the NKF numerical propagator compares favorably to the analytical orbit solutions. Figure 8-9. Analytical and numerical orbit propagation position diferences. 320 Figure 8-10. Analytical and numerical orbit propagation velocity diferences. With initial erors introduced to the initial conditions, the NKF is started with a solution that does not match the truth solution. This requires the NKF to detect and remove these state erors based upon the simulated range measurements. The performance of the NKF was determined by how wel these erors could be detected, and by quantifying the true erors of the NKF after selected periods of operation. During the state dynamics integration, the state transition matrix, ! , was simultaneously computed. The vehicle state estimate and transition matrix were provided to the NKF to proces a time-update of the covariance matrix. The initial standard deviations for the covariance matrix were chosen as ! "r 0 = 250 m and ! "v 0 = 0.25 m/s for each axis [136]. The one-sigma state proces noise was chosen as = 0.05 m and ! "v = 0.05 m/s, and asumed fixed for the entire simulation run [136]. A standard run 321 for each orbit utilized these initial covariance and proces noise values along with initial condition erors of 100 m position eror and 0.01 m/s velocity eror in each axis [136]. Large initial eror simulation runs were also investigated. In these runs, larger initial state eror of 100 times the standard run erors, at 10 km and 1 m/s, were used. Also, initial standard deviations for the covariance matrix were increased to ! "r 0 = 10 km and ! "v 0 = 0.01 km/s for each axis so that the NKF began with a larger eror estimate of each state. To create simulated pulsar-based range measurements, the NKF incorporates the higher order relativistic time transfer expresion of Eq. (7.12). Note that currently the highest order Eq. (4.28) cannot be implemented within a navigation system due to the limited knowledge of source position, namely acurate source distance. Simulated eror, with a variance equal to the pulsar range measurement acuracy, is added to these simulated measurements to create realistic values. The NKF?s procesing utilizes the measurement model from Eq. (8.72) to blend the measurement data with the spacecraft dynamics. The measurement noise, !t () , asociated with Eq. (8.72) was computed based upon the range acuracy of each pulsar based upon the results of the SNR-based calculations in Chapter 3 asuming a 1-m 2 deector. To emulate potential navigation system erors, an additional 2% was added to the range acuracy value for each pulsar. This would incorporate erors due to photon timing, X-ray background, and detector ineficiencies within the measurement. To simulate the random efects of this one-sigma range acuracy, a normalized random number with a standard deviation equal to one was multiplied by the total range acuracy value for each pulsar. Thus, the NKF received and procesed a range measurement that included random statistical eror, as opposed to a 322 fixed value of eror. The relativistic time transfer and range measurement were computed asuming spacecraft coordinate time, although the efects of proper time to coordinate time conversion of Eq. (8.81) wil be incorporated in future analysis. The thre top RPSRs of Chapter 3 were chosen as the pulsars available to the NKF. These were primarily chosen due to the knowledge of al their parameters, as most other sources currently have only estimated values. It was asumed that only one pulsar could be detected during a single fixed 500 s observation window. The priority of observation was based upon the measurement acuracies of thre RPSRs: B0531+2: 109 m, B1821- 24: 325 m, and B1937+21: 344. If the visibility of a pulsar was obscured during an observation, the next pulsar in the priority list was utilized. If none were visible, the measurement cycle was skipped, and the succesive cycle would begin. To avoid using only a single pulsar for a long duration within the simulation and increase observability of eror in al thre axes, after a set amount of time a diferent pulsar is used for up to six succesive measurements. Total navigation solution eror is reduced when using multiple pulsars along diferent line-of-sight vectors. Table 8-2 provides a listing of the simulation specific information used for each orbit. The duration of the simulation runs is provided and was usualy chosen as several multiples of the orbit period. Due to the procesing time for the simulation and orbit length, although the total simulation duration may be longer, the number of orbit periods may not be large. However enough orbital periods were completed to represent the performance of the NKF of these spacecraft. The table also provides the times after two orbits and several orbits used to investigate the filter performance. The time to check whether to use additional pulsars is also listed for each vehicle, although ARGOS orbit 323 does not require this since the visibility of any source in this orbit is only a fraction of its orbit period. Table 8-2. Spacecraft Simulation Information. Orbit Simulation Duration (s) Filter Setling Time #1 (s) Filter Setling Time #2 (s) Elapsed Time to Check Aditional Pulsars (s) ARGOS 185,00 (~30 orbits) 12,20 (~2 orbits) 124,00 (~20 orbits) Not Neded LAGEOS-1 204,00 (~15 orbits) 28,00 (~2 orbits) 163,00 (~12 orbits) 13,50 GPS Block IA-16 PRN-01 216,00 (~5 orbits) 87,00 (~2 orbits) 173,00 (~4 orbits) 14,00 DirecTV 2 (DBS 2) 431,00 (~5 orbits) 173,00 (~2 orbits) 345,00 (~4 orbits) 25,00 LRO 218,00 (~30 orbits) 15,00 (~2 orbits) 146,00 (~20 orbits) 10,00 Since some orbits have the ability to observe a single pulsar during the entire orbit period, an investigation of the use of a single pulsar for navigation system operation was pursued. If the performance of a single-pulsar navigation system was aceptable, this may alow X-ray detectors to remain fixed on an inertialy stabilized spacecraft, thus not requiring a gimbal system. For Earth-orbiting spacecraft that are nadir pointing, this may alow the X-ray detector to view the source only periodicaly during the orbit. Studies could be pursued to determine if the eror growth in the solution is aceptable during the spans betwen observations. The Crab Pulsar is used as the single source for the GPS and DirecTV orbit simulations presented below. Although al atempts have been made to make the most up to date, and acurate, estimate of pulsar-based range measurements, it is conceivable that it is dificult to achieve these theoretical values. Perhaps no detector system of current technology may 324 achieve the necesary photon timing or energy resolution, or no pulsar can be shown to produce sufficiently periodic pulsations that can be succesfully predicted over the long term. Therefore, a study of the NKF performance of reduced measurement acuracy was pursued. Values of 10 and 100 times the current estimate of measurement acuracy were simulated and performance of these simulation runs are reported. 8.5.2 Simulation Results For each orbit analysis, the simulation was executed for five distinct runs in each spacecraft orbit. An individual run used a diferent seding for the normalized random number generator than the other runs. The data from each run was stored and the average of each of the five runs was computed. This simulation method was used to create a statistical representation of the performance of the algorithms in each orbit. By using five runs, each generated using diferent random number sets, and then taking the average of these results, the reported values provides a description of the performance independent of any single run. The primary reported values are the root mean square (RMS) of the eror NKF?s output, the mean of the NKF covariance estimate of each state, and the mean radial spherical eror (MRSE) value of the NKF position eror. The RMS value signifies the total eror of the filter output with respect to the truth orbit. The covariance estimate provides a representation of the NKF?s estimate of its performance and the mean is given since the covariance varies as a sinusoid over the orbit period due to the state dynamics. The MRSE value provides a single value representation of the NKF?s performance. The performance values are reported over durations of the entire run, after two orbits, and 325 after a specified number of orbits to demonstrate the performance with zero filter setling time and after a certain amount of filter setling. Plots of the NKF?s output are provided that show the performance of the algorithms over time. Covariance envelope plots are created by graphing the NKF standard deviation (square root of the covariance values) of each state, both the positive and negative values. Overlaid on these plots is the eror in the NKF navigation solution output with respect to the truth solution. To show the benefit of the NKF solution, separate plots of the eror in the NKF solution and the eror in a fre-running uncorrected orbit solution are also provided. The fre-running uncorrected solution represents a navigation solution that would result if no correction whatsoever were implemented within a navigation system. Since initial eror in the solution is introduced within the simulation, the fre-running uncorrected solution wil diverge significantly from the truth solution over the simulation duration. Tables of performance values and plots of selected run results are provided. The performance values are reported in the radial, along-track, and cross-track (RAC) axes of the orbit, as the inertial XYZ values can vary significantly for diferent orbits. Descriptions of the results for each orbit are discussed in detail below. 8.5.2.1 ARGOS Orbit Performance Results Figure 8-11 provides the standard deviation envelope and NKF eror plot within the ARGOS orbit for the RAC position axes of an example simulation run. Over the duration of the simulation run, the NKF erors remain within the one-sigma standard deviation envelope. Figure 8-12 shows a similar plot for the RAC velocity axes, and the eror can also be sen to stay within the standard deviation envelope. 326 Figure 8-15 shows the graph of the NKF position eror magnitude along with the uncorrected orbit solution eror magnitude. With both solutions starting with standard run erors in their initial conditions with respect to the truth orbit the plot shows that the NKF eror remains bounded and is eventualy reduced to a smal value (< 100 m), yet the uncorrected solution eror continues to grow unbounded, reaching 8 km after 30 orbits. Table 8-3 lists the performance values for the four diferent simulation type runs for the ARGOS spacecraft orbit. For the standard run type the RMS erors of NKF position solution is les than 120 m per axis for the entire run, whereas after twenty full orbits of this vehicle the RMS eror reduces to les than 80 m. The MRSE value after twenty orbits is 81 m. The velocity performance of the NKF for this orbit is on the order of 0.1 m/s. This demonstrates the significant performance achievement of the NKF using pulsar- based range measurements. If initial eror is increased to 100 times the standard simulation run values, for the entire run the RMS value is as high as 1011 m per axis due to high initial erors. However, after twenty orbits the large initial eror has been corrected and the RMS eror per axis is down to les than 150 m and the MRSE is near that standard run value at 91 m. Although increasing the measurement eror reduces the performance of the NKF position solution, after twenty orbits the MRSE grows to only about 350 m when 10 times the current estimate of measurement eror is introduced. The MRSE is about 1100 m for 100 times the current measurement eror. 8.5.2.2 LAGEOS-1 Orbit Performance Results Table 8-4 provides performance values of the four simulation type runs for the LAGEOS-1 orbit. Although nearly twice the orbit radius of the ARGOS orbit, it is 327 interesting to note that the NKF position and velocity performance is nearly the same for each orbit. The MRSE value for the standard run and 100 times initial eror run are about 100 m after twelve orbits, very similar to ARGOS orbit. After twelve orbits, with 10 times the current measurement eror, the MRSE value is about 380 m, whereas with as much as 100 times the measurement eror, the MRSE value approaches 1 km. 8.5.2.3 GPS Block IA-16 PRN-01 Orbit Performance Results Figure 8-13 provides an example standard deviation envelope and NKF eror plot within the GPS satelite orbit for the thre RAC position axes, and the erors are shown to remain within the envelope. Within approximately one half of the orbit period a majority of the initial simulation eror is detected and removed. Figure 8-14 provides a similar plot for the thre RAC velocity axes. A graph of the NKF position eror magnitude along with the uncorrected orbit solution eror magnitude is provided in Figure 8-16. The graphs in the plot show that the NKF eror remains bounded and is eventualy reduced to a smal value (< 100 m), yet the uncorrected solution eror continues to grow unbounded, reaching nearly 19 km within five orbits. Table 8-5 presents the simulation performance results for the five types of runs that were investigated. The significant performance achievement of the NKF is again demonstrated with these results. After only two GPS orbits, using the pulsar-based range measurements with the NKF, the MRSE value is les than 80 m for both the standard run and 100 times initial eror run, and les than 70 m after four orbits. Velocity erors on the order of 10 m/s are also achieved after some filter setling time. 328 Providing some type of backup navigation system for GPS satelites is considered an enhancement to its overal system, especialy during unforesen events or catastrophic ground segment failures. Enhancing the ability of GPS satelites to improve their own auto-navigation solution would alow for continuous operation of the system. Although the GPS user range acuracy index (URA) would increase to 8 or 9 with this solution, it would continue to provide a vital navigation service to Earth-based systems until the ground segment can be brought back into ful operation [156]. If the NKF can only be supplied range measurements that are 10 or 100 times more pesimistic than the standard simulation values, the RMS eror and MRSE would increase for the GPS satelite, although these values are similar to both the ARGOS and LAGEOS orbits. With 10 times the measurement eror the URA would increase to 10 based upon the 312 m MRSE value, and with 100 times the measurement eror the URA would increase to 12 based upon the 1213 m MRSE. If the X-ray detector afixed to the GPS satelite were able to only view the Crab Pulsar during the entire orbit, after two orbits the MRSE would reduce to about 110 m, with the URA set at 9. Using only a single pulsar may potentialy alow reduced complexity within the navigation system if the detector can be mounted on the satelite such that the Crab Pulsar is always in the detector?s field of view. 8.5.2.4 DirecTV 2 Orbit Performance Results Table 8-6 presents the performance values for the DirecTV 2 orbit. The orbit was chosen as a representative geosynchronous orbit that is beneficial for commercial telecommunication spacecraft operators. Again, similar to the ARGOS, LAGEOS, and GPS orbits, the NKF position solution can atain RMS erors below 100 m per axis and 329 MRSE value of les than 110 m after only two orbits for the DirecTV orbit. The NKF velocity solution achieves RMS velocity erors on the order of 10 m/s. Use of this type of pulsar-based navigation system ay help to reduce ground operations cost by alowing the spacecraft to autonomously detect position erors from its nominal orbit, and correct for these smal deviations using its onboard control system. The output of the NKF navigation solution could be sent to the vehicle?s control system to fire thrusters, such as electrostatic ion or Hal efect thrusters, to maintain its orbit. As the measurement eror is increased, the performance of the NKF in this geosynchronous orbit fals off similarly as the lower Earth orbits. With 10 times the measurement acuracy, after four orbits the MRSE is 338 m and the velocity RMS eror is about 30 m/s. If 100 times measurement eror is present in the system, then the position eror increases to a MRSE of 1268 m. As studied in the GPS orbit, if only one pulsar were available for this system during the entire orbit of the DirecTV orbit, the performance of the NKF is stil quite remarkable. After only two orbits the MRSE is below 130 m, whereas after four orbits the MRSE is below 125 m. For geosynchronous vehicles that have a portion of the vehicle inertialy stabilized, a single pulsar-based navigation system would provide acurate position and velocity solutions. It is interesting to note that the velocity performance is very good in this GEO orbit, as wel as the MEO orbit of GPS, with erors on the order of 10 m/s even after initial erors as large as 1 m/s. Maintaining an acurate velocity estimate is as important as the position estimate within the NKF. Thus, with these pulsar-based measurements it is 330 significant to se that the NKF is able to blend these range measurements to correct both position and velocity. 8.5.2.5 LRO rbit Performance Results The LRO simulations were implemented in a slightly diferent manner than the previous four orbit types. The orbit dynamics and the NKF for this vehicle were implemented as a selenocentric system. Therefore, it uses the Moon as the primary gravitational efect and Earth as a third-body efect for the orbit propagator and the state transition matrix. The Moon?s potential was simulated using its known J 2 -J 5 terms [132]. However, orbits about the Moon are a chalenge to simulate due to the lumped mas of this object. Future investigations should consider a higher order terms due to the Moon?s complex gravitational potential. The pulsar-based measurements were implemented using the same SB time transfer schemes as the other four orbits, however, the NKF filter interpreted range measurements to be with respect to the Moon?s center, and not Earth?s center as in the other cases. Table 8-7 provides the performance of the NKF within the LRO orbit. This orbit about the Moon begins to demonstrate the NKF performance capabilities in deep space. For both the standard run and the run with 100 times initial condition eror, the position performance is only slightly larger than the ARGOS, LAGEOS-1, GPS, and DirecTV 2 geocentric orbits, with 165 m MRSE for the standard LRO run after sufficient filter setling versus about 100 m for the other runs. The velocity performance for these LRO runs is much more similar to the ARGOS LEO case than the other higher Earth orbit cases. 331 To produce the LRO simulation runs for the 10 times and 100 times of the measurement acuracy, two new considerations were applied. The measurement residual threshold limit was reduced and runs that converged replaced runs where the filter diverged. By reducing the threshold limit from 5 to 2, the LRO NKF esentialy ignores measurements that could cause large efects on the state erors. However, this also reduces the total number of measurements procesed within each run, as measurements with residuals higher than this limit were ignored. This filter design trade-off must determine the proper threshold limit versus number of measurements to achieve best overal performance. By choosing limit value of 2, many of the measurements that would have produced overly large or poor state adjustments were not procesed through this filter, which asisted the NKF?s improved performance. It is important to consider that stability of the NKF is reduced as the measurement acuracy is reduced [65]. Divergence of the state erors can happen if the NKF reduces the estimate of the state covariances to low values while the actual erors are stil large. In this scenario, the NKF?s solution can diverge causing the state erors to grow unbounded while the NKF covariance estimate remains reasonably smal. During simulated LRO runs, this scenario was most evident in the 100 times measurement acuracy runs. To produce the reported performance values, two simulation runs out of the original five were replaced by two runs that produced stable, converging results. These simulation runs used diferent random number generator seds in order to produce the new results. Although the current implementation of the LRO NKF could diverge if these original set of measurements were procesed, for this analysis it was more important to produce tangible performance results than test the stability of an individual run. In future filter 332 implementations, the stability of the NKF could be improved by using various techniques, such as a fading or finite memory filter, adding proces noise, or reviewing and improving the state dynamics and measurement models to ensure best and most realistic performance [65]. In cases where the measurements are not as acurate as the expected dynamics (as in the case of the 100 times of measurement acuracy), the NKF stability must be verified. Another consideration is that part of the divergence was brought about due to the unique combination of the LRO orbit dynamics and the specific geometrical distribution of the thre chosen pulsars. Adding additional pulsars along diferent line-of-sight directions would improve the geometry of the signals (GDOP), which would also improve performance. The reported values of Table 8-7 are those for al the runs that remained stable throughout the simulation duration. When measurement eror is increased by 10 times the standard values, the performance of the NKF for the LRO orbit is on the order of the other runs, with 437 m MRSE for LRO position versus 350 m for the other orbits. The erors for 100 times the measurement acuracy is roughly thre times the value of the other orbit runs. This is largely due to the significant along-track eror in the LRO orbit runs, which appears to be created by the larger radial velocity eror. Future investigations could consider methods to reduce this velocity eror, potentialy considering producing measurements at a much diferent rate than the 500 s current rate. This would alter each measurement?s individual acuracy, with the intent of improving overal performance. It is likely that additional filter parameter tuning may be required for the LRO orbit analysis. Increasing the NKF?s proces noise to compensate for any potential dynamics modeling erors would help improve the performance somewhat. However, increasing 333 this noise also limits the NKF?s ability to proces good measurements since the covariance values are kept high with higher proces noise. Although lacking the high-order time transfer expresions from this disertation research, an early analysis compared radar range measurement to first-order pulsar-based range measurements for an interplanetary trajectory to Pluto. This early analysis showed that a pulsar-based system performed wel for distant misions [186]. With this LRO mision analysis, most of the results demonstrate the potential benefits of this pulsar- based navigation system for misions above the GPS constelation orbit and for continuous operation perhaps behind the Moon, where radar contact from Earth would be unavailable. Dep space and interplanetary misions would be significant beneficiaries of this navigation system?s performance. 334 Figure 8-11. Position standard deviation and eror for ARGOS orbit. Figure 8-12. Velocity standard deviation and eror for ARGOS orbit. 335 Figure 8-13. Position standard deviation and eror for GPS orbit. Figure 8-14. Velocity standard deviation and eror for GPS orbit. 336 Figure 8-15. Uncorrected and NKF position eror magnitude for ARGOS orbit. Figure 8-16. Uncorrected and NKF position eror for GPS orbit. 337 Table 8-3. ARGOS Simulation Performance Values. Entire Simulation Run After Two Orbits Filter Setling After Twenty Orbits Filter Setling Simulation Type Parameter NKF Eror RMS NKF Cov. Mean NKF Eror RMS NKF Cov. Mean NKF Eror RMS NKF Cov. Mean Position: R (m) A C 38 19 54 46 171 96 25 105 53 34 15 91 17 79 27 25 126 69 Velocity: R (m/s) A C 0.1 0.034 0.056 0.17 0.04 0.09 0.097 0.026 0.05 0.15 0.034 0.093 0.074 0.017 0.028 0.12 0.025 0.071 Standard Run MRSE (m) 130 12 81 Position: R (m) A C 835 854 101 268 46 324 29 320 240 37 267 178 17 91 38 26 145 85 Velocity: R (m/s) A C 1.2 0.52 0.71 0.59 0.19 0.31 0.32 0.030 0.25 0.27 0.038 0.18 0.087 0.018 0.039 0.14 0.026 0.087 10 Times Initial Eror MRSE (m) 150 354 91 Position: R (m) A C 106 481 15 165 62 205 9 423 15 148 579 202 87 352 127 127 50 187 Velocity: R (m/s) A C 0.46 0.1 0.12 0.58 0.16 0.21 0.39 0.10 0.12 0.53 0.15 0.21 0.32 0.090 0.13 0.46 0.13 0.19 10 Times Measurement Eror MRSE (m) 504 44 351 Position: R (m) A C 127 2853 103 29 3535 246 90 2738 103 273 3439 246 63 2165 101 259 2524 247 Velocity: R (m/s) A C 2.9 0.09 0.1 3.6 0.29 0.25 2.8 0.07 0.1 3.5 0.28 0.25 2.2 0.063 0.10 2.6 0.27 0.25 10 Times Measurement Eror MRSE (m) 2549 2392 1098 338 Table 8-4. LAGEOS-1 Simulation Performance Values. Entire Simulation Run After Two Orbits Filter Setling After Twelve Orbits Filter Setling Simulation Type Parameter NKF Eror RMS NKF Cov. Mean NKF Eror RMS NKF Cov. Mean NKF Eror RMS NKF Cov. Mean Position: R (m) A C 5 10 120 46 91 129 18 53 10 23 69 10 17 57 81 20 63 74 Velocity: R (m/s) A C 0.047 0.019 0.057 0.045 0.017 0.060 0.021 0.082 0.052 0.027 0.010 0.047 0.023 0.076 0.037 0.026 0.085 0.034 Standard Run MRSE (m) 169 127 101 Position: R (m) A C 759 512 1426 261 28 651 19 54 121 24 69 106 17 58 83 20 64 75 Velocity: R (m/s) A C 0.36 0.25 0.45 0.21 0.10 0.27 0.021 0.087 0.058 0.028 0.010 0.049 0.023 0.078 0.039 0.026 0.086 0.035 10 Times Initial Eror MRSE (m) 1691 136 102 Position: R (m) A C 149 424 187 159 462 373 96 289 198 12 382 369 91 268 246 96 346 348 Velocity: R (m/s) A C 0.17 0.062 0.087 0.19 0.068 0.17 0.1 0.045 0.092 0.15 0.052 0.17 0.10 0.042 0.1 0.14 0.04 0.16 10 Times Measurement Eror MRSE (m) 497 375 378 Position: R (m) A C 286 201 72 42 2635 407 23 1745 73 37 2403 407 22 139 78 34 187 406 Velocity: R (m/s) A C 1.0 0.1 0.03 1.2 0.19 0.19 0.80 0.10 0.034 1.1 0.17 0.19 0.60 0.10 0.036 0.82 0.16 0.19 10 Times Measurement Eror MRSE (m) 2185 1631 834 339 Table 8-5. GPS Block IA-16 PRN-01 Simulation Performance Values. Entire Simulation Run After Two Orbits Filter Setling After Four Orbits Filter Setling Simulation Type Parameter NKF Eror RMS NKF Cov. Mean NKF Eror RMS NKF Cov. Mean NKF Eror RMS NKF Cov. Mean Position: R (m) A C 138 138 140 103 149 135 24 59 40 47 83 62 23 5 31 47 82 56 Velocity: R (m/s) A C 0.024 0.012 0.013 0.023 0.016 0.020 0.074 0.031 0.058 0.012 0.05 0.091 0.072 0.028 0.045 0.012 0.05 0.081 Standard Run MRSE (m) 241 7 67 Position: R (m) A C 15 2032 2545 419 916 1025 24 59 43 47 83 64 23 5 3 47 82 56 Velocity: R (m/s) A C 0.25 0.35 0.46 0.16 0.23 0.27 0.074 0.031 0.062 0.012 0.05 0.093 0.073 0.028 0.048 0.012 0.05 0.082 10 Times Initial Eror MRSE (m) 3438 78 68 Position: R (m) A C 41 530 349 314 574 47 82 267 264 129 398 361 72 231 28 124 376 328 Velocity: R (m/s) A C 0.093 0.041 0.050 0.08 0.039 0.069 0.03 0.012 0.038 0.050 0.018 0.053 0.031 0.010 0.03 0.048 0.017 0.048 10 Times Measurement Eror MRSE (m) 768 38 312 Position: R (m) A C 906 2601 326 86 2807 1071 51 1598 373 428 2090 105 507 178 43 390 180 1035 Velocity: R (m/s) A C 0.36 0.1 0.047 0.41 0.1 0.16 0.20 0.074 0.05 0.29 0.061 0.15 0.14 0.073 0.064 0.26 0.056 0.15 10 Times Measurement Eror MRSE (m) 2580 152 1213 Position: R (m) A C 148 14 181 104 185 292 24 62 89 45 124 23 23 63 85 45 124 232 Velocity: R (m/s) A C 0.025 0.013 0.023 0.029 0.016 0.043 0.083 0.029 0.013 0.018 0.053 0.034 0.084 0.029 0.012 0.018 0.052 0.034 Using Only One Pulsar MRSE (m) 274 107 103 340 Table 8-6. DirecTV 2 Simulation Performance Values. Entire Simulation Run After Two Orbits Filter Setling After Four Orbits Filter Setling Simulation Type Parameter NKF Eror RMS NKF Cov. Mean NKF Eror RMS NKF Cov. Mean NKF Eror RMS NKF Cov. Mean Position: R (m) A C 16 235 192 140 187 149 48 78 53 78 9 75 51 87 50 78 9 71 Velocity: R (m/s) A C 0.015 0.01 0.012 0.016 0.012 0.013 0.057 0.028 0.040 0.086 0.043 0.05 0.060 0.030 0.037 0.085 0.043 0.051 Standard Run MRSE (m) 343 104 108 Position: R (m) A C 154 2934 237 41 187 101 48 78 56 78 9 76 51 87 51 78 9 71 Velocity: R (m/s) A C 0.21 0.34 0.27 0.1 0.19 0.18 0.057 0.028 0.043 0.086 0.043 0.056 0.061 0.030 0.038 0.085 0.043 0.052 10 Times Initial Eror MRSE (m) 3946 107 10 Position: R (m) A C 428 512 403 404 63 475 90 32 208 178 431 307 8 35 161 176 423 287 Velocity: R (m/s) A C 0.047 0.020 0.028 0.051 0.026 0.035 0.02 0.056 0.015 0.029 0.01 0.02 0.02 0.05 0.012 0.028 0.01 0.021 10 Times Measurement Eror MRSE (m) 78 37 38 Position: R (m) A C 165 2642 131 1045 2675 1586 216 1754 1232 42 1949 1395 183 1820 896 409 1867 1281 Velocity: R (m/s) A C 0.20 0.062 0.094 0.21 0.063 0.12 0.13 0.014 0.090 0.13 0.029 0.10 0.13 0.012 0.06 0.13 0.028 0.093 10 Times Measurement Eror MRSE (m) 305 1827 1268 Position: R (m) A C 162 240 201 140 252 286 46 98 90 79 175 23 41 93 90 79 176 235 Velocity: R (m/s) A C 0.015 0.01 0.013 0.020 0.012 0.023 0.070 0.027 0.06 0.014 0.04 0.017 0.06 0.024 0.06 0.014 0.04 0.017 Using Only One Pulsar MRSE (m) 343 127 123 341 Table 8-7. LRO Simulation Performance Values. Entire Simulation Run After Two Orbits Filter Setling After Twenty Orbits Filter Setling Simulation Type Parameter NKF Eror RMS NKF Cov. Mean NKF Eror RMS NKF Cov. Mean NKF Eror RMS NKF Cov. Mean Position: R (m) A C 63 207 37 92 270 28 51 190 31 75 243 24 39 17 20 62 216 19 Velocity: R (m/s) A C 0.16 0.049 0.032 0.21 0.075 0.025 0.14 0.04 0.027 0.18 0.064 0.021 0.14 0.034 0.017 0.16 0.053 0.016 Standard Run MRSE (m) 217 196 165 Position: R (m) A C 148 1647 634 469 673 74 106 310 34 12 304 30 51 196 18 76 236 21 Velocity: R (m/s) A C 2.0 0.6 0.25 0.6 0.31 0.081 0.21 0.091 0.030 0.20 0.096 0.026 0.14 0.045 0.015 0.17 0.065 0.018 10 Times Initial Eror MRSE (m) 230 323 186 Position: R (m) A C 134 935 151 26 1438 163 16 838 150 243 139 157 12 64 134 21 1087 128 Velocity: R (m/s) A C 0.79 0.10 0.13 1.2 0.2 0.14 0.71 0.097 0.13 1.1 0.21 0.14 0.54 0.094 0.12 0.89 0.19 0.1 10 Times Measurement Eror a MRSE (m) 87 74 437 Position: R (m) A C 287 7632 98 464 8264 26 287 7868 98 434 8326 26 357 976 96 379 5875 265 Velocity: R (m/s) A C 6.6 0.18 0.085 7.1 0.31 0.23 6.8 0.18 0.084 7.2 0.30 0.23 8.5 0.2 0.082 5.1 0.27 0.23 10 Times Measurement Eror a MRSE (m) 6252 6346 3414 a Measurement residual threshold reduced from 5 to 2. 342 Chapter 9 Conclusions ?The future influences the present just as much as the past.? ? Friedrich Nietzsche 9.1 Results This disertation has presented a new spacecraft navigation methodology based upon the use of variable celestial X-ray sources. These sources are shown to be useful for time, atitude, position, and velocity determination. While numerous variable celestial source types can be used to aid spacecraft navigation, this work has emphasized a subset of periodic, stable, and unique sources known as neutron stars, or pulsars. Pulsars emit radiation throughout a broad range of the electromagnetic spectrum from the radio to the gama-ray bands with periods ranging from a few miliseconds to thousands of seconds. This disertation examines the clas of pulsars that emit in the X-ray band, since these can be detected by X-ray sensors on the order of 1-m 2 that are of practical dimensions for many vehicle designs. There are significant advantages of these variable celestial sources that are apparent from the discussions within the text. Since these sources are visible for sufficient observation durations due to their vast distances from the solar system, navigation 343 solutions can be computed anywhere in solar system. This spacecraft navigation concept is not limited by the line-of-sight of Earth observation stations or fixed navigation beacons, thus, it can function in many locations where existing methods cannot operate, such as on the far-side of planets and moons. There are numerous sources available, and several of these sources can produce high acuracy measurements. It is projected that with continued sky observations, new sources wil be discovered that wil provide additional capability. As with any system, however, limitations remain with this navigation system that must be addresed through either continued research or other augmentation. The acuracy of the line-of-sight data for each source may limit their use over large distances from the inertial origin. The intensity of the signal from many of the sources is low, which requires long observation times. Intrinsic characteristics of sources make their signal procesing a chalenge. The transient efects of several sources make their availability infrequent. Rare flares and bursts from various sources may potentialy produce false identifications. The timing glitches that have been detected in several sources require frequent monitoring of sources and intermitent updates to source almanac data. Most of these isues suggest that the characteristic parameters of sources needs to be further investigated within the astrophysical and astronomical communities in order to determine the best possible known values. The main focus of this disertation research has concentrated upon the aspects of position, velocity, and time determination proceses, and primarily has investigated LEO, MEO, GEO, and lunar orbits. These were selected because of the wealth of previous research and demonstrations on atitude determination using celestial sources, and the 344 selection of candidate orbits that would alow verification of the produced results. It is anticipated that the navigation performance of interplanetary trajectories would have similar performance since the analysis methods and algorithms are applicable throughout the solar system. The entire methodology for using variable celestial X-ray sources is developed within the disertation including information about source location and parameters, source time of arival modeling and acuracy, and time transfer measurements within an inertial frame that incorporates important general relativistic corrections. With the fundamental pulsar pulse physics as a foundation, various navigation approaches are presented including absolute and relative position, and corrections to estimated navigation solutions. In terms of absolute position determination, new pulse phase cycle ambiguity algorithms have been presented to solve the lost-in-space problem when a spacecraft has no a priori knowledge of its location within the thre-dimensions of the solar system. Using a database of X-ray pulsars, with their known angular positions and detailed models of their pulse time of arival properties, results indicate that by using phase crossings from multiple pulsars, these methods can determine an initial thre-dimensional position solution to within several tens of kilometers. Since no prior information about the spacecraft?s position is known, these absolute position determination algorithms can be implemented based upon inteligent choices of the suspected orbit, such as geocentric, selenocentric, or heliocentric orbits. After the initial procesing mode, this position solution can be refined through an iterative resolution proces, or be provided as an initial state to other position update techniques presented in this disertation. This absolute 345 position determination method is significant since it suggests that pulsars provide a scheme for spacecraft to autonomously determine an estimate of its thre-dimensional location. Results from the delta-correction method when coupled to the recursive extended navigation Kalman filter appear to be even more profound in terms of thre-dimensional position and velocity determination. Asuming 500 s observation lengths of individual pulsars, detailed numerical simulations of several candidate LEO, MEO, GEO, and lunar orbits suggest this approach is able to determine a spacecraft?s position to within 100 m MRSE and its velocity to within 10 m/s RMS. Furthermore, comparisons against actual X-ray detector data from the USA experiment indicate that existing technology and pulsar data knowledge can already produce range estimates within one or two orders of magnitude of the simulated results. Asuming improved detector capabilities and photon timing technologies, it is projected that newly developed navigation systems wil be able to achieve this simulated navigation performance for many spacecraft misions. However, even with the chalenges imposed by the various stated isues, the potential benefits of the proposed system could be significant and warant further investigation and research. If only a fraction of the analytical acuracy determined by this research could be achieved, many future spacecraft misions would stil be enhanced by the added capability provided by this system. With the currently proposed crewed misions to the Moon and Mars within the next several decades [5], the autonomous navigation capabilities aforded by this new system improves mision survivability and succes. Fortunately, this method would not require the enormous infrastructure and cost of producing and implementing navigation beacon satelite constelations centered about 346 these planets or the entire solar system. Also, as space travel to these planetary bodies becomes more frequent, the ability for a spacecraft and its crew to determine their own full navigation solution helps reduce mision cost and improves exploration capabilities. Hence, this research has ilustrated that variable celestial sources that emit in the X- ray band may serve as possible inertialy referenced navigation beacons for spacecraft time, atitude, position, and velocity determination throughout the solar system. While the techniques presented have primarily focused upon position and velocity, the additional capability of using these sources for acurate atitude determination, as wel as potentialy correcting spacecraft clock drift, demonstrate that a full navigation solution is atainable by this system. Although the performance results are significant, it is important to point out that this is only a preliminary investigation into the overal feasibility to variable celestial sources for spacecraft navigation. Additional analyses in terms of detailed mision and system studies must yet be pursued to develop this concept into an operational system. 9.1.1 Navigation System Comparison A variable celestial source navigation system can be used to complement current day systems that are able to use the GPS, GLONAS (and other human-made global navigation systems) and/or DSN. This system could serve as a back up in the event of failures or catastrophes of human-made systems. Many recent algorithmic techniques implemented for GPS/GLONAS could conceivably be implemented within a navigation system using sources with pulsed radiation, thus research on both systems benefits one another. For spacecraft within Earth orbit above the GPS constelation, such as a highly eliptical orbit, this secondary system could supplement obscured or unavailable GPS 347 data. The benefits of the DSN system providing acurate range and range-rate information from Earth observation stations may also be realized with systems using these sources. Combining measurements from these celestial sources with DSN range observations would reduce erors along the transverse orbit axes. Although the initial intent of a variable celestial X-ray source-based navigation system would be to complement existing human-made navigation systems and be used in regions where human-made systems are inacesible, comparisons of the capability betwen these two types of systems are inevitable. Table 9-1 provides a list of various aspects of both types systems, based upon current known information. Each type of system has advantages and limitations based upon the availability of their signal and the acuracy of the overal solution. It is projected here that eventualy new spacecraft navigation systems wil be developed that blend information from each of the GPS/GLONAS, DSN, and X-ray source navigation systems in order to compute the best overal navigation solution. An onboard Kalman filter that propagates an orbit solution and incorporates measurements from each system could produce navigation solutions with greater performance than any of the single systems alone. 348 Table 9-1. Navigation System Comparison [88, 156, 177]. Characteristic GPS & GLONAS DSN Variable Celestial X-ray Sources Number of Sources (Design) 24 Satelites 3 Ground Locations >50 Visible Sources (at spacecraft) ~12 Satelites (LEO) 1 to 2 In View (due to Earth?s rotation) 1 ? Several (Detector FOV) Signal Wavelength GPS L1: 0.1903 m L2: 0.242 m GLONAS L1: 0.185 ? 0.187 m L2: 0.14 ? 0.146 m Older System: 0.0357 m Newer System: 0.1303 m X-ray Band 10 -1 ? 10 -8 m Cycle/Pulse Period GPS L1: 6.35E-10 s L2: 8.15E-10 s GLONAS L1: 6.24E-10 s L2: 8.03E-10 s Older System: 4.35E-10 s Newer System: 1.19E-10 s ~0.01 ? 10 6 s Solution Acuracy Time Range Position ~ 15 ns (1-?) 0 ? 614 m (URA 0-14) < 10 m (SEP, SPS) < 10 ?s 2 m per AU 1 ? 10 km < 1 ?s ~ 10 m ~ 10 m (MRSE) Usable Signal LEO - MEO LEO ? Heliopause Interstelar Isues Atmospheric Efects Multipath High Power Signal Almanac Required Human-Controled Atmospheric Efects Line Of Sight Only Signal Fades with Distance Scheduling & Cordination Human-Controled Above Atmosphere Line Of Sight Only Low Intensity Signal Almanac Required Universe-Controled 9.2 Sumary of Contributions As the various chapters within this disertation demonstrate, the investigated methods to determine navigation solutions from variable celestial sources have fulfiled the goals set forth in Chapter 1. Although there are stil more studies required to investigate its full potential, this research has added to the knowledge of the development of this concept. Specificaly, there are several notable contributions of this work, which include: ? Variable Celestial X-ray Source Catalogue (Chapter 2) A comprehensive source catalogue has been asembled from a wide variety of articles and databases, and represents a complete database of X-ray sources 349 with characteristics conducive to spacecraft navigation. Numerous sources are listed in this catalogue and their parameter data can be used to develop the navigation concepts. ? Pulse Time of Arival Modeling and Range Acuracy (Chapter 3) New techniques were developed using the SNR equations to analyze the pulse TOA and its acuracy. These techniques, as wel as the new source quality figure of merit, provides methods to evaluate the catalogued sources for diferent aspects of navigation. ? Solar System Time Transfer Equations (Chapter 4) Existing methods of pulsar pulse timing were investigated and a new time transfer equation for use within the entire solar system was derived. This equation demonstrates the theoretical potential of computing photon arival times at the sub-nanosecond level, and simplified forms of the equation with reduced acuracy are provided. ? Absolute and Relative Position Determination (Chapter 6) New algorithms were developed to determine the absolute position of a spacecraft. No current single type of onboard system has the ability to independently compute the absolute position of a deep space vehicle. The methods use phase measurements from multiple pulsars to determine the unknown number of whole phase cycles betwen a vehicle and a chosen inertial reference location. Once resolved, the phase measurement can be converted to range diferences in order to calculate the absolute position of a spacecraft. These new schemes also demonstrate the ability to calculate highly 350 acurate relative position information. With multiple detectors aboard a vehicle, atitude of the vehicle could also be determined using these measured phase diferences, although methods using images of these sources similar to optical sources may provide a more direct path to creating new atitude sensors. With additional procesing, vehicle velocity can be detected based on phase measurements from multiple sources. ? Delta-Correction Position Estimation (Chapter 7) Methods to correct a previously existing estimate of position or orbit solution using measurements from these celestial sources are developed. These schemes provide imediate implementation approaches that can utilize current day technology. The empirical validation of this technique has been demonstrated using actual recorded spacecraft data. ? Navigation Kalman Filter and Performance Analysis (Chapter 8) From the delta-correction techniques proposed in Chapter 7 and using the new time transfer equations of Chapter 4, a recursive extended Kalman filter was designed to blend the spacecraft dynamics and the pulsar-based range measurements. Simulations were produced to demonstrate the significant potential of this system. By varying both the eror in the initial vehicle state and the pulsar-based range measurement, investigations were pursued to determine which isues contribute to the navigation performance values. The filter design primarily incorporates position and velocity states of the vehicle, but can also include spacecraft clock time states to determine al thre parameters. 351 9.3 Future Research Recommendations Although this disertation presents numerous analyses and results on the various aspects of spacecraft navigation, no single unit of research can addres al the isues for the scope of a navigation system such as the one described here. Therefore, to asist future research, below are several recommended areas of research to be pursued to further enhance the analysis of utilizing these sources for navigation. 9.3.1 Higher Fidelity Simulation The orbit dynamics simulation was developed to sufficiently portray al the significant perturbation efects foresen to impact the chosen mision analyses. Although al atempts were made to ensure the dynamics were as acurate as possible, below are several efects that should be implemented for further analysis. The current simulation implements a fixed time step for the numerical integration of al orbits. Although the current procesing time is reasonable for analysis, investigations of orbits high above Earth or highly eliptical orbits would benefit from integration schemes that can use a variable step integrator in order to reduce procesing time. Several such variable step integration schemes are provided in the literature. High-order gravitational potential models should be provided as an option for the simulated vehicle dynamics. The current use of zonal terms to describe Earth?s gravitational potential ignores the sectorial and teseral term efects. Although these are only higher order efects, the true motion of a space vehicle is afected by even these slight perturbations and over time the simulation would grow in eror compared to recorded truth data. Various high order Earth gravitational models exist, such as the NASA Joint Gravitational Model (JGM-2, degre and order 70) and the NASA and 352 National Imagery and Mapping Agency (NIMA) Earth Gravitational Model (EGM96, degre and order 360). Additionaly, higher order gravitational models of other planetary bodies, such as the Moon and Mars, are available or are in development. These models could be incorporated into the simulation for improved overal acuracy. For near-Earth applications, more acurate atmospheric models would enhance the analysis of vehicles that are significantly afected by drag. More complex models such as the Jachia-Roberts model or the Rusian GOST model could replace the Haris-Priester model used by this simulation. As they become improved, atmospheric models of planets should also be implemented within this simulation for navigation analysis in orbits about those bodies. To remain valid, these more sophisticated atmosphere models require more acurate spacecraft parameters, such as coeficients of drag and mas. 9.3.2 Photon-Level Simulation The simulation currently produces source pulse TOA measurements based upon specified observations. Future versions of the simulation should pursue the analysis more deeply and implement the measurements of the single photon level ariving at the spacecraft. Although the measurement to the Kalman filter may remain as a single TOA measurement, procesing at the finer photon-level may eventualy produce deper integration schemes within the navigation system, potentialy leading to improved navigation performance. 9.3.3 Source Observation Scheduling Due to the importance of coordinating highly acurate pulsar TOA measurements with the availability of the source?s signal, new methods of scheduling the observations 353 of sources should be pursued. A predictor program, based on the navigation system?s own solution, could be developed to provide the system a means to schedule each source?s observation based upon their predicted availability. Additionaly, schemes to switch betwen fixed observations times and indefinite observations for improved acuracy should be investigated. During the development of a vehicle?s mision, simulations using these prediction programs could asist in the analysis of when specific sources would be available and how to optimize their observations for best overal navigation solutions. 9.3.4 Doppler Velocity Measurement Much of the disertation research has focused on time and position determination from the pulsed radiation of these celestial sources. As a spacecraft advances towards or recedes away from a particular source during its natural orbital revolution about a planetary body, Doppler efects wil become apparent in the received signal from the source. This efect is currently removed from the photon arival times during their transfer to the inertial origin. Alternatively, spacecraft velocity could be measured directly from the observed Doppler efect. Future planned investigations should determine the acuracy of the velocity measurement. 9.3.5 Kalman Filter Models The existing orbital dynamics models and the Kalman filter state transition matrix provide sufficient fidelity for the analysis pursued within this disertation. Future implementations of these dynamics wil be enhanced to include higher fidelity, with the intent on matching the true dynamics of the space vehicles as closely as posible. As the 354 gravitational potential models are increased from those currently used, in order for the Kalman filter to track this dynamics correctly, the state transition matrix must be appropriately modified to include the efects of those new terms. For example, higher order zonal terms (J 7 and greater) may be included, and the sectorial and teseral term efects should also be included. If the simplification of using only the first derivative within the state transition matrix is no longer valid for this higher order dynamics, then 2 nd order derivative efects must also be added to the state transition matrix. As more higher order perturbation efects are added to the filter dynamics, it is asumed that the improved simulated dynamics wil track the true vehicle dynamics to greater precision. These improved dynamics models should alow a reduction in the NKF proces noise and covariances, which would improve the overal performance of the filter. Although analytical models are straightforward to implement, testing of these higher order terms are more chalenging in the real-world environment. Thus, new methods to test these models while on-orbit must be devised. 9.3.6 Pulsar Observation Models Existing methods to determine pulsar pulse parameters, such as the pulse timing model parameters, pulse TOAs, and binary orbit parameters, may benefit from the dynamic gain computations of a Kalman filter implementation in contrast to the existing fixed gain weighted least-square techniques. The Kalman filter could include dynamics of the observation station, whether ground-based or space-based, to reduce the efects of these dynamics on determining these parameters. The comparison of a measured pulse profile with a standard template profile may also be implemented directly into a Kalman filter scheme. Any future research into refining the estimates of these important 355 parameters, and implementing these new schemes such that real-time procesing can be incorporated into navigation systems, would enhance the development of these systems and asist future astrophysical science observations. 9.3.7 Pulsar Range Measurement Sensitivity Based upon the SNR equations, the sensitivity of the range measurement acuracy for pulsars could be determined with respect to the individual source parameters. The SNR equation may also be expanded to include specific detector characteristics, such as photon detection eficiency and X-ray background rejection. The sensitivity of source parameters versus detector characteristics could be investigated to determine which terms produce a greater efect on range acuracy. 9.3.8 Multiple Detector Systems Using a single detector limits the amount of observation time for multiple sources. Systems that utilize multiple detectors, either separate or combined within one unit, can provide additional benefits and improvements to the navigation solution. If enough detectors are onboard a vehicle, simultaneous observations of sources could be generated, and absolute position determination could be acomplished. A system using coarse and fine resolution detectors, one to provide les acurate, short term, frequent measurements and another to provide high acuracy, long term, infrequent measurements, would generate an overal high quality, continuous navigation solution. 9.3.9 Previous Celestial Source Navigation Methods Existing methods using visible celestial sources for diferent aspects of spacecraft navigation could be investigated for use by variable celestial sources. The methods of 356 determining position relative to a planetary body either through source occultation or source elevation angles should be further researched in order to provide viable backup algorithms for verifying navigation solutions. However as noted, aeronomy research must be continued for each of the planetary bodies with appreciable atmospheres for these types of methods to be succesful. 9.3.10 Mission Analysis Further spacecraft mision analysis should be continued to investigate the utility of a navigation system using these variable celestial sources within various orbits, including future interplanetary misions. Misions to support the continued exploration of the Moon and Mars are of particular current interest. While in orbit about these bodies, the loss of contact with spacecraft during a vehicle?s occultation behind these bodies is an important opportunity for this proposed system to provide a continuous navigation capability. An interesting orbit to analyze would be the stable Lagrange points (L4 and L5) within the Earth-Moon system for an orbiting variable celestial source base station. Also, the Sun- Earth system L2 Lagrange point, such as that proposed for the James Webb Space Telescope orbit, would be of interest for future astronomy misions. Use of the system proposed here may alow autonomous navigation and control at these distant locations. For future misions to the outer planets, analysis of the potential performance of this celestial-based navigation system may asist in reducing lifetime mision costs. For misions that may extend beyond the outer planets, used to investigate the outer solar system regions and perhaps traverse the heliopause, applications of this navigation system ay only require infrequent vehicle contact with Earth ground stations. 357 9.3.11 Additional Applications The use of X-ray pulsars, and other variable X-ray sources, is not limited to single spacecraft navigation. Based upon the research pursued during this disertation, other technological concepts used for navigation and new applications can be envisioned utilizing these types of sources. Several of these new concepts are described below. ? Diferential/Relative Position: An orbiting base station may be used to detect variable source signals and to broadcast pulse arival times signal erors to other spacecraft. This base station could also be used to monitor and update pulsar almanac information. Ideal orbiting locations for these base stations include geosynchronous orbits, and Sun-Earth and Earth-Moon Lagrange points. Receiving spacecraft are able to navigate with improved information relative to the base station. Relative positioning from a lead vehicle could also be implemented in a satelite formation-flying concept. ? GPS System Time Complement: Pulsar-based systems could be used as time- only reference systems, such as for aiding high-data rate communication betwen satelites and ground stations. ? Radio-based Systems on Earth and in Space: Although the atmosphere absorbs X-ray signals, navigation systems for Earth applications based upon celestial radio signals could be pursued. Using these sources as celestial clocks and/or navigation aides would be a viable alternative to X-ray sources, as long as an application could support large antennas, such as aboard a large naval vesel or a solar-sail spacecraft. 358 ? Planetary Rovers: With rovers continuing to be suggested for future planetary misions, these celestial sources could provide a navigation system for exploratory mobile vehicles. Upon landing, the rover?s base station could monitor pulsar signals and provide a relative positioning system for rovers that navigate over the surface terain. Planetary bodies with a thin or negligent atmosphere, including Earth?s Moon or Mars, are good candidates for this method. ? X-ray Communication: With increased X-ray detector research for development of this navigation system, new methods to transmit and receive modulated X-ray pulses could be pursued. These transmited modulated signals could cary information. Due to the direct line-of-sight requirements for X-ray photons, secure communication links may be established. ? Enhanced Planetary Ephemeris: If base stations are placed upon planetary bodies and data is compared to measured data on Earth, methods to determine acurate body location could be established. This information would provide improved ephemeris data for these bodies. 359 9.4 Final Sumary Celestial object navigation methods, which use sources at great distance from Earth, wil continue to benefit future space system architectures. X-ray emiting rotation- powered and acretion-powered pulsars represent a smal, but important, subset of al possible variable celestial X-ray sources. These unique sources provide pulsed radiation that can be utilized in an X-ray based navigation system for spacecraft. Given their vast distances from Earth, these sources provide good signal coverage for space vehicle operations near Earth, on to the Moon, on to Mars, throughout the solar system, and conceivably, the Galaxy. Although isues with these sources exist that makes their use complicated, further algorithmic and experimental study may addres these complications. Also, by complementing existing systems, such as GPS or DSN, this new system can increase the overal navigation performance of many spacecraft misions. Hence, this disertation has ilustrated the potential of these objects to determine acurate vehicle position, velocity, and time is significant towards increased autonomous vehicle operation. With the capability of generating a complete navigation solution, including time, position, velocity, atitude, and atitude rate, variable celestial X-ray sources remain atractive for creating a new celestial-based spacecraft navigation system. Once implemented, this system may eventualy be refered to as the X-ray pulsar positioning system (XPS) or in more general terms, the X-ray navigation (XNAV) system. 360 Appendices Apendix A Suplementary Matter A.1 Constants and Units Table A-1. Fundamental Constants [16, 183]. Quantity Symbol Value Units Sped of Light (vacum) c 29792458 ms Universal Gravitational Constant G 6.67259?10 -1 m 3 kg!s 2 () Planck Constant h 6.626075?10 -34 J! Thompson Cros-Section 8!r e 2 3 6.652?10 -25 cm !2 Stefan-Boltzman Constant ! 5.67051?10 -5 ergcm 2 !K 4 !s ( ) Table A-2. Astronomical Constants [16, 183]. Quantity Symbol Value Units Astronomical Unit AU 1.49597870?10 1 m Light Time 1 AU AULTSEC 49.04782 s Light Year ly 9.461?10 15 m Parsec pc 3.086?10 16 3.262 ly Heliocentric Gravitational Constant ? 1.32712438?10 20 m 3 s 2 Radius of Sun R 6.96?10 8 m Geocentric Gravitational Constant E 3.98605?10 14 Radius of Earth 6378136 m Lunar Gravitational Constant M 4.90279?10 6 Radius of Mon 173800 m 361 Table A-3. Unit Conversions [183]. Quantity Units Conversion Value Angstrom ? = 1.0?10 -10 m Electron Volt eV = 1.6021917?10 -19 J = 1.6021917?10 -12 erg keV = 1.6021917?10 -9 erg Erg (= g?cm 2 /s) erg = 1.0?10 -7 J Jansky Jy = 1.0?10 -26 Wm 2 Hz Jy = 1.0?10 -23 ergs!cm 2 !Hz ( ) Steradian sr = 3.283?10 3 deg 2 = 4.25?10 10 arcsec 2 Proper Motion masyr = 1.536282?10 -16 rads Arcsecond (arcsec) as = 1/360 deg = 1/(pi*20) rad Day d = 24 hr = 140 min = 8640 s Julian Year = 365.25 d = 876 = 315760 A.1.1 Additional Notes 1Joule!1N"m!1kg"m 2 s 2 1Watt!1Js!1kg"m 2 s 3 In Degres:Minutes:Seconds (D:M:S): 1 ?second? = 1 arcsec In Hours:Minutes:Seconds (H:M:S): 1?second? = 15 arcsec 362 A.2 Time Standards and Coordinates Description of systems from Explanatory Supplement to the Astronomical Almanac [183] and Valado [213]. A.2.1 Terrestrial Time Standards ? TAI: Temps Atomique International International Atomic Time Based upon cycles of a high-frequency electrical circuit maintained in resonance with Cesium-133 atomic transition. ? UT: Universal Time Mean solar time at Grenwich ? UT0: Observation of UT at a particular observation/ground station ? UT1: UT0 corrected for polar motion, so time is independent of station location ? UT2: UT1 corrected for seasonal variations ? UTC: Coordinated Universal Time Derived from atomic time, follows UT1 within ?0.9s Bridge betwen TAI and UT1 A.2.2 Coordinate Time Standards ? T: Terestrial Time = TDT (Terestrial Dynamical Time) 363 ? TCB: Temps Coordonn?e Baricentrique Barycentric Coordinate Time Coordinate time for coordinate system with center of mas of solar system ? TCG: Temps Coordonn?e G?ocentrique Geocentric Coordinate Time Coordinate time for coordinate system with center of mas of Earth ? TDB: Temps Dynamique Baricentrique Barycentric Dynamical Time Independent variable of the equations of motion with respect to the barycenter of the solar system. ? ET: Ephemeris Time A.3 Coordinate Reference Systems Description of systems from Explanatory Supplement to the Astronomical Almanac [183] and Valado [213]. A.3.1 Terrestrial Coordinate Reference Systems A.3.1.1 Terestrial Inertial Systems ? GCRS: Geocentric Celestial Reference System Family of reference systems Intended for applications of framework of general relativity ? ECI: Earth Centered Inertial = CIS: Conventional Inertial System = IJK: Geocentric Equatorial System 364 ? FK5: Fundamental Katalog System Based upon FK5 star catalog ? GCRF: Geocentric Celestial Reference Frame Close to FK5, but no nutation ? TEME: True Equator Mean Equinox Includes precesion but no nutation ? MEME: Mean Equator Mean Equinox A.3.1.2 Terestrial-Fixed Non-Inertial Systems ? ITRF: International Terestrial Reference Frame = BF: Body-Fixed Coordinate System = ECEF: Earth-Centered Earth-Fixed = EFG: Earth-Fixed Grenwich System ? SEZ: South-East-Up Observation station local coordinates = Topocentric Horizon Coordinate System ? I T J T K T : Topocentric-Equatorial Coordinate System IJK frame with origin at topocenter, on surface of Earth A.3.2 Interplanetary Coordinate Reference Systems A.3.2.1 Interplanetary Inertial Systems ? BCRS: Barycentric Celestial Reference System Family of reference systems Intended for applications of framework of general relativity 365 ? ICRF: International Celestial Reference Frame Equator and equinox of J2000 Origin at barycenter of solar system ? XYZ: Heliocentric Coordinate System A.4 X-ray Flux Conversion A.4.1 X-ray Spectrum Although the X-ray spectrum is defined broadly, there are no definitive boundary values that are relative to X-ray observation work. In the disertation text the upper bound is listed as 200 keV. X-rays normaly emit by atomic transitions, whereas gama rays and higher are emited by nuclear transitions. The positron annihilation line is at 511 keV, so we wil use this value for now. So, the approximate range for this spectrum: Wavelength: 1?10 -8 ? 2.426?10 -1 m Frequency: 3?10 16 ? 1.236?10 20 Hz Quantum Energy: 0.1 ? 511 keV Wavelength is ! , and frequency is ! . Relation is c!"# . Energy can be in units of Joules, ergs, or electron volts. Relation is E ph !hv!hc/" . Wil use E ph to represent photon energy of photons in a beam (so not to confuse with exponents). A.4.2 Energy X-ray sources are measured over a specific energy range. This is typicaly measured in electron Volts (eV). X-ray Range in Electromagnetic Spectrum: 0.1 ? 511 keV. 366 Soft X-ray Range: 0.1 ? ~4 keV (note ROSAT PSPC = 0.1 ? 2.4 keV). Hard X-ray Range: ~4 ? higher keV (could also be to 10 keV, or > 20 keV). A.4.3 Flux Flux is energy per unit area per unit time. Thus, using flux one can determine acumulated amount of energy received in a given area over a specific time period. Several units are used, including wattsm 2 (mks system), ergcm 2 s (cgs system), photonscm 2 s , and Crab (based on flux of Crab Pulsar over the energy range in question). Flux is related to flux density as described below. Flux density ( S ! ) is the flux per unit frequency interval. Sometime flux density ( S E ) is defined as the flux per unit energy interval (such as flux/keV). The flux density is often measured in Jansky ( Jy ) units. One Jansky is defined as 1.0?10 -26 Wm -2 Hz -1 = 1.0?10 -26 W/m 2 /s (mks system) = 1?10 -23 erg s -1 cm -2 Hz -1 (cgs system). Flux ( F ) is simply an integral of the flux density over the frequency or energy range in question: therefore, F=S ! d ! min ! max " =S E dE E min E max " . A.4.3.1 Flat Spectrum If an observation has a flat spectrum, where S ! () =1?Jy for al ! , then a simple flux density conversion from Jansky to ergcm 2 s is the following: 1?Jy=2.4!10 "12 ergcm 2 s ( ) keV ( ) #range in keV ( ) Ex. Flat spectrum of 0.5 ?Jy (2?20 keV) => 0.5!2.4"10 #12 !(20#2) = 1.2!10 "12 #(18) = 2.16?10 -1 2 s . 367 Note that most sources, including X-ray sources do not have a flat spectrum, thus flux must be determined using integration of their spectral shape. For much of the catalog work, the full spectrum of each source was not investigated, so it was chosen to use the simple conversion method if flux density was given. A.4.3.2 Photon Flux Flux densities are often quoted in units of photons, rather than ergs. The unit of photons is a quantum measure, and is unitles. A flux density just needs to be divided by h! to convert to photon units. For a spectrum that is a power law in photon energy E ph , this reduces the spectral index by 1. Thus, an energy spectral index of ?1 corresponds to a photon spectral index of ?2. A.4.3.3 Crab Flux Unit Source fluxes are often quoted in units of the flux of the Crab Nebula and Pulsar (combined). 1Crab(ph/cm 2 /s)=10! ph "2.05 ( ) keV min keV max # e "$n H ( ) dE ph where this equation is integrated in energy range keV min ?keV max ( ) , and n H is the neutral hydrogen column density, with n H = 3?10 21 /cm 2 , and ? is the photoelectric cross section for hydrogen (Thompson cross section). Typicaly, most sources are measured in terms of mili-Crab (mCrab). A.4.4 Luminosity Luminosity is the rate of emision of energy, so it has units of energy per unit time. Luminosity is the total power emited from the source. Several units are used, including watts (mks system) and ergs (cgs system). 368 Asuming isotropic emision from a source, luminosity ( L ) and flux ( F ) are related by L=F!4"d 2 , where d is the distance from the source. If using erg/cm 2 /s or ph/cm 2 /s, remember to put distance in units of cm, where 1 parsec = 1pc = 3.086?10 18 cm. A.4.5 Other Conversions To get number of photons per second use Power/E ph =#photon/s , where power is in units of Wats, and E ph is in units of Joules. A.4.6 Experiment Conversion Factors A.4.6.1 ROSAT Singh?s paper states for the ROSAT PSPC a value of: 1counts/s=1ct/s=9.4!10 "12 erg/cm 2 /s for energy range (0.1 ? 2.4 keV). So using Singh?s result, or simply 1counts/s=1ct/s=1!10 "11 erg/cm 2 /s for until shown otherwise. This value is not the same for the HRI detector on ROSAT. A simple, quick calculation of ROSAT counts to flux: 1counts/s=1ct/s=1.44!10 "11 erg/cm 2 /s for energy range (0.1 ? 2.4 keV), which is very similar to Singh?s result. Also approximately for range (0.1 ? 2.4 keV): 1.0!10 "11 g/ 2 =4.989!10 "3 photons/ 2 #5!10 "3 photons/m 2 A.4.6.2 PIMS This UNIX tool can be used to convert betwen various flux units, such as Crab, Jansky, ergs, and photons. The tool is interactive or can read an input file. For most of analysis chose to use the Crab spectrum as the model spectrum for al sources with unknown flux. As above, this has an exponent of 2.05 and hydrogen column 369 density of 3?10 21 . Pims was run from the UNIX command line using the following commands: ? model power 2.05 3E21 ? from flux [photons, mJansky, Crab, or erg] [energy range, ex. 2-10] ? instrument flux [photons, mJansky, Crab, or erg] [energy range, ex. 2-10] ? show (shows the set up before running) ? go # (input a value of flux for the ?from? category) Also the above can be put into an input file with an ?.xco? extension to run from a file, as in ?pims @input.xco? (don?t forget the ?@? symbol!) WebPIMS: Runs much like PIMS, only has a GUI interface. Se this at: http:/heasarc.gsfc.nasa.gov/Tools/w3pims.html 370 Apendix B X-ray Navigation Source Catalogue B.1 Description The XNAVSC variable celestial X-ray source catalogue provides parameter listings of sources that have potential application for spacecraft navigation. Chapter 2 provides a complete description of the XNAVSC catalogue and how it was asembled. The catalogue is composed of thre main lists ? Simple List, Detailed List, and 2?10 keV Energy List. Source parameters are listed for each source depending on the type of data needed in each list. Not al parameters are currently available for each source. For those parameters that are either unpublished or unavailable currently, these entries are blank with the catalogue. The sections within this Appendix provide details on the parameter lists within each of these lists, as wel as the data from each list. In addition to the information about each type provided in Chapter 2, Table B-1 provides a listing of the various types of Cataclysmic Variable sources within the XNAVSC, as wel as a short description of these types [2, 178]. 371 Table B-1. CV Sources Within the XNAVSC Database. B.2 Parameters Within Catalogue Lists This section provides a description of the thre main lists within the XNAVSC. The parameters that are stored within each list are identified, along with a brief description of the parameter and any units that represent the data. For those parameters that have no units, or none are needed, a ?N/A? value for Not Applicable is stated. B.2.1 Simple List Parameters Table B-2. Parameters for Simple List in XNAVSC. Parameter Definition Units Instal Number Number of source in order it was instaled into catalogue N/A Comon Names List of comon names used for this source N/A Notes General coments about a source, including type, location, companion, etc. N/A Catalogue J-Name Catalogue specific name composed of catalogued J200 Right Ascension and Declination position Jhm?dm format J-Name J200 frame based name used by external reference catalogues (if diferent from the Catalogue J-Name) Reference?s format B-Name B1950 frame based name used by external references Bhm?d format Object Type Type of object N/A Reference Catalog Number of specific reference used for the object?s data N/A Object Description Number of Sources CV, AM AM Her System 2 CV, D Degenerate/Detached 3 CV, DN Dwarf Nova 15 CV, IP Intermediate Polar 29 CV, N Clasical Nova 18 CV, NL Nova-Like 3 CV, P Polar 43 CV, RN Recurent Nova 1 CV, S S Cygni-type 6 CV, U SU rsae Majoris-type 5 CV, X UX Ursae ajoris-type 1 CV, Z Z Cameloparalis-type 3 Unknown CV Type 12 Total 141 372 B.2.2 Detailed List Parameters Table B-3. Parameters for Detailed List in XNAVSC. Parameter Definition Units Instal Number Number of source in order it was instaled into catalogue N/A Catalogue J-Name Catalogue specific name composed of catalogued J200 Right Ascension and Declination position Jhm?dm format B-Name B1950 frame based name used by external references Bhm?d format Object Type Type of object N/A Clas Clas of object type N/A N a m e & T y p e Sub-Clas Sub-type of object type clas N/A RA J200 Right Ascension position of object h:m:s.ss RA Eror Uncertainty of Right Ascension value, as reported by references arcseconds Dec J200 Declination position of object ?d:m:s.ss Dec Eror Uncertainty of Declination value, as reported by references arcseconds Gal. Longitude Galactic Longitude (?LI?) of object position (derived from RA and Dec) 0 to 360 degres Gal. Latitude Galactic Latitude (?BI?) of object position (derived from RA and Dec) -180 to +180 degres Distance From Earth Distance of object from Earth kiloparsecs Galactic Plane Z-Distance Distance of object above/below galactic plane ?parsecs Proper-Motion RA-Direction Proper-motion of object in the Right Ascension direction ?arcseconds/year P o s i t i o n Proper-Motion Dec-Direction Proper-motion of object in the Declination direction ?arcseconds/year Energy Range Energy range of measured X-ray flux of object (4.5 keV is chosen maximum for this range) kilo electron-Volts Flux X-ray flux of source photons/cm 2 /second Soft X-rays <4.5 keV Flux X-ray flux of source ergs/cm 2 /second Energy Range Energy range of measured X-ray flux of object kilo electron-Volts Flux X-ray flux of source photons/cm 2 /second Hard X-rays >4.5 keV Flux X-ray flux of source ergs/cm 2 /second Neutral Hydrogen Column Density Number of neutral hydrogen atoms in a cylinder of unit cros-sectional area 1/cm 2 Photon Index Index parameter for X-ray flux power law model unitles Pulsed Fraction Fraction of measured flux that is pulsed; ratio of pulsed flux to mean flux fraction Pulse Width (50%) Width of measured pulse at 50% of height above pulse flor seconds Pulse Width (10%) Width of measured pulse at 10% of height above pulse flor seconds E n e r g y Magnetic Field Magnitude of magnetic field of object Gaus 373 Transient Characteristics Stability of Signal (S = Steady, T = Transient) N/A Stability Code Code related to stability of object (Bi = Binary System, Bu = Burster, Gl = Glitch, Zsrc = Z-Source) N/A S t a b i l i t y Timing Stability Stability value of object (curently not used) N/A Pulse Period Duration of ful one cycle period of pulse seconds Pulse Period Deriv. First time derivative of pulse period seconds/seconds Pulse Period 2 nd Deriv. Second time derivative of pulse period seconds/seconds 2 Epoch Date epoch of measured pulse period and period derivatives Modified Julian Date Characteristic Age Rate of rotation slow down years Binary Orbit Period Orbit period of objects within binary system days P e r i o d i c i t y Other Period Other important period terms (curently not used) N/A Reference Catalog Number of specific reference used for the object?s data N/A Reference Code Code for reference information (curently not used) N/A R e f e r e n c e s Notes General coments about a source, including type, location, companion, etc. N/A 374 B.2.3 2?10 keV Energy List Parameters Table B-4. Parameters for 2-10 keV Energy List in XNAVSC. Parameter Definition Units Instal Number Number of source in order it was instaled into catalogue N/A Catalogue J-Name Catalogue specific name composed of catalogued J200 Right Ascension and Declination position Jhm?dm format B-Name B1950 frame based name used by external references Bhm?d format Object Type Type of object N/A Clas Clas of object type N/A Sub-Clas Sub-type of object type clas N/A N a m e & T y p e Proper-Motion Dec- Direction Proper-motion of object in the Declination direction ?arcseconds/year Energy Range Energy range of measured X-ray flux of object (4.5 keV is chosen maximum for this range) kilo electron-Volts Flux X-ray flux of source photons/cm 2 /second Soft X-rays <4.5 keV Flux X-ray flux of source ergs/cm 2 /second Energy Range Energy range of measured X-ray flux of object kilo electron-Volts Flux X-ray flux of source photons/cm 2 /second E n e r g y Hard X-rays >4.5 keV Flux X-ray flux of source ergs/cm 2 /second Energy Range Energy range of measured X-ray flux of object kilo electron-Volts Flux X-ray flux of source photons/cm 2 /second 2 - 1 0 k e V X - r a y Flux X-ray flux of source ergs/cm 2 /second 375 B.3 Catalogue Data Lists This section provides the actual data lists from the XNAVSC. As these tables of data are quite long, care must be taken by the reader to asure proper alignment of the pages of information. These tables are a text version of the electronic database of the XNAVSC. To reduce the overal pages of the data, some repeated parameters betwen Lists have been omited, and are identified within each section below. B.3.1 Simple List The following table provides al the data in the Simple List of the XNAVSC. Al the data from this list is provided. The first page of this table provides the headings of each column of the table. Descriptions of the parameters within this table are provided in Table B-2. The actual list begins on the following page. Note that is orientated in landscape format. For the parameter of the Catalogue J-Name, this is source name unique to the XNAVSC. For a name that is of format Jhhmm-ddmm and writen in blue ink, this name has been modified from the original citation?s J-name or was derived from the position of the source if only a B-name is known for that source. This Catalogue J-Name is only created to produce a consistent naming convention for al the XNAVSC sources, and should not be used as an external name for the source. 376 I n s t a l N u m b e r C o m o n N a m e s N o t e s C a t a l o g u e J-N a m e J-N a m e B-N a m e O b j e c t T y p e R e f e r e n c e C a t a l o g ( J h m -d m F o r m a t ) ( F r o m R e f e r e n c e s ) ( F r o m R e f e r e n c e s ) 1 C r a b P u l s a r ; P S R B 0 5 3 1 + 2 1 ; 1 H 0 5 3 1 + 2 1 9 ; T a u X -1 ; C M T a u J 0 5 3 4 + 2 0 ? B 0 5 3 1 + 2 1 N S 1 , 5 , 1 2 V e l a P u l s a r ; 4 U 0 8 3 -4 5 0 J 0 8 3 5 -4 5 1 0 ? B 0 8 3 ?4 5 N S 1 , 5 , 3 G e m i n g a ; S N 4 3 7 ; P S R J 0 6 3 + 1 7 4 6 ; 1 E 0 6 3 0 + 1 7 8 ; P S R B 0 6 3 0 + 1 7 ( P S R B 0 6 3 + 1 7 ) J 0 6 3 + 1 7 4 6 ? B 0 6 3 + 1 7 N S 1 , 5 , 1 4 G 3 4 3 . 1 -0 2 . 3 ; P S R B 1 7 0 6 -4 ; 2 C G 3 4 2 -0 2 J 1 7 0 9 ?4 2 8 ? B 1 7 0 6 ?4 N S 1 , 5 , 5 M S H 1 5 -5 2 ; P S R B 1 5 0 9 -5 8 ; U 1 5 1 0 -5 9 G 3 2 0 . 4 -1 . 2 J 1 5 3 ?5 9 0 8 ? B 1 5 0 9 ?5 8 N S 1 , 5 , 1 6 P S R B 1 9 5 1 + 3 2 ; C T B 8 0 J 1 9 5 2 + 2 5 2 ? B 1 9 5 + 3 2 N S 1 , 5 , 7 P S R B 1 0 4 6 -5 8 ; V e l a T w i n J 1 0 4 8 ?5 8 3 2 ? B 1 0 4 6 ?5 8 N S 1 , 5 , 8 P S R B 1 2 5 9 -6 3 ; S 2 8 3 ; " R o s e t a " B e -s t a r / b i n J 1 3 0 2 ?6 3 0 ? B 1 2 5 9 ?6 3 N S 1 , 5 9 P S R B 1 8 2 3 -1 3 V e l a l i k e J 1 8 2 6 ?1 3 4 ? B 1 8 2 3 ?1 3 N S 1 , 5 , 1 1 0 G 8 . 7 -0 . 1 ; 0 -2 1 J 1 8 0 3 ?2 1 3 7 ? B 1 8 0 ?2 1 N S 1 , 5 , 1 1 P S R B 9 2 9 + 0 J 1 9 3 2 + 5 9 ? B 1 9 2 9 + N S 1 , 5 , 1 , 2 7 1 2 P S R J 4 3 7 -4 7 1 5 m s P u l s a r J 0 4 3 7 ?4 7 1 5 J 0 4 3 7 ?4 7 1 5 ? N S 1 , 5 , 1 1 3 P S R B 1 8 2 1 -2 4 ; M 2 8 m s , i n M 2 8 J 1 8 2 ?2 4 5 2 ? B 1 8 2 1 ?2 4 N S 1 , 5 , 1 , 2 5 , 2 6 1 4 P S R B 0 6 5 6 + 1 c o l i n g N S J 0 6 5 9 + 1 1 4 ? B 0 6 5 6 + 4 N S 1 , 5 , 1 1 5 P S R B 0 5 4 -6 9 S o u r c e i n L C J 0 5 4 ?6 9 1 9 ? B 0 5 4 ?6 9 N S 1 , 5 , 1 , 4 9 1 6 P S R J 2 1 2 4 -3 m s P u l s a r J 2 1 2 4 ?3 5 8 J 2 1 2 4 ?3 5 8 ? N S 1 , 5 , 1 1 7 P S R B 1 9 5 7 + 2 0 ; B l a c k W i d o w u l s a r m s P u l s a r J 1 9 5 9 + 8 ? B 1 9 5 7 + 2 N S 1 , 5 , 2 1 8 P S R B 0 9 5 0 + 0 8 J 0 9 5 3 + 0 7 5 ? B 0 9 5 0 + 0 8 N S 1 , 5 , 1 , 2 7 1 9 P S R B 1 6 1 -5 0 J 1 6 1 4 ?5 0 4 7 ? B 1 6 1 ?5 0 N S 1 , 5 2 0 G 1 8 0 . 0 -1 . 7 J 0 5 3 8 + 2 8 1 7 J 0 5 3 8 + 2 8 1 7 ? N S 1 , 5 , 1 2 1 P S R J 1 0 1 2 + 5 3 0 7 m s P u l s a r J 1 0 1 2 + 0 7 J 1 0 1 2 + 0 7 ? N S 1 , 5 , 1 , 2 2 P S R B 1 0 5 -5 2 c o l i n g N S J 1 0 5 7 ?5 2 6 ? B 1 0 5 ?5 2 N S 1 , 5 , 1 2 3 P S R B 0 3 5 + 4 J 0 3 5 8 + 4 3 ? B 0 3 5 + 4 N S 1 , 5 , 1 2 4 G 1 4 . 3 + 0 . 3 ; P S R J 2 3 7 + 6 1 5 1 J 2 3 7 + 6 ? B 2 3 4 + 6 N S 1 , 5 , 377 2 5 P S R J 0 2 1 8 + 4 2 3 2 m s P u l s a r J 0 2 1 8 + 4 2 3 2 J 0 2 1 8 + 4 2 3 2 ? N S 1 , 5 , 1 , 2 , 2 5 , 2 6 2 6 P S R B 0 8 2 3 + 6 J 0 8 2 6 + 6 3 7 ? B 0 8 2 3 + 2 6 N S 1 , 5 , 1 , 2 7 2 7 P S R J 0 7 5 1 + 1 8 7 m s P u l s a r J 0 7 5 1 + 1 8 7 J 0 7 5 1 + 1 8 7 ? N S 1 , 5 , 1 2 2 8 4 U 0 1 4 2 + 6 1 5 J 0 1 4 2 + 6 0 J 0 1 4 2 + 6 ? N S 4 , 2 2 9 J 0 5 2 5 ?6 0 7 J 0 5 2 5 ?6 0 7 ? N S 4 3 0 1 E 1 0 8 . 1 -5 9 3 7 J 1 0 4 8 ?5 9 3 7 J 1 0 4 8 ?5 9 3 7 ? N S 4 , 2 3 1 R X J 7 8 4 9 -4 0 J 1 7 0 8 ?4 0 8 J 1 7 0 8 ?4 0 8 ? N S 4 , 2 3 2 S G R 1 8 0 6 -2 0 ; A X J 1 8 0 8 . 6 -2 0 2 ; S N R G 1 0 . 0 -0 . 3 S N R : G 1 0 . 0 -0 . 3 J 1 8 0 8 ?2 0 2 J 1 8 0 8 ?2 0 2 ? N S 4 , 6 3 1 E 1 8 4 1 -0 4 5 S N R : K e s 7 3 J 1 8 4 ?0 4 5 6 J 1 8 4 ?0 4 5 6 ? N S 4 , 2 3 4 A X J 1 8 4 5 . 0 -0 3 SN R : G 2 9 . 6 J 1 8 4 5 ?0 2 5 6 J 1 8 4 5 ?0 2 5 6 ? N S 4 , 2 3 5 S G R 1 9 0 + S N R : G 4 2 . 8 + 0 . 6 J 1 9 0 7 + 0 9 1 9 J 1 9 0 7 + 0 9 1 9 ? N S 4 3 6 1 E 2 5 9 + 5 8 6 S N R : G 1 0 9 . 1 -0 . 1 J 2 3 0 + 5 5 2 J 2 3 0 + 5 5 2 ? N S 4 , 2 3 7 R X J 0 3 2 . 9 -7 3 4 8 : B H y i : H R 9 8 J 0 3 -7 3 4 8 J 0 3 . 9 -7 3 4 8 ? H M X B 3 3 8 A X J 0 4 9 -7 3 2 J 0 4 9 -7 3 1 0 J 0 4 9 -7 3 2 ? H M X B 3 , 3 2 3 9 A X J 0 4 9 -7 2 9 ; R J 0 . 1 -7 2 5 0 J 0 4 9 -7 2 5 0 J 0 4 9 -7 2 9 ? H M X B 3 4 0 S M C X -3 S o u r c e i n S M C J 0 5 2 -7 2 6 ? B 0 5 0 -7 2 7 H M X B 3 4 1 R X J 0 5 0 . 7 -7 3 1 6 ; A J 0 5 1 -7 3 . 3 J 0 5 -7 3 1 6 J 0 5 0 . 7 -7 3 1 6 ? H M X B 3 , 6 4 2 A X J 0 5 1 -7 2 ; S C X -3 S o u r c e i n S M C J 0 5 -7 2 1 J 0 5 1 -7 2 ? H M X B 3 4 3 2 E 0 5 0 . 1 -7 2 4 7 ; R X J 0 5 1 . 8 -7 2 1 ; 1 W A G J 0 5 1 . 8 -7 2 3 1 ; A V 1 ; 2 1 6 8 S o u r c e i n M C J 0 5 1 -7 2 3 1 J 0 5 1 . 8 -7 2 3 1 ? H M X B 3 , 6 4 A X J 0 5 1 . 6 -7 3 1 ; R X J 0 5 1 . 9 -7 3 1 ; S M C 2 5 S o u r c e i n M C J 0 5 1 -7 3 1 0 J 0 5 1 . 9 -7 3 1 ? H M X B 3 4 5 R X J 0 5 2 . 1 -7 3 1 9 ; S M C X -2 S o u r c e i n M C J 0 5 2 -7 3 1 9 J 0 5 2 . -7 3 1 9 ? H M X B 3 , 3 7 4 6 2 E 0 5 1 . 1 -7 2 1 4 ; A X J 0 5 . 9 -7 1 5 7 ; R X J 0 5 2 . 9 -7 1 5 8 ; S M C 4 6 S o u r c e i n S M C J 0 5 2 -7 1 5 8 J 0 5 2 . 9 -7 1 5 8 ? H M X B 3 4 7 S M C X -2 S o u r c e i n M C J 0 5 4 -7 3 4 1 ? B 0 0 5 3 -7 3 9 H M X B 3 4 8 4 U 0 5 3 + 6 0 ; g a m a C a s ; H D 5 3 9 4 J 0 5 6 + 6 0 3 ? B 0 5 3 + 6 0 4 H M X B 3 4 9 X T E J -7 2 4 ; 1 W G A J 0 5 3 . 8 -7 2 6 J 0 5 3 -7 2 6 J 0 5 3 . 8 -7 2 6 ? H M X B 3 5 0 X T E J 0 5 4 -7 2 0 J 0 5 4 -7 2 0 4 J 0 5 4 -7 2 0 ? H M X B 3 5 1 X T E J 0 5 -7 2 4 ; 1 S A X J 0 5 4 . 9 -7 2 6 J 0 5 4 -7 2 6 J 0 5 -7 2 4 ? H M X B 3 378 5 2 J 0 5 8 -7 2 0 3 ; A X J 0 5 8 -7 2 0 J 0 5 7 -7 2 0 2 J 0 5 8 -7 2 . 0 ? H M X B 3 5 3 J 0 5 8 -7 2 3 0 J 0 5 8 . 2 -7 2 3 1 ? H M X B 3 5 4 R X J 0 5 9 . 2 -7 1 3 8 J 0 5 9 -7 1 3 8 J 0 5 9 . 2 -7 1 3 8 ? H M X B 3 5 R X J 0 1 0 1 . 0 -7 2 0 6 , C X O U J 0 1 0 1 0 2 . 7 -7 2 0 6 5 8 J 0 1 1 -7 2 0 6 J 0 1 1 . -7 2 0 6 ? H M X B 3 , 3 2 5 6 1 S A X J 0 1 0 3 . 2 -7 2 0 9 ; 1 E 0 1 0 1 . 5 -7 2 5 J 0 1 3 -7 2 0 9 J 0 1 3 -7 2 ? H M X B 3 5 7 0 1 0 -7 5 0 J 0 1 9 -7 4 4 ? B 0 1 0 3 -7 6 2 H M X B 3 5 8 A X J 0 1 0 5 -7 2 ; R X J 5 . 3 -7 2 1 0 ; D E M S 1 2 8 J 0 1 5 -7 2 1 J 0 1 0 5 -7 2 ? H M X B 3 5 9 J 0 1 5 -7 2 1 J 0 1 6 . 2 -7 2 0 5 ? H M X B 3 6 0 X T E J 0 1 1 . 2 -7 3 1 7 J 0 1 5 -7 2 1 3 J 0 1 1 . 2 -7 3 1 ? H M X B 3 6 1 2 S 0 1 4 + 6 5 0 ; L S I + 6 5 1 0 J 0 1 8 + 6 7 ? B 0 1 4 + 6 5 0 H M X B 3 6 2 V 6 3 5 C a s ; 1 H 0 1 5 + 6 3 5 ; 4 U 0 1 5 + 6 3 4 J 0 1 8 + 6 3 4 ? B 0 1 5 + 6 3 H M X B 3 , 6 6 3 4 U 0 1 -7 3 7 ; R X J 7 . 1 -7 3 2 7 ; S M C X -1 S o u r c e i n S M C J 0 1 7 -7 3 2 6 ? B 0 1 5 -7 3 7 H M X B 3 6 4 R X J 0 1 7 . 6 -7 3 0 J 0 1 7 -7 3 0 J 0 1 7 . 6 -7 3 0 ? H M X B 3 6 5 R X J 0 1 4 6 . 9 + 6 1 2 1 ; L S I + 6 1 2 3 5 J 0 1 4 3 + 6 0 6 J 0 1 4 6 . 9 + 1 2 1 ? H M X B 3 6 G T ; V 6 1 5 C a s ; L I + 6 3 0 3 J 0 2 4 + 6 3 ? B 0 2 3 6 + 6 1 0 H M X B 3 6 7 V 0 3 2 + 5 3 ; B Q C a m J 0 3 4 + 5 3 ? B 0 3 1 + 5 0 H M X B 3 6 8 4 U ; X P e r ; X P e r s e i ; P e r X -1 ; H D 2 4 5 3 4 J0 3 5 + 1 ? B 0 3 5 2 + 9 H M X B 3 6 9 J 0 4 1 9 + 5 9 J 0 4 2 1 + 5 6 0 ? H M X B 3 7 0 R X J 0 4 0 . 9 : + 4 3 1 ; B S D 2 -4 9 1 J 0 4 + 4 1 J 0 4 . 9 4 3 1 ? H M X B 3 7 1 C A L 9 J 0 5 1 -7 0 3 J 0 5 1 . 6 -7 0 3 4 ? H M X B 3 7 2 R X J 0 5 0 2 . 9 -6 2 6 ; C A L E J 0 5 2 -6 2 6 J 0 5 2 . 9 -6 2 6 ? H M X B 3 7 3 J 0 5 1 2 -6 7 1 7 J 0 5 1 2 . 6 -6 7 1 7 ? H M X B 3 7 4 J 0 5 1 6 -6 9 1 J 0 5 1 6 . -6 9 1 ? H M X B 3 7 5 J 0 5 2 -6 9 3 2 J 0 5 2 . -6 9 3 2 ? H M X B 3 7 6 S A O 5 7 9 5 0 J 0 5 2 + 3 7 4 ? B 0 5 2 1 + 3 7 3 H M X B 3 7 R X J 0 5 2 9 . 8 -6 5 6 J 0 5 2 9 -6 5 6 J 0 5 2 9 . 8 -6 5 6 ? H M X B 3 7 8 E X O B 0 5 3 1 0 9 -6 0 9 . 2 J 0 5 3 1 -6 0 7 ? B 0 5 3 1 0 9 -6 0 9 . 2 H M X B 3 7 9 J 0 5 3 1 -6 5 1 8 J 0 5 3 1 . 5 -6 5 1 8 ? H M X B 3 8 0 L M C X -4 ; 1 H 0 5 3 4 -6 7 ; 2 U 0 5 3 2 -6 ; 2 A ; 4 U S o u r c e i n L M C J 0 5 3 2 -6 2 ? B 0 5 3 2 -6 4 H M X B 3 , 6 8 1 J 0 5 3 2 -6 5 3 5 J 0 5 3 2 . 4 -6 5 3 5 ? H M X B 3 379 8 2 R X J 0 5 3 2 . 5 -6 5 1 , S k -6 5 6 J 0 5 3 2 -6 5 1 J 0 5 3 2 . 5 -6 5 1 ? H M X B 3 8 3 J 0 5 3 -6 7 0 J 0 5 3 5 . 0 -6 7 0 ? H M X B 3 8 4 0 5 3 8 -6 J 0 5 3 -6 5 1 ? B 0 5 3 5 -6 8 H M X B 3 8 5 A 0 5 3 5 + 2 6 ; V 7 2 5 T a u ; H D 2 4 5 7 0 ; 1 H 0 5 3 6 + 2 6 J 0 5 3 8 + 2 6 1 8 ? B 0 5 3 + 2 6 2 H M X B 3 , 6 8 6 J 0 5 3 5 -6 5 3 0 J 0 5 3 5 . 8 -6 5 3 0 ? H M X B 3 8 7 C A L 7 0 ; R X J 0 5 3 8 . 9 -6 4 0 5 ; L M C X -3 ; L M C 3 0 6 S o u r c e i n L M C J 0 5 3 8 -6 4 0 ? B0 5 3 8 -6 4 1 H M X B 3 8 C A L 7 8 ; 1 H 0 5 4 -6 9 7 ; R X J 0 5 3 9 . 6 -6 9 4 ; L M C X -1 S o u r c e i n L M C J 0 5 3 9 -6 9 4 ? B 0 5 4 0 -6 9 7 H M X B 3 8 9 J 0 5 4 1 -6 9 3 6 J 0 5 4 1 . 4 -6 9 3 6 ? H M X B 3 9 0 J 0 5 4 1 -6 8 3 2 J 0 5 4 1 . -6 8 3 ? H M X B 3 9 1 J 0 5 4 -6 3 ? B 0 5 4 -6 5 H M X B 3 9 2 R X J 0 5 4 . 1 -7 1 0 ; 1 S A X J 0 5 4 . 1 -7 1 0 J 0 5 4 -7 1 0 J 0 5 4 . 1 -7 1 0 ? H M X B 3 9 3 J 0 5 + 2 8 7 ? B 0 5 6 + 2 8 6 H M X B 3 9 4 S A X J 0 6 3 5 . 2 + 0 5 3 ; P S R J 0 6 3 5 + 0 5 3 J 0 6 3 + 3 J 0 6 3 5 + 3 ? H M X B 3 9 5 W G A J 0 6 4 8 . 0 -4 1 8 ; H D 4 9 7 9 8 ; R X J 0 6 4 8 . 1 - 4 1 9 J 0 6 4 8 -4 1 8 J 0 6 4 8 . 0 -4 1 9 ? H M X B 3 9 6 3 A 0 7 2 6 -2 6 0 ; 4 U 0 7 2 8 -2 5 J 0 7 2 8 -2 6 0 6 ? B 0 7 2 6 -2 6 0 H M X B 3 9 7 S A O 2 3 5 1 5 J 0 7 4 -5 3 1 9 ? B 0 7 3 9 -5 2 9 H M X B 3 9 8 S A O 2 5 0 1 8 J 0 7 5 6 -6 1 0 ? B 0 7 4 9 -6 0 H M X B 3 9 R X J 0 8 1 2 . 4 -3 1 4 J 0 8 1 2 -3 1 4 J 0 8 1 2 . 4 -3 1 4 ? H M X B 3 1 0 G S 0 8 3 4 -4 3 0 ; G R 0 8 3 1 -4 2 9 J 0 8 3 5 -4 3 1 ? B 0 8 3 4 -4 3 0 H M X B 3 , 6 1 0 V e l a X -1 ; G X 2 6 3 + 3 ; H D 7 5 8 1 J 0 9 2 -4 0 3 ? B 0 9 -4 0 3 H M X B 3 1 0 2 G R O J 1 0 8 -5 7 J 1 0 -5 8 1 7 J 1 0 8 -5 7 ? H M X B 3 1 0 3 T H ( a l p h a ) 3 5 -4 2 ; 1 E 1 0 2 4 . 0 -5 7 3 2 J 1 0 2 5 -5 7 4 ? B 1 0 2 4 . -5 7 3 2 H M X B 3 1 0 4 4 U 1 0 3 6 -5 6 , S A O 2 3 8 1 3 J 1 0 3 -5 7 0 4 ? B 1 0 3 6 -5 6 5 H M X B 3 1 0 5 R X J 1 0 3 7 . 5 -5 6 4 7 ; 3 A 1 0 3 6 -5 6 5 ; 4 U 1 0 3 6 -5 6 ; L S 1 6 9 8 J 1 0 3 7 -5 6 4 J 1 0 3 7 . 5 -5 6 4 7 ? H M X B 3 1 0 6 1 E 1 0 4 8 . 1 -5 9 3 7 J 1 0 5 0 -5 9 5 3 ? B 1 0 4 8 . 1 -5 9 3 7 H M X B 3 1 0 7 A 1 1 8 -6 1 6 ; H e n -6 4 0 J 1 2 -6 1 4 ? B 1 8 -6 1 5 H M X B 3 1 0 8 4 U ; G P S ; C e n X -3 ; 1 H 1 1 8 -6 0 2 J 1 2 -6 0 3 7 ? B 1 9 -6 0 3 H M X B 3 , 6 380 10 9 4 U 1 4 5 -6 1 9 ; V 8 0 1 C e n ; H D 1 0 2 4 6 7 ; 1 H 1 4 -6 1 7 J 1 4 8 -6 2 1 2 ? B 1 4 5 -6 1 9 H M X B 3 , 6 1 0 1 E 4 5 . -6 1 4 J 1 4 7 -6 1 5 7 ? B 1 4 5 . -6 1 4 1 H M X B 3 1 G X 3 0 1 -2 , W r a 9 7 ; 4 U 1 2 3 -5 2 ; 1 H 1 2 1 -6 2 3 J 1 2 6 -6 2 4 ? B 1 2 3 -6 2 4 H M X B 3 , 6 1 2 J 1 2 4 -6 0 1 ? B1 2 3 9 -5 9 H M X B 3 1 3 J 1 2 4 7 -6 0 3 8 ? B 1 2 4 -6 0 4 H M X B 3 1 4 J 1 2 4 9 -5 9 0 7 ? B 1 2 4 6 -5 8 H M X B 3 1 5 S A O 2 5 2 0 2 J 1 2 4 -6 3 0 3 ? B 1 2 4 9 -6 3 7 H M X B 3 1 6 S A O 2 5 6 9 6 7 J 1 2 3 9 -7 5 2 ? B 1 2 5 3 -7 6 1 H M X B 3 1 7 H D 1 2 0 9 1 J 1 2 5 4 -5 7 1 0 ? B 1 2 5 -5 6 H M X B 3 1 8 G X 3 0 4 -1 , * 2 ( M V ) ; 4 U 1 2 5 8 -6 2 ; 1 H 1 2 5 7 - 6 1 0 J 1 3 0 -6 1 3 6 ? B 1 2 5 8 -6 1 3 H M X B 3 , 6 1 9 1 3 2 3 -6 1 9 6 ; S A X J 1 3 2 4 . 4 -6 2 0 J 1 3 2 4 -6 2 0 J 1 3 2 4 . 4 -6 2 0 ? H M X B 3 1 2 0 4 U 1 4 1 7 -6 2 4 ; 2 S 4 1 7 -6 7 J 1 4 2 -6 2 4 1 ? B 1 4 1 7 -6 2 4 H M X B 3 1 2 S A X J 1 4 5 2 . 8 -5 9 4 9 J 1 4 5 2 -5 9 4 9 J 1 4 5 2 . 8 -5 9 4 9 ? H M X B 3 1 2 1 H 1 5 3 8 -5 2 ; G X 3 2 7 + . ; Q V N o r ; 4 U 1 5 3 8 -5 2 * 1 2 J 1 5 4 2 -5 2 3 ? B 1 5 3 8 -5 2 H M X B 3 1 2 3 M X 1 5 3 -5 4 2 J 1 5 7 -5 4 2 4 ? B 1 5 3 -5 4 2 H M X B 3 1 2 4 J 1 5 4 -5 1 9 ? B 1 5 -5 2 H M X B 3 1 2 5 O A O 1 6 5 7 -4 1 5 J 1 7 0 -4 1 4 0 ? B 1 6 5 7 -4 1 H M X B 3 1 2 6 V 8 4 S c o J 1 7 0 3 -3 7 5 0 ? B 1 7 0 -3 7 H M X B 3 1 2 7 J 1 7 0 0-4 1 5 J 1 7 0 0 6 -4 1 5 7 ? H M X B 3 1 2 8 E X O 1 7 2 -3 6 3 ; G P S 1 7 2 -3 6 3 J 1 7 2 5 -3 6 2 ? B 1 7 2 -3 6 3 H M X B 3 1 2 9 J 1 7 3 8 -3 0 1 5 J 1 7 3 9 -3 0 2 ? H M X B 3 1 3 0 J 1 7 3 9 -2 9 4 2 J 1 7 3 9 . 5 -2 9 4 2 ? H M X B 3 1 3 J 1 7 4 -2 7 1 3 J 1 7 4 . -2 7 1 3 ? H M X B 3 1 3 2 A X J 1 7 4 9 . 2 -2 7 2 5 J 1 7 4 9 -2 7 5 J 1 7 4 9 . 2 -2 7 5 ? H M X B 3 1 3 R X J 1 7 5 0 -2 7 ; G R O J 1 7 5 0 -2 7 J 1 7 4 9 -2 6 3 8 J 1 7 5 0 -2 7 ? H M X B 3 1 3 4 J 1 8 0 -1 0 5 ? B 1 8 0 7 -1 0 H M X B 3 1 3 5 A X J 1 8 2 0 . 5 -1 4 3 4 J 1 8 2 0 -1 4 3 4 J 1 8 2 0 . 5 -1 4 3 4 ? H M X B 3 , 6 1 3 6 R X J 1 8 2 6 . 1 -1 4 5 0 J 1 8 2 6 -1 4 5 0 J 1 8 2 6 . -1 4 5 0 ? H M X B 3 381 1 3 7 S c t X -1 ; 1 H 1 8 3 2 -0 7 6 J 1 8 3 6 -0 7 3 6 ? B 1 8 3 -0 7 6 H M X B 3 , 6 1 3 8 J 1 8 4 -0 5 1 ? B 1 8 3 9 -0 6 H M X B 3 1 3 9 J 1 8 4 -0 4 2 7 ? B 1 8 3 9 -0 4 H M X B 3 1 4 0 J 1 8 4 5 + 0 5 7 ? B 1 8 4 3 + 0 H M X B 3 1 4 A X J 1 8 4 5 . 0 -0 3 0 ; K e s 7 5 J 1 8 4 7 -0 3 0 9 ? B 1 8 4 5 -0 3 H M X B 3 1 4 2 J 1 8 4 -0 2 5 ? B 1 8 4 5 -0 2 4 H M X B 3 1 4 3 J 1 8 4 7 -0 4 3 ? B 1 8 4 5 . 0 -04 3 H M X B 3 1 4 J 1 8 5 -0 2 4 ? B 1 8 5 -0 2 H M X B 3 1 4 5 X T E J 1 8 5 -0 2 6 J 1 8 5 -0 2 3 7 J 1 8 5 -0 2 6 ? H M X B 3 1 4 6 X T E J 1 8 5 + 0 3 4 J 1 8 5 + 0 3 2 J 1 8 5 + 0 3 4 ? H M X B 3 1 4 7 J 1 9 0 4 + 0 3 1 ? B 1 9 0 1 + 0 3 H M X B 3 1 4 8 X T E J 1 9 0 6 + 0 9 J 1 9 0 5 + 9 2 J 1 9 0 6 + 0 9 ? H M X B 3 1 4 9 3 A 1 9 0 7 + 0 9 ; 4 U 1 9 0 7 + 0 9 ; 1 H 1 9 0 9 + 9 J 1 9 0 + 4 ? B 1 9 0 7 + 0 7 H M X B 3 , 6 1 5 0 S 4 3 ; V 1 3 4 3 A q l ; S N R W 5 0 ; 1 H 1 9 0 8 + 0 4 7 J 1 9 + 4 5 8 ? B 1 9 0 + 4 8 H M X B 3 , 6 1 5 J 1 9 3 2 + 5 3 5 2 ? B 1 9 3 6 + 5 4 1 H M X B 3 1 5 2 X T E J 1 9 6 + 2 7 4 ; G R O J 1 9 4 + 2 6 ; 3 A 9 4 2 + 2 7 4 J 1 9 4 5 + 7 J 1 9 4 6 + 2 7 4 B 1 9 4 2 + 2 7 4 H M X B 3 1 5 3 J 1 9 4 + 3 0 1 ? B 1 9 4 7 + 3 0 H M X B 3 1 5 4 G R O J 1 9 4 8 + 3 2 J 1 9 4 8 + 3 2 0 J 1 9 4 8 + 3 2 ? H M X B 3 1 5 J 1 9 5 + 3 2 0 6 ? B 1 9 5 4 + 3 H M X B 3 1 5 6 C y g X -1 ; V 1 3 5 7 C y g ; H D 2 6 8 6 8 ; 1 H 1 9 5 6 + 3 5 0 J 1 9 5 8 + 3 1 ? B 1 9 5 6 + 3 0 H M X B 3 , 6 1 5 7 V 1 3 5 7 C y g ; E X O B 2 0 3 0 + 3 7 5 J 2 0 3 2 + 3 7 8 ? B 2 0 3 0 + 3 7 H M X B 3 1 5 8 C y g X -3 ; V 1 5 2 1 C y g J 2 0 3 + 4 0 ? B 2 0 3 + 4 7 H M X B 3 1 5 9 J 2 0 3 + 4 7 5 J 2 0 3 0 . 5 + 4 7 5 1 ? H M X B 3 1 6 0 G R O J 2 0 5 8 + 4 2 J 2 0 5 9 + 4 1 J 2 0 5 8 + 4 2 ? H M X B 3 1 6 S A X J 2 1 0 3 . 5 + 4 5 4 5 J 2 1 0 3 + 4 5 J 2 1 0 3 . 5 ? H M X B 3 1 6 2 G S 2 1 3 8 + 5 6 ; C e p X -4 ; 1 H 2 1 3 8 + 5 7 9 J 2 1 3 9 + 5 7 3 ? B2 1 3 8 + 5 6 8 H M X B 3 1 6 3 S A O 5 1 5 6 8 J 2 0 + 5 0 ? B 2 0 2 + 5 0 1 H M X B 3 1 6 4 4 U 2 0 6 + 5 4 3 ; 1 H 2 0 5 + 5 8 J 2 0 7 + 5 4 1 ? B 2 0 6 + 5 4 H M X B 3 , 6 1 6 5 J 2 6 + 6 1 ? B 2 1 4 + 5 8 9 H M X B 3 1 6 J 2 3 9 + 1 J 2 3 9 . 3 + 6 1 6 ? H M X B 3 382 1 6 7 X N P e r 1 9 2 ; 4 U 0 4 2 + 3 2 J 0 4 + 3 0 1 ? B 0 4 2 + 3 2 3 LM X B 2 1 6 8 G R O J 0 4 2 + 3 2 ; V 5 1 8 P e r ; X N P e r 9 2 J 0 4 1 8 + 3 2 4 7 J 0 4 2 + 3 2 ? L 2 1 6 9 4 U 0 5 1 3 -4 0 ; 1 H 0 5 1 2 -4 0 1 ; 2 S 0 5 1 2 -4 0 ; 2 A 5 2 -3 9 , N G C 1 8 5 1 J 0 5 1 -4 0 2 ? B 0 5 1 2 -4 0 1 L M X B 2 1 7 0 C A L 3 0 ; 1 H 0 5 2 1 -7 2 0 ; R X J 0 5 2 0 . 4 -7 1 5 7 ; L M C X -2 S o u r c e i n L M C J 0 5 2 0 -7 1 5 7 ? B 0 5 2 1 -7 2 0 L M X B 2 1 7 1 J 0 5 3 2 -6 9 2 6 J 0 5 3 2 . 7 -6 9 2 6 ? L M X B 2 1 7 2 V 1 0 5 O r i ; 2 S 6 4 + 9 1 ; U 0 6 1 4 + 0 9 ; 1 H 0 6 1 0 + 0 9 1 J 0 6 1 7 + 0 9 8 ? B 0 6 1 4 + 0 9 1 L M X B 2 , 6 , 5 3 1 7 3 M o n X -1 ; N . M o n 1 9 7 5 , 1 9 1 7 ; V 6 1 6 M o n J 0 6 2 -0 2 0 ? B 0 6 2 0 -0 3 L M X B 2 1 7 4 J 0 6 5 8 -0 7 1 5 ? B 0 6 5 -0 7 2 L M X B 2 1 7 5 E X O 0 7 4 8 -6 7 6 ; U Y V o l J 0 7 4 8 -6 7 4 5 ? B 0 7 4 8 -6 7 6 L M X B 2 1 7 6 J 0 8 3 5 + 5 1 8 J 0 8 3 5 . 9 + 5 1 8 ? L M X B 2 1 7 G S 0 8 3 6 -4 2 9 ; M X 0 8 3 6 -4 2 J 0 8 3 7 -4 2 5 3 ? B 0 8 3 6 -4 2 9 L M X B 2 1 7 8 J 0 9 2 -5 1 ? B 0 9 1 -5 4 9 L M X B 2 1 7 9 2 S 0 9 2 1 -6 3 0 ; 2 A ; H ; V 3 9 5 C a r J 0 9 2 -6 3 1 7 ? B 0 9 2 1 -6 3 0 L M X B 2 1 8 0 M V e l ; X N V e l 1 9 3 ; G R S 1 0 9 -4 5 J 1 0 1 3 -4 5 0 4 ? B 1 0 -4 5 L M X B 2 1 8 K V U m a ; J 1 1 8 + 4 8 0 J 1 8 + 4 8 0 J 1 1 8 + 4 8 0 ? L M X B 2 1 8 2 G U u s ; G S 1 2 4 -6 8 4 ; G R S 1 2 1 -6 8 4 ; N M u s 1 9 1 J 1 2 6 -6 8 4 0 ? B 1 2 4 -6 8 4 L M X B 2 1 8 3 G R M u s ; 1 H 1 2 5 4 -6 9 0 ; 2 S 1 2 5 4 -6 9 0 J 1 2 5 7 -6 9 1 7 ? B 1 2 5 4 -6 9 0 L M X B 2 1 8 4 4 U 1 3 2 3 -6 2 0 ; E X O 1 3 2 3 . 5 -6 1 8 0 ; 1 3 2 3 -6 1 5 2 J 1 3 2 6 -6 2 0 8 ? B 1 3 2 3 -6 1 9 L M X B 2 1 8 5 B W C i r ; G S 1 3 5 4 -6 4 2 9 ; M X 1 3 5 3 -6 4 ; C e n X -2 J 1 3 5 8 -6 4 4 ? B 1 3 5 4 -6 4 5 L M X B 2 1 8 6 C e n X -4 ; V 8 2 C e n J 1 4 5 8 -3 1 4 0 ? B 1 4 5-3 1 4 L M X B 2 1 8 7 C i r X -1 ; B P C i r ; 1 H 1 5 1 6 -5 6 9 ; 2 S J 1 5 2 0 -5 7 1 0 ? B 1 5 6 -5 6 9 L M X B 2 1 8 T r A X -1 * N J 1 5 2 8 -6 1 2 ? B 1 5 2 4 -6 1 7 L M X B 2 1 8 9 3 U 1 5 4 3 -4 7 ; 4 U 1 5 3 -4 5 J 1 5 4 7 -4 7 4 0 ? B 1 5 4 3 -4 7 5 L M X B 2 , 6 1 9 0 J 1 5 4 7 -6 2 3 ? B 1 5 4 3 -6 2 L M X B 2 1 9 J 1 5 0 -5 6 2 8 J 1 5 0 -5 6 4 ? L M X B 2 1 9 2 L U T r A ; 1 H 1 5 6 -6 0 5 ; 1 M ; U 1 5 6 -6 0 5 * X J 1 6 0 -6 0 4 ? B 1 5 6 -6 0 5 L M X B 2 1 9 3 U W C r B ; M S 6 0 3 + 2 0 ; 1 E 1 6 0 3 . 6 + 6 0 J 1 6 0 5 + 2 ? B 1 6 0 3 . + 2 6 0 L M X B 2 383 1 9 4 J 1 6 0 3 -7 5 3 J 1 6 0 3 . 9 -7 5 3 ? L M X B 2 1 9 5 G X 3 1 -1 ; Q X N o r ; 1 H 1 6 0 8 -5 2 ; 4 U 1 6 0 8 -5 2 J 1 6 2 -52 5 ? B 1 6 0 8 -5 2 L M X B 2 1 9 6 S c o X -1 ; V 8 1 8 S c o J 1 6 9 -1 5 3 8 ? B 1 6 7 -1 5 L M X B 2 , 5 3 1 9 7 N o r X R -1 ; V 8 0 A r a ; 1 H 1 6 2 4 -4 9 0 ; 4 U 1 6 2 -4 9 J 1 6 2 8 -4 9 ? B 1 6 2 4 -4 9 0 L M X B 2 1 9 8 K Z T r A ; 4 U 1 6 2 6 -6 7 * 4 J 1 6 3 2 -6 7 2 7 ? B 1 6 2 7 -6 7 3 L M X B 2 , 2 9 1 9 4 U 1 6 3 0 -4 7 2 J 1 6 3 4 -4 7 2 3 ? B 1 6 3 0-4 7 2 L M X B 2 2 0 J 1 6 3 -4 7 9 ? B 1 6 3 2 -4 7 L M X B 2 2 0 1 N o r X -1 ; V 8 0 1 A r a ; 4 U 1 6 3 6 -5 3 ; 1 H 1 6 3 6 -5 3 6 ; M X B 1 6 3 6 -5 3 * 3 J 1 6 4 0 -5 3 5 ? B 1 6 3 -5 3 6 L M X B 2 , 5 3 2 0 2 G X 3 4 0 + 0 J 1 6 4 5 -4 5 3 6 ? B 1 6 4 2 -4 5 L M X B 2 2 0 3 X N S c o 1 9 4 ; V 1 0 3 S c o ; G R O J 1 6 5 -4 0 ? N a m e ( 5 / 4 ? ) J 1 6 5 4 -3 9 5 0 J 1 6 5 -4 0 ? L M X B 2 2 0 4 H e r X -1 ; H Z H e r ; 1 H 1 6 5 6 + 3 5 4 J 1 6 5 7 + 3 2 0 ? B 1 6 5 6 + 3 5 L M X B 2 2 0 5 M X B 1 6 5 9 -2 9 ; V 2 1 3 4 O p h * T J 1 7 0 2 -2 9 5 6 ? B 1 6 5 8 -2 9 8 L M X B 2 2 0 6 G X 3 9 -4 ; V 8 2 A r a ; 1 6 5 9 -4 8 7 * V J 1 7 0 2 -4 8 4 7 ? B 1 6 5 9 -4 8 7 L M X B 2 2 0 7 S c o X -2 ; 4 + 2 ; 1 H 1 7 0 2 -3 6 3 ; 4 U 1 7 0 2 -3 6 J 1 7 0 5 -3 6 2 5 ? B 1 7 0 2 -3 6 3 L M X B 2 2 0 8 J 1 7 0 6 -4 3 0 2 ? B 1 7 0 2 -4 2 9 L M X B 2 2 0 9 J 1 7 0 6 + 2 3 5 8 ? B 1 7 0 4 + 4 L M X B 2 2 1 0 V 2 1 0 7 O p h ; N O p h 1 9 7 J 1 7 0 8 -2 5 0 5 ? B 1 7 0 5 -2 5 0 L M X B 2 2 1 4 U 1 7 5 -4 ; 1 H 1 7 0 2 -4 3 7 J 1 7 0 8 -4 0 6 ? B 1 7 0 5 -4 0 L M X B 2 , 6 2 1 J 1 7 2 -4 0 5 0 ? B 1 7 0 8 -4 0 8 L M X B 2 2 1 3 J 1 7 0 9 -2 6 3 9 J 1 7 0 9 -2 6 7 ? L M X B 2 2 1 4 J 1 7 0 -2 8 0 7 J 1 7 0 -2 8 1 ? L M X B 2 2 1 5 J 1 7 4 -3 4 0 ? B 1 7 1 -3 9 L M X B 2 2 1 6 J 1 7 2 -3 7 8 J 1 7 1 2 . 6 -3 7 3 9 ? L M X B 2 2 1 7 J 1 7 8 -3 2 1 0 ? B 1 7 1 5 -3 2 1 L M X B 2 2 1 8 V 2 9 3 O p h ; X N O p h 1 9 3 ; G R O J 1 7 1 9 -2 4 J 1 7 9 -25 0 1 ? B 1 7 6 -2 4 9 L M X B 2 , 6 2 1 9 J 1 7 8 -4 0 9 J 1 7 1 8 2 4 . 2 -4 0 2 9 3 4 ? L M X B 2 2 0 J 1 7 2 3 -3 7 3 9 J 1 7 2 3 -3 7 6 ? L M X B 2 2 1 J 1 7 2 -3 5 4 ? B 1 7 2 4 -3 5 6 L M X B 2 2 J 1 7 2 -3 0 4 8 ? B 1 7 2 4 -3 0 7 L M X B 2 384 2 3 M X B 1 7 2 8 -3 4 ; 4 U 1 7 2 8 -3 4 ; G X 3 5 4 -0 J 1 7 3 1 -3 5 0 ? B 1 7 2 8 -3 7 L M X B 2 , 5 3 2 4 G X 9 + 9 ; V 2 1 6 O p h ; 1 H 1 7 2 8 -1 6 9 ; 4 U 1 7 2 8 -1 6 J 1 7 3 -1 6 5 7 ? B 1 7 2 8 -1 6 9 L M X B 2 2 5 G X 1 + 4 ; V 2 1 6 O p h ; 1 H 1 7 2 8 -2 4 7 * G F J 1 7 3 2 -2 4 4 ? B 1 7 2 8 -2 4 7 L M X B 2 2 6 J 1 7 3 -3 1 3 ? B 1 7 3 0 -3 1 L M X B 2 2 7 M X B 1 7 3 0 -3 5 R a p i d B u r s t e r J 1 7 3 -3 2 ? B 1 7 3 0 -3 5 L M X B 2 2 8 J 1 7 3-2 0 2 ? B 1 7 3 0 -2 0 L M X B 2 2 9 K S 1 7 3 1 -2 6 0 J 1 7 3 4 -2 6 0 5 ? B 1 7 3 -2 6 0 L M X B 2 , 5 3 2 3 0 J 1 7 3 5 -3 0 8 ? B 1 7 3 2 -3 0 4 L M X B 2 2 3 1 J 1 7 3 6 -2 7 2 5 ? B 1 7 3 2 -2 7 L M X B 2 2 3 J 1 7 3 -2 9 1 0 ? B 1 7 3 4 -2 9 L M X B 2 2 3 J 1 7 3 8 -2 7 0 ? B 1 7 3 5 -2 6 9 L M X B 2 2 3 4 V 9 2 6 S c o ; 1 H 1 7 3 5 -4 4 ; M X B 1 7 3 5 -4 * 5 J 1 7 3 8 -4 ? B 1 7 3 5 -4 4 L M X B 2 2 3 5 J 1 7 3 8 -2 8 2 9 ? B 1 7 3 5 -2 8 L M X B 2 2 3 6 J 1 7 3 9 -2 9 4 3 ? B 1 7 3 6 -2 9 7 L M X B 2 2 3 7 J 1 7 3 9 -3 0 5 ? B 1 7 3 -3 1 L M X B 2 2 3 8 J 1 7 4 0 -2 8 1 8 ? B 1 7 3 -2 8 2 L M X B 2 2 3 9 J 1 7 4 2 -2 7 4 6 ? B 1 7 3 9 -2 7 8 L M X B 2 2 4 0 J 1 7 4 2 -3 0 3 0 ? B 1 7 3 9 -3 0 4 L M X B 2 2 4 1 G C X -4 J 1 7 4 3 -2 9 2 6 ? B 1 7 4 0 -2 9 4 L M X B 2 2 4 J 1 7 4 3 -2 9 4 ? B 1 7 4 0 . -2 9 4 2 L M X B 2 2 4 3 J 1 7 4 -2 9 0 ? B 1 7 4 . 2 -2 8 5 L M X B 2 2 4 M X B 1 7 4 3 -2 9 ? J 1 7 4 -2 9 1 ? B 1 7 4 -2 9 3 L M X B 2 2 4 5 J 1 7 4 5 -3 2 1 3 ? B 1 7 4 -3 2 L M X B 2 2 4 6 J 1 7 4 5 -2 8 5 4 ? B 1 7 4 . 9 -2 8 5 3 L M X B 2 2 4 7 J 1 7 4 5 -3 2 4 1 ? B 1 7 4 2 -3 2 6 L M X B 2 2 4 8 J 1 7 4 5 -2 8 5 9 ? B 1 7 4 2 . -2 8 5 7 L M X B 2 2 4 9 G C X -2 J 1 7 4 5 -2 9 7 ? B 1 7 4 2 -2 9 4 L M X B 2 2 5 0 A 1 7 4 2 -2 8 9 J 1 7 4 5 -2 9 0 1 ? B 1 7 4 2 -2 8 9 L M X B 2 2 5 1 J 1 7 4 5 -2 9 0 ? B 1 7 4 2 . 5 -2 8 5 9 L M X B 2 2 5 J 1 7 4 5 -2 8 4 6 ? B 1 7 4 2 . 5 -2 8 4 5 L M X B 2 385 2 5 3 J1 7 4 5 -2 9 0 3 ? B 1 7 4 2 . 7 -2 9 0 2 L M X B 2 2 5 4 J 1 7 4 6 -2 8 5 4 ? B 1 7 4 2 . 8 -2 8 5 3 L M X B 2 2 5 J 1 7 4 6 -2 8 5 3 ? B 1 7 4 2 . 9 -2 8 5 L M X B 2 2 5 6 G C X -1 J 1 7 4 6 -2 9 3 1 ? B 1 7 4 2 -2 9 4 L M X B 2 2 5 7 J 1 7 4 6 -2 8 5 1 ? B 1 7 4 2 . 9 -2 8 4 9 L M X B 2 2 5 8 J 1 7 4 6 -2 8 4 ? B 1 7 4 3 . -2 8 4 3 L M X B 2 2 5 9 J 1 7 4 6 -2 8 5 3 ? B1 7 4 3 . -2 8 5 L M X B 2 2 6 0 G X + 0 . 2 , -0 . 2 J 1 7 4 6 -2 8 5 3 ? B 1 7 4 3 -2 8 L M X B 2 2 6 1 J 1 7 4 -2 9 5 9 ? B 1 7 4 -2 9 L M X B 2 2 6 2 E 1 7 4 3 . 1 -2 8 4 2 , R O J 1 7 4 -2 8 J 1 7 4 -2 8 4 J 1 7 4 -2 8 ? L M X B 2 2 6 3 J 1 7 4 -3 0 ? B 1 7 4 -3 0 L M X B 2 2 6 4 G X 3 + 1 J 1 7 4 -2 6 ? B 1 7 4 -2 6 5 L M X B 2 2 6 5 J 1 7 4 8 -3 6 0 7 ? B 1 7 4 -3 6 1 L M X B 2 2 6 J 1 7 4 5 -2 9 0 1 J 1 7 4 5 . 6 -2 9 0 1 ? L M X B 2 2 6 7 J 1 7 4 8 -2 4 5 3 ? B 1 7 4 5 -2 4 8 L M X B 2 2 6 8 J 1 7 4 8 -2 0 ? B 1 7 4 5 -2 0 3 L M X B 2 2 6 9 J 1 7 4 9 -3 1 ? B 1 7 4 6 -3 1 L M X B 2 2 7 0 J 1 7 5 0 -3 2 5 ? B 1 7 4 6 . -3 2 4 L M X B 2 2 7 1 N G C 6 4 1 ; 4 U 1 7 4 6 -3 7 1 ; 1 H 1 7 4 6 -37 0 J 1 7 5 0 -3 7 0 ? B 1 7 4 6 -3 7 0 L M X B 2 2 7 J 1 7 5 0 -2 1 2 5 ? B 1 7 4 -2 1 4 L M X B 2 2 7 3 J 1 7 5 0 -3 1 7 ? B 1 7 4 -3 1 3 L M X B 2 2 7 4 J 1 7 4 8 -2 8 2 8 J 1 7 4 8 -2 8 ? L M X B 2 2 7 5 J 1 7 4 8 -2 0 1 J 1 7 4 8 . 9 -2 0 2 1 ? L M X B 2 2 7 6 G X + 1 . 1 , -1 . 0 J 1 7 5 2 -2 8 3 ? B 1 7 4 9 -2 8 5 L M X B 2 2 7 J 1 7 5 0 -2 9 0 J 1 7 5 0 . 8 -2 9 0 ? L M X B 2 2 7 8 J 1 7 5 2 -3 1 3 7 J 1 7 5 2 . 3 -3 1 3 8 ? L M X B 2 2 7 9 V 4 1 3 4 S g r ; S c o X R -6 ; 1 H 1 7 5 4 -3 8 ; 4 U 1 7 5 -3 J 1 7 5 8 -3 4 8 ? B 1 7 5 -3 8 L M X B 2 , 6 2 8 0 X T E J 1 7 5 -3 2 4 J 1 7 5 -3 2 8 J 1 7 5 -3 2 4 ? L M X B 2 2 8 1 1 H 1 7 5 8 -2 5 0 ; 4 U 8 -2 5 ; G X 5 -1 J 1 8 0 -2 5 0 4 ? B 1 7 5 8 -2 5 0 L M X B 2 , 5 3 2 8 J 1 8 0 -2 5 4 ? B 1 7 5 8 -2 5 8 L M X B 2 386 2 8 3 G X 9 + 1 J 1 8 0 1 -2 0 3 1 ? B 1 7 5 8 -2 0 5 L M X B 2 2 8 4 J 1 8 0 6 -2 4 3 5 ? B 1 8 0 3 -2 4 5 L M X B 2 2 8 5 J 1 8 0 6 -2 4 3 5 J 1 8 0 6 -2 4 6 ? L M X B 2 2 8 6 S A X J 1 8 0 8 . 4 -3 6 5 8 , X T E J 1 8 0 8 -3 6 9 J 1 8 0 -3 6 5 8 J 1 8 0 . 4 -3 6 5 8 ? L M X B 2 , 4 6 , 4 7 , 5 2 2 8 7 J 1 8 1 0 . 7-2 6 0 9 J 1 8 0 -2 6 0 9 J 1 8 0 . -2 6 0 9 ? L M X B 2 2 8 G X 1 3 + 1 ; 1 8 1 -1 7 1 0 J 1 8 4 -1 7 0 9 ? B 1 8 1 -1 7 1 L M X B 2 2 8 9 J 1 8 5 -1 2 0 5 ? B 1 8 2 -1 2 L M X B 2 2 9 0 N P S e r ; G X 1 7 + 2 ; 4 U 1 8 1 3 -1 4 J 1 8 6 -1 4 0 ? B 1 8 3 -1 4 0 L M X B 2 , 5 3 2 9 1 J 1 8 1 9 -2 5 4 J 1 8 9 -2 5 2 5 J 1 8 1 9 . 3 -2 5 2 5 ? L M X B 2 2 9 N G C 6 2 4 ; 1 H 1 8 2 0 -3 0 3 ; 4 U 1 8 2 0 -3 0 ; 1 8 2 0 - 3 0 2 J 1 8 2 3 -3 0 1 ? B 1 8 2 0 -3 0 3 L M X B 2 , 5 3 2 9 3 V 6 9 1 r A ; 1 H 8 2 -3 7 1 ; 2 A 1 8 2 -3 7 1 J 1 8 2 5 -3 7 0 6 ? B 1 8 2 -3 7 1 L M X B 2 2 9 4 J 1 8 2 5 -0 0 ? B 1 8 2 -0 0 L M X B 2 2 9 5 G S 1 8 2 6 -2 3 8 J 1 8 2 9 -2 3 4 7 ? B 1 8 2 6 -2 3 8 L M X B 2 2 9 6 J 1 8 3 5 -3 2 5 8 ? B 1 8 3 2 -3 0 L M X B 2 2 9 7 S e r X -1 ; M S e r ; 4 U 1 8 3 7 + 0 4 ; M X B 1 8 3 7 + 0 5 * D S J 1 8 3 9 + 0 0 ? B 1 8 3 7 + 0 4 9 L M X B 2 , 6 2 9 8 J 1 8 4 9 -0 3 0 3 ? B 1 8 4 6 -0 3 1 L M X B 2 2 9 N G C 6 7 2 ; 1 H 1 8 5 0 -0 8 7 ; 1 8 2 0 -3 0 2 3 J 1 8 5 3 -0 8 4 2 ? B 1 8 5 0 -0 8 7 L M X B 2 3 0 J 1 8 5 6 + 0 1 J 1 8 5 6 + 0 5 3 ? L M X B 2 3 0 1 J 1 8 5 + 2 3 9 J 1 8 5 9 + 2 ? L M X B 2 3 0 2 J 1 9 0 + 0 1 0 ? B 1 9 0 5 + 0 0 L M X B 2 3 0 A q l X R -1 ; V 1 3 3 A q l ; 4 U 1 9 0 8 + 0 5 J 1 9 + 3 ? B 1 9 0 8 + L M X B 2 , 5 3 3 0 4 J 1 9 5 + 0 5 8 ? B 1 9 5 + 5 L M X B 2 3 0 5 V 1 4 0 5 ; 4 U 1 9 1 5 -0 5 ; 1 H 1 9 1 6 -0 5 3 J 1 9 8 -0 5 1 4 ? B 1 9 6 -0 5 3 L M X B 2 3 0 6 J 1 9 2 0 + 4 1 ? B 1 9 8 + 4 L M X B 2 3 0 7 J 1 9 4 2 -0 3 5 4 ? B 1 9 4 0 -0 4 L M X B 2 3 0 8 V 1 4 0 8 A q l ; U 1 9 5 7 + 1 ; H 9 5 6 + 1 5 J 1 9 5 + 4 ? B 1 9 5 7 + 5 L M X B 2 , 6 3 0 9 Q Z V u l ; N V u l 1 9 8 ; G S 2 0 0 + 2 5 , * B J 2 0 2 + 2 1 ? B 2 0 0 + 2 1 L M X B 2 3 1 0 X T E J 2 0 1 2 + 3 8 1 J 2 0 1 + 3 8 1 J 2 0 1 2 + 3 8 1 ? L M X B 2 3 1 V 4 0 4 C y g ; N C y g 8 9 ; G S 2 0 2 3 3 8 J 2 0 4 + 3 5 ? B 2 0 2 3 + 3 8 L M X B 2 387 3 1 2 X T E J 2 1 2 3 -0 5 8 J 2 1 2 3 -0 5 4 7 J 2 1 2 3 -0 5 8 ? L M X B 2 3 1 M 1 5 ; A C 2 1 ; 1 H 2 1 2 8 + 1 2 0 ; 4 U 2 1 2 7 + 1 J 2 1 9 + 1 0 ? B 2 1 2 7 + 1 9 L M X B 2 , 6 3 1 4 V 1 7 2 7 C y g ; 4 U 2 2 9 + 4 7 ; H 1 3 1 + 4 7 3 J 2 1 3 + 4 7 7 ? B 2 1 9 + 4 0 L M X B 2 , 6 3 1 5 C y g X -2 ; V 1 3 4 1 C y g ; 1 H 2 1 4 2 + 3 8 0 J 2 1 4 + 8 ? B 2 1 4 + 3 8 0 L M X B 2 3 1 6 J 2 3 0 + 6 7 ? B 2 3 1 8 + 6 0 L M X B 2 3 1 7 R X J 0 7 2 0 . 4 -3 1 2 5 ; 1 E S 0 7 1 8 -3 1 . 3 J 0 7 0 -3 1 2 5 ? B 0 7 1 8 -3 1 8 N S 2 , 6 , 4 3 3 1 8 R X J 1 8 3 8 . 4 -0 3 0 ; S N R G 2 8 . + 1 . 5 J 1 8 3 8 -0 3 0 J 1 8 3 8 . 4 -0 3 0 1 ? N S 2 , 6 3 1 9 P G 1 2 3 2 + 7 9 ; W D ; A V n ; H Z 9 J 1 2 3 4 + 3 7 ? ? C V 6 , 7 3 2 0 G P C o m ; G 6 1 -2 9 J 1 3 0 5 + 0 1 ? ? C V 6 , 7 3 2 1 4 7 T u c ; N C 0 4 ; X 2 1 . 8 -7 2 1 J 0 2 4 -7 2 0 4 ? ? C V 6 , 7 3 2 L B 1 8 0 ; V 3 4 7 P u p ; 4 U J 0 6 1 -4 8 4 ? ? C V 6 , 7 3 2 V 3 4 8 P u p ; H 0 7 0 -3 6 0 ; 1 H 0 7 0 9 -3 6 0 J 0 7 1 2 -3 6 0 5 ? ? C V 6 , 7 3 2 4 H T C a s ; 0 1 0 7 + 5 9 8 J 0 1 + 6 0 4 ? ? C V 6 , 7 3 2 5 S A u r ; 1 H 6 3 4 7 J 0 6 1 3 + 4 4 ? ? C V 6 , 7 3 2 6 U G e m ; H 0 7 5 2 + 2 2 1 0 8 1 J 0 7 5 + 2 0 ? ? C V 6 , 7 3 2 7 Z C h a J 0 8 -7 6 3 2 ? ? C V 6 , 7 3 2 8 Z C a m J 0 8 2 5 + 7 3 0 6 ? ? C V 6 , 7 3 2 9 A C C n c ; H 0 8 5 0 + 1 3 J 0 8 4 + 1 2 ? ? C V 6 , 7 3 0 S Y n c ; B D + 1 8 2 1 0 1 J 0 9 1 + 1 7 5 3 ? ? C V 6 , 7 3 1 X L e o ; 0 9 5 1 + 1 9 J 0 9 5 1 + 5 2 ? ? C V 6 , 7 3 2 O Y C a r J 1 0 6 -7 0 1 4 ? ? C V 6 , 7 3 T W V i r ; P G 1 4 2 -0 4 1 J 1 4 5 -0 4 2 6 ? ? C V 6 , 7 3 4 A H e r ; P G 1 6 4 2 + 5 3 J 1 6 4 + 2 1 5 ? ? C V 6 , 7 3 5 V 4 2 6 O p h ; 1 8 0 5 + 0 5 8 J 1 8 0 7 + 0 5 ? ? C V 6 , 7 3 6 W Z S g e ; 2 0 5 + 7 J 2 0 7 + 2 ? ? C V 6 , 7 3 7 S C y g ; 1 1 4 0 4 3 J 2 1 4 + 4 3 5 ? ? C V 6 , 7 3 8 R U P e g ; 2 1 + 1 4 J 2 1 4 + 2 ? ? C V 6 , 7 3 9 V 7 0 9 C a s ; R X J 0 2 8 . 8 + 5 9 1 7 ; 4 U 0 2 7 + 5 9 ; 1 H 0 2 5 + 5 8 J 0 8 + 5 9 7 ? ? C V 6 , 7 3 4 0 H 0 2 0 4 -0 2 3 ; 1 0 2 0 1 -0 2 9 J 0 2 0 3 -0 2 4 3 ? ? C V 6 388 3 4 1 T A r i ; B D + 1 4 3 4 ; 1 H 0 1 5 7 + 1 4 2 1 J 0 2 0 6 + 1 5 1 7 ? ? C V 6 3 4 2 1 H 0 2 5 3 + 1 9 3 ; X Y A r i ; M B M 1 2 J 0 2 5 6 + 1 9 2 6 ? ? C V 6 , 7 3 4 G K P e r ; N P e r 1 9 0 1 J 0 3 1 + 4 3 5 4 ? ? C V 6 , 7 3 4 H 0 3 4 9 + 7 ; V 4 7 1 T a u ; B D + 1 6 5 1 6 J 0 3 5 + 7 ? ? C V 6 3 4 5 V 1 0 6 2 T a u ; 1 H 0 4 5 9 + 2 4 6 J 0 5 2 + 2 4 5 ? ? C V 6 3 4 6 C o l 1 ; U C o l ; R X J 0 2 -3 2 4 1 J 0 5 1 2 -3 2 4 1 ? ? C V 6 , 7 3 4 7 2 A 0 5 2 6 -3 2 8 ; T V C o l ; 1 H 0 5 2 7 -3 2 8 J 0 5 2 9 -3 2 4 9 ? ? C V 6 , 7 3 4 8 T W P i c ; H 0 5 3 4 -5 8 1 ; 1 H 0 5 3 8 -5 7 J 0 5 3 4 -58 0 1 ? ? C V 6 , 7 3 4 9 T X C o l ; 1 H 0 5 4 2 -4 0 7 J 0 5 4 3 -4 1 0 1 ? ? C V 6 , 7 3 5 0 A u r 1 ; V 4 0 5 u r ; R X J 5 8 5 3 5 3 J 0 5 8 + ? ? C V 6 , 7 3 5 1 M e n 1 ; H 0 5 1 -8 1 9 ; H 0 6 1 6 -8 1 8 J 0 6 1 -8 1 4 9 ? ? C V 6 3 5 2 B G C m i ; 3 A 0 7 2 9 + 0 3 J 0 7 3 1 + 9 6 ? ? C V 6 , 7 3 5 C a r 1 ; R X J 0 7 4 . 9 -5 2 5 7 J 0 7 4 -5 2 5 7 ? ? C V 6 3 5 4 P Q G e m ; R X J 0 7 5 1 + 1 4 4 ; R E J 0 7 5 1 + 1 4 J 0 7 5 1 + 1 4 ? ? C V 6 , 7 3 5 R X J 0 7 5 7 . 0 + 6 3 0 6 ; 1 R X S J 0 7 5 7 0 . 5 + 6 3 0 6 0 2 J 0 7 5 + 6 3 0 5 ? ? C V 6 3 5 6 P y x 2 ; W X P y x ; 1 E 0 8 3 0 . 9 -2 3 8 J 0 8 3 -2 4 8 ? ? C V 6 3 5 7 V Z P y x 1 ; 1 H 0 8 5 7 -2 4 2 ; 1 H 0 8 5 7 -2 4 2 J 0 8 5 9 -2 4 8 ? ? C V 6 , 7 3 5 8 D O D r a ; Y D r a ; E 1 4 0 . 8 + 7 1 5 8 ; P G 1 4 0 + 7 1 9 ; 3 A 1 4 8 + 7 1 9 ; P G 1 4 0 + 7 1 9 J 1 4 3 + 7 1 4 1 ? ? C V 6 , 7 3 5 9 R X J 1 2 3 8 -3 8 J 1 2 3 8 -3 8 4 5 ? ? C V 6 3 6 0 E X H y a ; 4 U 1 2 4 9 -2 8 ; 1 H 1 2 5 1 -2 9 1 J 1 2 5 -2 9 1 4 ? ? C V 6 , 7 3 6 1 V 7 9 5 e r ; S V S 6 1 3 ; G 7 1 + 3 6 J 1 7 + 3 1 ? ? C V 6 , 7 3 6 2 O p h 3 ; R X J 1 7 1 2 . 6 -2 4 1 4 J 1 7 2 -2 4 1 4 ? ? C V 6 , 7 3 6 V 5 3 H e r N H e r 9 3 J 1 8 4 + 4 5 ? ? C V 6 , 7 3 6 4 V 1 2 3 S g r ; 4 U 1 8 4 9 -3 1 ; 1 H 1 8 5 3 -3 1 2 J 1 8 5 -3 1 0 9 ? ? C V 6 , 7 3 6 5 A E A q r ; 2 0 3 7 -0 1 0 J 2 0 4 0 -0 5 2 ? ? C V 6 , 7 3 6 F O q r ; H 2 1 5 -0 8 6 J 2 1 7 -0 8 2 1 ? ? C V 6 , 7 3 6 7 R X J 2 3 5 3 . 0 -3 8 5 2 J 2 3 5 3 -3 8 5 1 ? ? C V 6 , 7 3 6 8 A H E r i J 0 4 -1 3 2 1 ? ? C V 6 , 7 3 6 9 K R u r J 0 6 1 5 + 8 ? ? C V 6 , 7 389 3 7 0 B Z C a m ; 0 6 2 3 + 7 1 J 0 6 2 9 + 7 1 0 4 ? ? C V 6 , 7 3 7 1 C P P u p ; N P u p 1 9 4 2 J 0 8 1 -3 5 2 1 ? ? C V 6 , 7 3 7 2 H 0 9 2 8 + 5 0 ; 0 9 2 8 + 5 0 4 ; 1 H 0 9 2 7 + 5 0 1 J 0 9 3 2 + 4 9 5 0 ? ? C V 6 , 7 3 7 R W S e x ; D -7 3 0 7 J 1 0 1 -0 8 4 1 ? ? C V 6 , 7 3 7 4 T L e o ; B D + 4 2 5 0 6 a ; 1 H 1 3 0 + 0 4 3 ; P G 1 3 5 + 0 3 6 J 1 3 8 + 3 2 ? ? C V 6 , 7 3 7 5 G Q M u s ; N M u s 1 9 8 3 J 1 5 2 -6 7 1 2 ? ? C V 6 , 7 3 7 6 T C r B ; H D 1 4 3 4 5 4 ; 1 5 9 + 2 5 9 J 1 5 9 + 5 ? ? C V 6 3 7 7 U S c o ; N S c o 9 8 7 ; 1 6 9 -1 7 8 J 1 6 2 -1 7 5 2 ? ? C V 6 , 7 3 7 8 V 1 0 1 7 S g r ; S g r 1 9 1 9 ; 1 8 3 2 -2 9 4 J 1 8 3 2 -2 9 2 3 ? ? C V 6 , 7 3 7 9 V 6 0 3 A q l ; N A q l 1 9 8 ; 8 4 6 + 0 5 J 1 8 4 + 0 3 5 ? ? C V 6 , 7 3 8 0 H 1 9 3 + 5 1 0 ; 1 H 1 9 2 9 + 5 0 J 1 9 3 4 + 5 7 ? ? C V 6 , 7 3 8 1 E C 1 9 3 1 4 -5 9 1 5 ; V 3 4 5 P a v ; 1 H 1 9 3 0 -5 8 9 J 1 9 3 5 -5 8 5 0 ? ? C V 6 3 8 2 V 7 9 4 A q l ; 2 0 1 7 -0 3 7 J 2 0 7 -0 3 9 ? ? C V 6 , 7 3 8 V S g e ; 2 0 2 0 + 2 1 ; 2 0 8 + 2 0 J 2 0 + 2 0 6 ? ? C V 6 , 7 3 8 4 H R D e l ; N D e l 1 9 6 7 J 2 0 4 + 1 9 9 ? ? C V 6 , 7 3 8 5 U X U m a ; 1 3 + 2 J 1 3 6 + 5 1 5 4 ? ? C V 6 , 7 3 8 6 V 2 3 0 1 O p h ; 1 H 1 7 5 0 8 1 J 1 8 0 + 0 8 1 0 ? ? C V 6 , 7 3 8 7 R X J 0 1 3 2 . 7 -6 5 4 ; H y i J 0 1 3 2 -6 5 4 ? ? C V 6 , 7 3 8 B L H y i ; H 0 1 3 9 -6 8 ; 1 H 0 1 3 6 -6 8 1 J 0 1 4 -6 7 5 3 ? ? C V 6 , 7 3 8 9 R X J 0 2 0 3 . 8 + 2 9 5 9 ; T r i J 0 2 3 + 2 9 5 9 ? ? C V 6 , 7 3 9 0 W H o r ; E O 4 -5 2 3 J 0 2 3 6 -5 2 1 9 ? ? C V 6 , 7 3 9 1 E F E r i ; 3 A ; 2 A 0 3 1 -2 7 ; 1 H 0 3 1 -2 7 J 0 3 1 4 -2 3 ? ? C V 6 , 7 3 9 2 V Y F o r ; E X O 0 3 2 9 5 7 -2 6 0 6 . 9 J 0 3 2 -2 5 6 ? ? C V 6 , 7 3 9 C a e 1 ; R S C a e ; R X J 0 4 3 -4 2 1 3 J 0 4 5 -4 2 1 3 ? ? C V 6 , 7 3 9 4 V 1 3 0 9 O r i ; R X J 0 5 1 5 + 0 1 0 4 ; R X J 0 5 1 5 . 6 + 0 1 0 5 J 0 5 1 5 + 1 0 4 ? ? C V 6 , 7 3 9 5 P i c 1 ; U W P i c ; X J 0 5 3 1 -4 6 2 4 J 0 5 3 1 -4 6 2 4 ? ? C V 6 , 7 3 9 6 H 0 5 3 8 + 6 0 8 ; B Y C a m ; 1 H 0 5 3 + 6 0 7 J 0 5 4 2 + 6 ? ? C V 6 3 9 7 R X J 0 7 1 9 . 2 + 6 5 7 ; 1 S 7 9 1 3 . 4 + 6 5 7 3 4 J 0 7 1 9 + 6 7 ? ? C V 6 3 9 8 V P u p ; 1 E 0 8 1 2 -1 8 5 4 J 0 8 1 5 -1 9 0 3 ? ? C V 6 , 7 3 9 E U C n c ; M 6 7 ; 5 + 1 8 J 0 8 5 1 + 4 6 ? ? C V 6 , 7 390 4 0 H y a 4 ; M N H y a ; R X 0 9 2 9 . 1 -2 4 0 4 J 0 9 2 9 -2 4 0 5 ? ? C V 6 , 7 4 0 1 R E J 1 0 2 -1 9 ; H y a J 1 0 2 -1 9 5 ? ? C V 6 , 7 4 0 2 L e o ; R X J 1 0 1 5 . 5 + 0 9 0 4 J 1 0 5 + 0 4 ? ? C V 6 , 7 4 0 3 E 1 0 1 3 -4 7 ; K O V e l ; 1 H 1 0 6 -4 7 2 J 1 0 5 -4 7 5 8 ? ? C V 6 , 7 4 0 F H U M a ; U M a 9 ; R X J 1 0 4 7 . 1 + 6 3 5 J 1 0 4 7 + 6 3 5 ? ? C V 6 , 7 4 0 5 E K U m a ; 1 E 1 0 4 8 . 5 + 5 4 2 1 ; 1 H 1 0 4 6 + 5 4 7 J 1 0 5 + 5 4 4 ? ? C V 6 , 7 4 0 6 A N U m a ; P G 1 0 1 + 4 5 3 J 1 0 4 + 4 3 ? ? C V 6 , 7 4 0 7 S T L m i ; C W 1 0 3 + 2 5 J 1 0 5 + 2 5 6 ? ? C V 6 , 7 4 0 8 A R U M a ; 1 S 1 1 3 + 4 3 2 ; 1 H 1 0 + 4 2 3 J 1 5 + 4 2 8 ? ? C V 6 , 7 4 0 9 D P L e o ; 1 E 1 1 4 + 1 8 2 J 1 7 + 7 7 ? ? C V 6 , 7 4 1 0 C e n 3 ; R X J 1 4 1 . 3 -6 4 1 0 J 1 4 -6 4 1 0 ? ? C V 6 4 1 E U m a E 9 + 2 8 J 1 4 9 + 2 8 4 5 ? ? C V 6 , 7 4 1 2 E V U m a ; R X J 1 3 0 7 + 5 3 5 ; R E J 0 7 5 3 5 J 1 3 0 7 + 5 3 5 ? ? C V 6 , 7 4 1 3 E 1 4 0 5 -4 5 1 ; V 8 3 4 ; 1 H 1 4 0 -4 5 0 J 1 4 0 9 -4 5 1 7 ? ? C V 6 4 1 M R S e r P G 1 5 0 + 9 1 J 1 5 2 + 8 5 6 ? ? C V 6 , 7 4 1 5 R X J 1 7 2 4 . 0 + 4 1 4 J 1 7 2 7 + 4 1 4 ? ? C V 6 4 1 6 H e r 5 ; V 8 4 H e r ; R X J 1 8 0 2 . 1 + 1 8 0 4 ; W G A J 1 8 0 2 . + 8 J 1 8 0 2 + 8 0 ? ? C V 6 , 7 4 1 7 H 1 8 1 6 + 4 9 A M r ; 1 H 1 8 4 + 4 9 8 J 1 8 1 6 + 4 9 5 ? ? C V 6 , 7 4 1 8 V 3 4 7 P a v ; R X J 1 8 4 -7 4 ; R E J 1 8 4 -7 4 J 1 8 4 -7 4 1 8 ? ? C V 6 , 7 4 1 9 E P D r a ; H 9 0 3 + 6 9 ; 9 7 + 6 9 0 J 1 9 0 7 + 6 9 0 8 ? ? C V 6 4 2 0 R X J 1 9 1 4 . 4 + 2 4 5 6 J 1 9 4 + 2 4 5 ? ? C V 6 , 7 4 2 1 Q S T e l ; R X J 1 9 3 8 . 6 -4 9 1 2 ; R E J 1 9 3 8 . 6 -4 9 1 2 J 1 9 3 8 -4 6 1 2 ? ? C V 6 , 7 4 2 Q V u l ; 2 0 3 + 2 5 2 0 5 + 2 J 2 0 5 + 2 3 9 ? ? C V 6 , 7 4 2 3 V 3 4 9 P a v ; D r i s e n V 2 1 b J 2 0 8 -6 5 2 7 ? ? C V 6 , 7 4 2 R X J 2 0 2 . 6 -3 9 5 4 ; V 4 7 3 8 S g r J 2 0 -3 9 5 4 ? ? C V 6 4 2 5 H U A q r ; R X J 2 1 0 7 . 9 -0 5 1 8 ; R E J 2 1 0 7 . -0 5 1 8 J 2 1 0 7 -0 5 1 7 ? ? C V 6 , 7 4 2 6 V 1 5 0 C y g ; N C y g 1 9 7 5 ; 1 0 9 4 7 9 J 2 1 + 4 8 9 ? ? C V 6 , 7 4 2 7 R X J 2 1 5 . 7 -5 8 4 0 ; E U V E J 2 1 5 -5 8 . 6 J 2 1 5 -5 8 4 0 ? ? C V 6 , 7 4 2 8 C E G r u ; G r u s I V J 2 1 3 7 -4 3 4 2 ? ? C V 6 , 7 391 4 2 9 A X J 2 3 1 5 -5 9 2 ; I R A S 2 3 1 2 8 -5 9 1 9 J 2 3 1 5 -5 9 1 0 ? ? C V 6 4 3 0 T P y x ; H V 3 4 8 ; 1 H 0 9 0 8 -3 2 6 J 0 9 0 4 -3 2 2 ? ? C V 6 , 7 4 3 1 W X H y i ; 0 2 0 8 -6 3 5 J 0 2 -6 3 1 8 ? ? C V 6 , 7 4 3 2 V H y i ; A N 1 . 1 9 3 2 J 0 4 9 -7 1 8 ? ? C V 6 , 7 4 3 Y Z C n c J 0 8 1 + 2 8 0 8 ? ? C V 6 , 7 4 3 S U m a ; P G 0 8 0 8 + 6 2 7 ; 1 H 0 8 1 + 6 2 5 J 0 8 1 2 + 6 2 3 6 ? ? C V 6 , 7 4 3 5 V 4 3 6 C e n ; 1 E 1 1 -3 7 2 4 J 1 1 4 -3 7 4 0 ? ? C V 6 , 7 4 3 6 E K T r A ; 1 5 0 9 -6 4 9 J 1 5 4 -6 5 0 5 ? ? C V 6 4 3 7 I X V e l ; C P D -4 8 1 5 7 J 0 8 -4 9 1 3 ? ? C V 6 , 7 4 3 8 E I U m a ; P G 0 8 3 4 + 4 8 1 H 3 2 4 8 J 0 8 3 + 4 8 3 8 ? ? C V 6 , 7 4 3 9 B V C e n J 1 3 1 -5 4 5 8 ? ? C V 6 , 7 4 0 A D r a J 1 9 4 9 + 7 4 ? ? C V 6 , 7 4 1 E Y C y g J 1 9 5 4 + 3 2 ? ? C V 6 , 7 4 2 V 3 8 5 S g r ; C D -4 2 1 4 6 2 ; 1 9 4 -4 2 1 J 1 9 4 7 -4 2 0 ? ? C V 6 , 7 4 3 W C e t ; 1 H 2 3 5 7 -1 2 6 J 0 -1 2 8 ? ? C V 6 , 7 4 R X A n d ; 1 E 0 0 1 + 4 1 0 1 J 0 1 4 + 4 1 ? ? C V 6 , 7 4 5 H L C m a ; 1 E 0 6 4 3 -1 6 4 8 J 0 6 4 5 -1 6 5 1 ? ? C V 6 , 7 4 6 T a u 3 ; J 0 4 5 9 . 7 + 9 2 9 J 0 4 5 9 + 1 9 2 6 ? ? C V 6 4 7 R X J 0 5 0 2 . 8 + 1 6 2 4 J 0 5 2 + 1 6 2 4 ? ? C V 6 4 8 L a n i n g 1 0 ; V 3 6 3 u r J 0 5 3 + 3 6 ? ? C V 6 , 7 4 9 R X J 1 3 2 6 . 9 + 4 5 3 2 ; D E C V n J 1 3 2 6 + 4 ? ? C V 6 4 5 0 L Y H y a 2 ; 1 3 2 9 -2 9 4 J 1 3 -2 9 4 0 ? ? C V 6 , 7 4 5 1 L X S e r ; 1 5 3 6 + 9 0 J 1 5 3 8 + 8 5 ? ? C V 6 , 7 4 5 2 V 8 2 5 H e r ; P G 7 1 7 + 4 J 1 7 8 + 4 1 5 ? ? C V 6 , 7 4 5 3 V 3 8 0 O p h ; 1 7 4 7 + 0 J 1 7 5 0 + 0 6 0 5 ? ? C V 6 , 7 4 5 V 8 2 7 H e r ; N o v a H e r 1 9 1 ; 1 8 4 + 1 2 J 1 8 4 6 + 2 2 ? ? C V 6 4 5 V 1 9 7 4 C y g ; N C y g 9 2 J 2 0 3 0 + 5 2 3 7 ? ? C V 6 , 7 4 5 6 C y g 6 ; R X J 2 1 2 3 . 7 + 4 2 J 2 1 3 + 4 2 1 7 ? ? C V 6 4 5 7 A 0 5 3 8 -6 ; X 0 5 3 5 -6 8 J 0 5 3 8 -6 5 2 ? ? H M X B 6 4 5 8 G S 1 8 4 3 -0 2 ; G R O J 1 8 4 -0 3 ; X 1 8 4 5 -0 2 4 J 1 8 4 9 -0 3 1 8 ? ? H M X B 6 392 4 5 9 V T u c ; H D 5 1 4 8 J 0 5 1 -7 1 5 9 ? ? L M X B 6 , 8 4 6 0 U C e p ; H D 5 6 7 9 J 0 1 2 + 8 5 2 ? ? L M X B 6 , 8 4 6 1 D S A n d ; N G C 7 2 J 0 1 5 7 + 3 8 0 4 ? ? L M X B 6 , 8 4 6 2 D O C a s ; H D 1 6 5 0 6 J 0 2 4 + 6 ? ? L M X B 6 , 8 46 3 R Z C a s ; H R 8 1 5 ; H D 1 7 1 3 8 ; 1 E 0 2 4 + 6 9 4 J 0 2 4 8 + 6 9 3 8 ? ? L M X B 6 , 8 4 6 B e t a P e r ; A l g o l J 0 3 8 + 5 7 ? ? L M X B 6 , 8 4 6 5 L a m b d a T a u ; S A O 9 3 7 1 9 J 0 4 + 1 9 ? ? L M X B 6 , 8 4 6 I M A u r ; H D 3 8 5 3 ; B V 2 6 J 0 5 1 5 + 6 2 4 ? ? L M X B 6 , 8 4 6 7 A R A u r ; H R 1 7 2 8 J 0 5 1 8 + 3 ? ? L M X B 6 , 8 4 6 8 A W C a m ; H D 4 8 0 4 9 ; B V 4 1 2 ; S A O 0 3 9 5 J 0 6 4 7 + 6 9 7 ? ? L M X B 6 , 8 4 6 9 S C n c ; H D 7 4 3 0 7 ; B 1 9 2 0 9 0 J 0 8 4 3 + 1 9 0 2 ? ? L M X B 6 , 8 4 7 0 T X U M a ; H D 4 3 0 3 J 1 0 4 5 + 5 3 ? ? L M X B 6 , 8 4 7 1 T H y a ; M S 1 1 0 -2 6 2 ; H D 9 7 5 2 8 J 1 3 -2 6 2 7 ? ? L M X B 6 , 8 4 7 2 Z D r a ; B D + 7 3 0 5 3 J 1 4 5 + 7 2 1 ? ? L M X B 6 , 8 4 7 3 1 E 1 2 4 7 . 0 -0 5 4 8 ; S A O 1 3 8 9 8 3 J 1 2 4 9 -0 6 0 4 ? ? L M X B 6 4 7 S C e n ; H 1 4 7 2 0 J 1 3 3 -6 4 9 ? ? L M X B 6 , 8 4 7 5 D e l t a L i b ; H D 1 3 2 7 4 2 I N C A 2 6 9 J 1 5 0 -0 8 3 1 ? ? L M X B 6 , 8 4 7 6 U C r B ; H D 1 3 6 1 7 5 J 1 5 8 + 3 8 ? ? L M X B 6 , 8 4 7 T W D r a ; S A O 0 6 7 6 ; V 3 7 4 J 1 5 3 + 6 3 4 ? ? L M X B 6 , 8 4 7 8 A l p h a C r B ; A l p h e k a ; H R 5 7 9 3 ; H D 1 3 9 0 6 J 1 5 3 4 + 2 6 4 2 ? ? L M X B 6 , 8 4 7 9 R A r a ; H 1 4 9 7 3 0 ; S A O J 1 6 3 9 -5 6 5 9 ? ? L M X B 6 , 8 4 8 0 V 1 0 1 0 O p h ; H D 1 5 1 6 7 6 ; H R 6 2 4 0 ; S A O 1 6 0 1 6 J 1 6 4 9 -1 5 4 0 ? ? L M X B 6 , 8 4 8 1 A I D r a ; C S V 1 0 1 6 2 0 J 1 6 5 + 5 2 4 ? ? L M X B 6 , 8 4 8 2 V 8 4 6 O p h ; H D 3 6 7 J 1 7 3 9 -2 8 5 1 ? ? L M X B 6 , 8 4 8 3 X Z S g r ; H D 1 6 8 7 1 0 ; V 3 0 4 J 1 8 2 -2 5 1 4 ? ? L M X B 6 , 8 4 8 B S S c t ; N G C 6 7 0 5 ; S V S 9 1 J 1 8 5 2 -0 6 1 4 ? ? L M X B 6 , 8 4 8 5 R S V u l ; H D 1 8 0 9 4 9 ; S O 0 8 7 0 3 5 J 1 9 7 + 6 ? ? L M X B 6 , 8 4 8 6 B E V u l ; H D 3 4 0 2 0 1 ; S S 4 7 5 ; S A O 0 8 6 3 J 2 0 2 5 + 2 2 ? ? L M X B 6 , 8 4 8 7 D F P e g ; S A O 1 0 7 4 9 J 2 1 5 4 + 4 3 ? ? L M X B 6 , 8 4 8 D I P e g ; S A O 1 0 8 6 J 2 3 + 5 8 ? ? L M X B 6 , 8 393 4 8 9 1 E 1 7 4 0 . 7 -2 9 4 2 ; G r e a t A n i h i l a t o r J 1 7 4 -2 9 4 3 ? ? L M X B 6 4 9 0 E X O 1 8 4 6 -0 3 1 J 1 8 4 9 -0 3 0 8 ? ? L M X B 6 4 9 1 Z e t a A n d ; H R 2 1 5 ; B D 2 3 0 1 0 6 ; S A O 0 7 4 2 6 7 ; H R 2 1 5 J 0 4 7 + 2 1 6 ? ? L M X B 6 , 8 4 9 2 C F T u c ; H D 5 3 0 3 J 0 5 3 -7 4 3 9 ? ? L M X B 6 , 8 4 9 3 U V P s c , H D 7 0 ; S A O 1 0 9 7 8 J 0 1 6 + 0 6 4 8 ? ? L M X B 6 , 8 4 9 B I C e t ; H D 8 3 5 8 ; 1 E S 0 1 2 0 + 0 4 J 0 1 2 + 4 2 ? ? L M X B 6 , 8 4 9 5 A R P s c ; H D 8 3 5 7 ; 1 H 2 3 + 0 7 5 J 0 1 2 + 7 2 5 ? ? L M X B 6 , 8 4 9 6 T Z T r i A ; H R 6 4 2 A J 0 2 1 2 + 3 8 ? ? L M X B 6 , 8 4 9 7 L X P e r ; S O 3 8 5 1 J 0 3 1 3 + 4 8 0 6 ? ? L M X B 6 , 8 4 9 8 1 E 0 3 1 5 . 7 -1 9 5 J 0 3 1 8 -1 9 4 ? ? L M X B 6 4 9 U X A r i ; H 0 3 2 4 + 2 8 J 0 3 2 5 + 2 4 2 ? ? L M X B 6 , 8 5 0 I X P e r ; H D 2 2 4 J 0 3 5 + 0 ? ? L M X B 6 , 8 5 0 1 V 7 1 T a u ; H R 1 0 9 ; 1 H 0 3 2 7 + 0 0 J 0 3 6 + ? ? L M X B 6 , 8 5 0 2 V 8 3 T a u ; H D 2 4 3 ; B D 2 5 5 8 0 J 0 3 7 + 2 5 9 ? ? L M X B 6 , 8 5 0 3 R Z E r i ; H D 3 0 5 0 J 0 4 -1 0 3 9 ? ? L M X B 6 , 8 5 0 4 H R 1 6 2 3 ; 1 2 C m ; 1 0 5 + 5 9 J 0 5 6 + 5 9 0 1 ? ? L M X B 6 5 0 1 E 0 5 0 5 . 0 -0 5 2 7 ; M S 0 5 0 5 . 0 -0 5 2 7 J 0 5 7 -0 5 2 4 ? ? L M X B 6 5 0 6 A l p h a A u r ; H D 3 4 0 2 9 ; 1 E 0 5 1 3 + 4 5 9 ; C a p e l a A + B J 0 5 1 6 + 4 9 ? ? L M X B 6 , 8 5 0 7 A B D o r ; H D 3 6 7 0 5 ; 1 E 0 5 2 8 4 0 -6 4 2 9 J 0 5 2 8 -6 5 2 7 ? ? L M X B 6 5 0 8 C Q A u r ; H D 2 5 0 8 1 J 0 6 3 + 3 1 9 ? ? L M X B 6 , 8 5 0 9 S V C a m ; E X O 0 6 3 0 + 8 2 3 ; H 6 3 0 + 2 J 0 6 4 1 + 8 2 1 6 ? ? L M X B 6 , 8 5 1 0 V M o n ; B D -5 1 9 3 5 J 0 7 3 -0 5 4 ? ? L M X B 6 , 8 5 1 S C a m ; H V 3 1 0 J 0 7 1 6 + 2 ? ? L M X B 6 , 8 5 1 2 A R M o n ; H D 5 7 6 4 J 0 7 2 -0 5 1 5 ? ? L M X B 6 , 8 5 1 3 A E L y n ; H D 6 5 6 2 6 ; H R 3 1 9 ; S A 0 2 6 3 4 J 0 8 2 + 5 ? ? L M X B 6 , 8 5 1 4 R U C n c ; 0 8 3 4 + 2 3 7 J 0 8 3 7 + 3 3 ? ? L M X B 6 , 8 5 1 R Z C n c ; 7 3 4 3 ; S A O 6 0 5 4 J 0 8 3 9 + 1 4 7 ? ? L M X B 6 , 8 5 1 6 T Y P y x ; H D 7 1 ; R E 0 8 5 9 -2 7 4 J 0 8 5 9 -2 7 4 9 ? ? L M X B 6 , 8 394 5 1 7 W Y C n c ; C S V 1 3 9 7 ; S 4 7 5 1 J 0 9 0 1 + 2 6 4 1 ? ? L M X B 6 , 8 5 1 8 X Y U M a ; S A O 2 7 1 4 3 J 0 9 + 5 4 9 ? ? L M X B 6 , 8 5 1 9 L R H y a ; H D 9 1 8 1 6 ; S A O 1 5 6 0 9 0 J 1 0 3 6 -1 5 4 ? ? L M X B 6 , 8 5 2 0 1 E 1 2 7 . 9 -1 5 0 2 ; M S 1 2 7 . 8 -1 5 0 2 ; H D 1 0 0 2 ; S A O 1 5 6 7 2 0 J 1 3 -1 5 9 ? ? L M X B 6 5 2 1 E X O 3 4 8 -3 7 4 6 ; V 8 5 8 C e n ; S A O 2 0 2 6 1 8 J 1 3 6 -3 8 0 2 ? ? L M X B 6 5 2 R W U m a ; 1 3 5 3 + 5 2 5 J 1 4 0 + 5 1 5 9 ? ? L M X B 6 5 2 3 9 3 L e o ; H D 1 0 2 5 0 9 ; S A O 8 1 J 1 4 7 + 2 1 ? ? L M X B 6 , 8 5 2 4 D K D r a ; H R 4 6 5 ; H D 1 0 6 7 ; 1 E S 1 2 1 3 + 7 2 8 J 1 2 5 + 2 3 ? ? L M X B 6 , 8 5 2 I L C o m ; H D 1 0 8 1 0 2 ; M S 1 2 2 + 2 5 J 1 2 5 + 3 ? ? L M X B 6 , 8 5 2 6 H Z C o m ; B D + 2 5 2 5 1 J 1 2 9 + 4 3 ? ? L M X B 6 , 8 5 2 7 U X C o m ; B V 2 9 5 J 1 3 0 + 8 3 7 ? ? L M X B 6 , 8 5 2 8 R S C V n ; H D 1 4 5 1 9 ; 3 3 + 3 8 J 1 3 0 + 5 6 ? ? L M X B 6 , 8 5 2 9 B L C V n ; H D 1 5 7 8 2 S A O 6 4 6 J 1 3 8 + 2 6 ? ? L M X B 6 , 8 5 3 0 B H C V n ; H R 5 1 0 J 1 3 4 + 3 7 1 0 ? ? L M X B 6 , 8 5 3 1 R V L i b ; H D 1 2 8 1 7 J 1 4 3 5 -1 8 0 2 ? ? L M X B 6 , 8 5 3 2 S B o ; D + 3 9 4 9 J 1 5 3 + 8 ? ? L M X B 6 , 8 5 3 T Z C r B ; s i g m a C r B ; R E 1 6 4 + 3 J 1 6 4 + 5 ? ? L M X B 6 , 8 5 3 4 W D r a ; H D 1 5 0 7 0 8 ; H 3 9 8 J 1 6 3 9 + 0 2 ? ? L M X B 6 , 8 5 3 e p s i l o n U M i ; H D 1 5 3 7 5 1 J 1 6 4 5 + 8 2 0 2 ? ? L M X B 6 , 8 5 3 6 V 7 9 2 H e r ; H 1 5 6 3 8 ; H 1 7 0 8 + 4 9 J 1 7 0 + 8 7 ? ? L M X B 6 , 8 5 3 7 V 8 2 4 A r a ; H D 1 5 5 5 ; E X O 1 7 1 2 4 -6 5 3 . 9 J 1 7 -6 5 6 ? ? L M X B 6 , 8 5 3 8 V 9 6 5 S c o ; H D 1 5 8 3 9 3 ; S A O 2 0 8 9 5 ; 1 7 2 7 -3 6 J 1 7 3 0 -3 3 9 ? ? L M X B 6 , 8 5 3 9 Z H e r ; H y a d e s ; I N C A 1 8 9 J 1 7 5 8 + 5 8 ? ? L M X B 6 , 8 5 4 0 M H e r ; H D 3 4 1 4 7 5 ; S A O 0 8 0 J 1 7 5 8 + 2 0 8 ? ? L M X B 6 , 8 5 4 1 V 7 2 H e r A a b ; H D 1 7 5 9 0 A ; S A O 0 8 5 7 2 3 J 1 8 0 5 + 2 6 ? ? L M X B 6 , 8 5 4 2 P W H e r ; S 4 7 7 J 1 8 0 + 3 7 ? ? L M X B 6 , 8 5 4 3 A W H e r ; H D 3 4 8 6 3 5 ; S S 1 6 3 J 1 8 2 5 + 8 1 7 ? ? L M X B 6 , 8 5 4 V 1 4 3 0 A q l ; 1 E 1 9 1 9 + 0 4 2 7 J 1 9 2 + 0 4 3 2 ? ? L M X B 6 5 4 V 1 8 1 7 C y g ; H R 7 4 2 8 ; D 1 8 4 9 8 / J 1 9 3 + 5 4 3 ? ? L M X B 6 , 8 395 5 4 6 V 1 7 6 4 C y g H D 1 8 5 1 5 1 J 1 9 3 6 + 2 7 5 3 ? ? L M X B 6 , 8 5 4 7 C G C y g ; B D + 3 4 4 2 7 J 2 0 5 8 + 5 1 0 ? ? L M X B 6 , 8 5 4 8 E R V u l ; H D 2 0 3 9 1 ; S A O 0 8 9 3 9 6 ; 1 E S 2 1 0 + 2 7 6 J 2 1 0 + 2 7 4 8 ? ? L M X B 6 , 8 5 4 9 H R 8 1 7 0 ; H D 2 0 3 5 4 J 2 1 2 1 + 4 ? ? L M X B 6 , 8 5 0 A D C a p ; C S 5 4 5 2 ; H D 2 0 6 0 4 6 J 2 1 3 9 -1 6 0 ? ? L M X B 6 , 8 5 1 F q r ; S A O 1 4 5 8 0 B -3 5 3 5 7 J 2 0 -0 2 4 ? ? L M X B 6 , 8 5 2 R T L a c ; H D 2 0 9 3 1 ; S A O 0 5 5 J 2 0 1 + 4 3 5 ? ? L M X B 6 , 8 5 3 A L a c ; H 2 1 0 3 4 ; H 2 0 7 + 4 5 J 2 0 8 + 4 5 ? ? L M X B 6 , 8 5 4 R T A n d ; B + 5 8 3 a J 2 3 1 + 5 3 ? ? L M X B 6 , 8 5 S Z P s c ; H D 2 1 9 1 3 ; I N C A 1 2 6 3 ; S A O 1 2 8 0 4 1 J 2 3 1 + 0 4 ? ? L M X B 6 , 8 5 6 K T P e g ; H D 2 2 3 1 7 ; S A O 0 9 1 4 0 5 J 2 3 9 + 8 4 ? ? L M X B 6 , 8 5 7 H R 9 0 2 4 ; 2 3 5 0 + 3 6 4 J 2 3 4 9 + 6 2 5 ? ? L M X B 6 , 8 5 8 1 H 2 3 5 4 + 2 8 5 I P e g a s i ; A 0 0 + 2 8 J 2 3 5 + 8 8 ? ? L M X B 6 5 9 H V 1 5 4 ; R X J 0 5 2 7 . 8 -6 9 5 4 J 0 5 7 -6 9 2 1 ? ? L M X B 6 5 6 0 C A L 8 7 ; L H G 8 7 ; 1 E ; L M C 3 6 3 S o u r c e i n L M C J 0 5 4 6 -7 1 0 8 ? ? L M X B 6 , 7 5 6 1 B 0 5 6 . 8 -7 1 6 4 ; N 6 7 ? J 0 5 8 -7 1 3 5 ? ? L M X B 6 5 6 2 O A O ; V 8 6 1 S c o ; D 1 5 2 6 J 1 6 5 6 -4 0 4 9 ? ? L M X B 6 5 6 3 R X J 0 0 2 + 6 2 4 6 ; G 1 7 . 7 + 0 . J 0 0 2 + 2 4 6 ? ? N S 6 5 6 4 P S R J 0 1 7 + 5 9 1 4 ; P S R B 0 1 5 J 0 1 7 + 5 9 1 4 ? B 0 1 4 + 5 8 N S 6 , 1 5 6 P S R J 0 6 3 1 + 1 0 J 0 6 2 8 + 3 8 ? ? N S 6 5 6 G 2 9 0 . 1 -0 8 ; 2 E G 1 0 3 -6 1 0 6 ; P S R J 1 0 5 -6 1 0 7 J 1 5 -6 1 0 7 ? ? N S 6 , 1 5 6 7 S N R 3 2 . 4 -0 . 4 ; A X J 1 6 1 7 0 -5 0 5 0 5 ; 1 E 1 6 1 3 4 8 -5 0 5 ; P S R J 1 6 1 7 3 0 -5 0 5 ; R C W 1 0 3 J 1 6 7 -5 0 5 ? ? N S 6 , 1 5 6 8 M 4 ; P S R B 1 6 2 0 -2 6 J 1 6 2 3 -2 6 3 1 ? B 1 6 2 0-2 6 N S 6 , 1 5 6 9 P S R 1 6 4 2 -0 3 ; P S R J 1 6 4 5 -0 3 1 7 J 1 6 4 5 -0 3 1 7 ? ? N S 6 5 7 0 1 R X S J 1 7 8 4 9 . 0 -4 0 9 1 0 J 1 7 0 8 -4 0 9 ? ? N S 6 5 7 1 P S R J 1 7 4 0 -3 0 1 5 ; P S R B 1 7 3 7 -3 0 J 1 7 4 0 -3 0 1 5 ? ? N S 6 5 7 2 4 U 1 7 4 3 -2 9 ; 1 H 7 4 -2 9 3 J 1 7 4 8 -2 9 2 4 ? ? L M X B 6 , 5 3 5 7 3 A X J 1 8 1 . 5 -1 9 6 ; S N R G 1 . 2 -0 . 3 J 1 8 -1 9 6 ? ? N S 6 , 1 396 5 7 4 P S R J 1 9 1 7 + 1 3 5 3 ; P S R B 1 9 1 5 + 1 3 J 1 9 1 7 + 1 3 5 3 ? ? N S 6 5 7 P S R B 1 9 3 7 + 2 1 J 1 9 3 + 2 3 4 ? B 1 9 3 7 + 2 1 N S 6 , 1 , 2 5 , 2 6 5 7 6 1 W G A J 1 9 5 8 . 2 + 3 2 3 2 J 1 9 5 8 + 2 3 ? ? H M X B 6 5 7 P S R J 2 3 2 + 2 0 5 J 2 3 2 + 2 0 5 7 ? ? N S 6 , 1 5 7 8 B e t a C e t i ; 0 4 -1 8 0 J 0 4 -1 7 5 9 ? ? N S 6 5 7 9 R X J 1 8 5 6 . 5 -3 7 5 4 J 1 8 5 6 -3 7 5 4 ? ? N S 6 5 8 0 B G P s c ; H D 9 0 2 ; E X O 0 1 3 4 2 5 + 2 0 2 7 J 0 1 3 7 + 2 ? ? L M X B 6 5 8 1 M S 0 2 4 . 8 -0 4 2 ; S A O 1 3 0 1 3 J 0 2 4 7 + 0 3 7 ? ? L M X B 6 5 8 2 s i g m a e m ; H D 6 2 0 4 ; 1 H 0 7 4 + 2 8 9 J 0 7 4 3 + 8 5 ? ? L M X B 6 5 8 3 2 A 1 0 5 2 + 6 0 6 ; D M U m a ; 1 H 1 0 5 + 6 7 ; S A O 0 1 5 3 8 J 1 0 5 + 6 ? ? L M X B 6 5 8 4 H U V i r ; H 1 0 6 2 5 J 1 2 1 3 -0 9 0 4 ? ? L M X B 6 5 8 K N U M a ; R X J 1 2 3 9 . 8 + 5 1 ; G S C 3 8 4 . 0 3 1 7 J 1 2 3 9 + 5 ? ? L M X B 6 5 8 6 P G 1 4 1 3 + 0 1 0 J 1 4 6 + 0 4 6 ? ? L M X B 6 5 8 7 M S 1 5 2 0 . 2 + 2 5 4 8 ; U V C r ; S A O 8 3 7 9 5 J 1 5 2 + 2 5 7 ? ? L M X B 6 5 8 M S 1 5 2 0 . 7 -0 6 2 5 ; X L i b ; S 1 4 4 9 J 1 5 2 3 -0 6 3 6 ? ? L M X B 6 5 8 9 D R D r a ; 9 D r a ; H D 1 6 0 5 3 8 ; 1 7 3 + 7 4 2 J 1 7 3 2 + 7 4 1 3 ? ? L M X B 6 5 9 0 U S g e J 1 9 4 2 + 7 0 5 ? ? L M X B 6 5 9 1 H K L a c ; 2 0 4 9 + 4 7 2 J 2 0 4 + 1 4 ? ? L M X B 6 5 9 2 H 2 3 1 + 7 ; H D 2 0 1 4 0 ; 1 H 3 1 3 + 7 8 3 E X O 2 3 1 8 + 7 8 7 3 J 2 3 1 9 + 7 0 ? ? L M X B 6 5 9 3 l a m b d a A n d ; H 2 2 1 0 7 1 H 3 6 4 6 2 J 2 3 7 + 4 6 7 ? ? L M X B 6 5 9 4 V 7 3 T a u ; D 2 8 3 4 7 J 0 4 1 4 + 2 8 1 ? ? T S 6 5 9 L k C a ; 0 4 1 6 3 6 + 7 4 J 0 4 1 9 + 7 9 ? ? T S 6 5 9 6 B P T a u ; 0 4 1 6 + 2 8 5 9 J 0 4 1 9 + 2 0 6 ? ? T S 6 5 9 7 T T a u ; 0 4 1 9 + 9 2 4 J 0 4 2 1 + 3 ? ? T S 6 5 9 8 H D E 2 8 3 5 7 2 ; S A O 7 6 5 6 7 J 0 4 2 1 + 8 8 ? ? T S 6 5 9 R Y T a u ; 0 4 1 8 + 2 8 1 9 J 0 4 2 1 + 8 6 ? ? T S 6 6 0 D F T a u ; 0 4 2 + 2 5 3 5 J 0 4 2 7 + 5 ? ? T S 6 6 0 1 D H T a u ; 0 4 2 6 7 + 6 2 6 X 1 J 0 4 2 9 + 6 3 ? ? T S 6 397 6 0 2 U X T a u A ; 0 4 2 7 1 + 1 8 0 7 X 2 J 0 4 3 0 + 1 8 1 3 ? ? T S 6 6 0 3 T A P 4 0 ; 0 4 2 8 3 5 + 1 7 0 J 0 4 3 1 + 1 7 6 ? ? T S 6 6 0 4 T A P 4 1 ; 2 9 1 6 + 1 7 J 0 4 3 2 + 7 5 ? ? T S 6 6 0 5 V 8 2 6 a u ; 0 + 7 9 J 0 4 3 2 + 1 8 0 ? ? T S 6 6 0 V 8 2 7 a u ; 0 2 9 + 1 8 J 0 4 3 2 + 1 8 ? ? T S 6 6 0 7 G I T a u ; 0 4 3 0 5 + 4 X 1 J 0 4 3 + ? ? T S 6 6 0 8 G K T a u ; 0 4 3 5 + 2 2 J 0 4 3 + 2 2 1 ? ? T S 6 6 0 9 V 8 3 0 a u ; 0 4 3 + 7 4 J 0 4 3 + 2 4 ? ? T S 6 6 1 0 A T a u ; 4 3 1 + J 0 4 3 + 2 8 ? ? T S 6 6 1 D N T a u ; 0 4 3 2 + 2 J 0 4 3 5 + 2 1 4 ? ? T S 6 6 1 2 G M A u r ; 0 4 5 1 9 + 0 7 J 0 4 5 + 1 ? ? T S 6 6 1 3 S U A u r ; 0 4 5 2 8 + 9 J 0 4 5 + 3 4 ? ? T S 6 6 1 4 T A P 5 7 N W ; 0 4 5 2 5 1 + 3 0 1 6 J 0 4 5 6 + 3 2 1 ? ? T S 6 6 1 5 V 8 3 6 T a u ; 0 5 0 + 2 3 J 0 5 3 + 2 2 ? ? T S 6 6 1 R W A u r ; I R A S 0 5 6 + 3 0 2 J 0 5 7 + 4 ? ? T S 6 6 1 7 V 1 3 2 1 O r i ; P r 1 7 2 4 J 0 5 3 -0 5 0 8 ? ? T S 6 6 1 8 W D 0 2 3 2 + 0 3 5 ; F e i g e 2 4 J 0 2 3 + 4 ? ? W D 6 6 1 9 R E 2 0 1 3 + 4 0 J 2 0 1 3 + 4 0 2 ? ? W D 6 6 2 0 R X J 2 1 7 . 1 + 3 4 1 2 ; P G 1 5 9 ; V 2 0 2 7 C y g J 2 1 7 + 4 1 2 ? ? W D 6 6 2 1 1 E 0 3 5 . 4 -7 2 3 0 ; S M C 1 S o u r c e i n S M C J 0 3 7 -7 2 1 4 ? ? ? ? 6 , 7 6 2 M 3 X -8 J 0 1 3 + 0 3 9 ? ? ? 6 6 2 3 1 H 0 5 3 8 -6 4 1 ; L C X -3 S o u r c e i n L M C J 0 5 3 8 -6 4 0 4 ? ? H M X B 6 6 2 4 R 1 4 0 a 2 ( W N 6 ) ; 3 0 D o r a d u s ; H D 2 6 9 a J 0 5 3 8 -6 9 0 5 ? ? ? ? 6 6 2 5 G R S 1 7 5 8 -2 5 8 J 1 8 1 -2 5 4 7 ? ? ? 6 6 2 N o v a A q l 1 9 2 ; G R S 1 9 1 5 + 1 0 5 J 1 9 5 + 6 ? ? ? 6 6 2 7 P S R J 1 9 0 7 + 0 ; S 0 4 J 1 9 0 7 + 0 9 1 8 ? ? ? 6 6 2 8 R O A T 5 8 ; E i n s t e i n 6 9 ; M 3 J 0 4 2 + 4 1 ? ? ? 6 6 2 9 R O S A T 6 0 ; E i n s t e i 7 ; M 3 1 J 0 4 2 + 1 6 ? ? ? 6 6 3 0 P S R B 1 2 5 7 + 1 2 J 1 3 + 1 0 ? B 1 2 5 7 + 1 2 ? 6 , 1 6 3 1 P S R B 1 5 3 4 + 1 2 ; P S R J 1 5 3 7 + 1 5 J 1 5 3 7 + 1 5 ? B 1 5 3 4 + 1 2 ? 6 , 1 398 6 3 2 T e r z a n 5 ; X B 1 7 4 5 -2 5 ; P S R 1 7 4 -2 4 A J 1 7 4 8 -2 4 6 ? B 1 7 4 -2 4 A L M X B 6 , 5 4 6 3 G S 1 8 4 3 + 0 9 ; G P S 1 8 4 0 + 0 1 J 1 8 4 5 + 0 5 0 ? ? ? ? 6 6 3 4 P S R J 2 0 1 9 + 2 4 2 5 J 2 0 9 + 2 2 5 ? ? ? 6 , 1 6 3 5 F A n d ; G l i e s e 2 9 . 1 ; R E 0 2 + 3 5 3 J 0 4 + 3 5 3 ? ? ? 6 6 3 V 4 0 5 n d ; B Y D ; R J 0 2 2 . 4 7 2 9 J 0 2 2 + 7 2 ? ? ? 6 6 3 7 C E r i ; H D 1 6 1 5 7 J 0 2 3 4 -4 3 4 7 ? ? ? 6 6 3 8 Y G e m ; C a s t o r C 1 H 0 7 + 3 1 6 J 0 7 3 4 + 1 5 ? ? ? 6 6 3 9 Y Z C M i ; J 2 8 5 ; 1 H 0 7 4 3 + 7 J 0 7 4 + ? ? ? 6 6 4 0 E Q V i r J 1 3 4 -0 8 2 0 ? ? ? 6 6 4 1 C M D r a ; G L I E S E 6 3 0 . 1 ; 1 6 3 4 + 5 7 1 J 1 6 3 4 + 5 0 9 ? ? ? 6 6 4 2 A U i c ; H D 1 9 7 4 8 1 ; S A O 2 2 0 2 J 2 0 4 5 -3 1 2 0 ? ? ? 6 6 4 3 H D 2 1 8 7 3 8 ; S A O 5 2 7 5 3 J 2 3 0 9 + 7 7 ? ? ? 6 6 4 H D 1 8 5 0 ; 1 H 1 9 3 4 -0 6 3 J 1 9 3 9 -0 6 0 3 ? ? ? 6 6 4 5 1 E S 1 3 2 8 + 2 4 ; F K C o m ; H D 7 5 J 1 3 0 + 4 1 3 ? ? ? 6 6 4 R E 0 7 2 0 -3 1 8 ; E U V E J 0 7 2 0 -3 1 7 J 0 7 2 0 -3 1 4 6 ? ? ? 6 6 4 7 Q R A n d ; R X J 0 1 9 . + 2 5 6 J 0 1 9 + 5 6 ? ? ? 6 , 7 6 4 8 R X J 0 5 1 3 . 9 -6 9 5 1 ; H V 5 6 8 2 ; L M C 6 5 S o u r c e i n L M C J 0 5 1 3 -6 9 5 1 ? ? L M X B 6 , 7 6 4 9 C A L 8 3 ; L H G 8 3 ; L M C 3 4 8 S o u r c e i n L M C J 0 5 4 3 -6 8 2 ? ? L M X B 6 , 7 6 5 0 M R V e l ; R X J 0 9 2 5 -4 7 5 8 J 0 9 2 -4 7 5 ? ? ? ? 6 , 7 6 5 1 A G D r a ; B D + 6 7 9 2 ; 1 6 1 + 6 9 J 1 6 1 + 6 8 ? ? ? 6 6 5 2 e t a C a r ; H 9 3 0 1 0 4 5 -5 9 7 J 1 0 4 5 -5 9 4 1 ? ? ? 6 6 5 3 E Z C M ; 5 0 8 6 ; 6 5 -2 3 9 J 0 6 5 4 -2 3 ? ? ? 6 6 5 4 H D 1 9 3 7 9 3 ; V 1 6 8 7 C y g J 2 0 2 + 3 5 ? ? ? 6 6 5 Y E r i ; 0 4 0 9 -1 0 6 J 0 4 1 -1 0 2 8 ? ? ? 6 6 5 W U m a ; 0 9 3 + 5 6 0 J 0 9 4 3 + 5 5 7 ? ? ? 6 6 5 7 X Y L e o ; 0 9 5 + 1 7 6 J 1 0 1 + 1 7 2 4 ? ? ? 6 6 5 8 4 i B o ; H D 1 3 6 4 J 1 5 0 3 + 4 7 3 9 ? ? ? 6 6 5 9 R E J 2 0 3 7 + 7 5 3 ; V W C e p ; 1 H 2 0 4 1 + 7 5 6 J 2 0 3 7 + 7 5 5 ? ? ? 6 6 0 1 E 2 1 9 . 7 + 1 6 5 J 2 1 + 8 ? ? ? 6 6 1 M S 1 2 1 . 8 + 1 2 0 6 ; A H V i r ; S A O 1 0 0 3 J 1 2 1 4 + 1 4 9 ? ? ? 6 399 6 2 V 8 2 9 H e r ; 1 E 1 6 5 3 . 9 + 3 5 1 5 J 1 6 5 + 3 5 1 0 ? ? ? ? 6 6 3 M S 1 8 0 6 . 0 + 6 9 4 J 1 8 0 5 + 9 4 ? ? ? 6 6 4 R E 0 4 + 0 ; B D + 0 8 0 2 J 0 4 + 9 3 2 ? ? ? 6 6 5 R X J 0 1 0 3 . 8 -7 2 5 4 ; 1 J 0 0 3 -7 6 2 ; S M C 1 0 6 S o u r c e i n S M C J 0 1 3 -7 2 5 4 ? ? ? 6 6 M 3 X -7 J 0 1 3 + 2 ? ? ? 6 6 7 t h e t a 1 O r i C ; H D 3 7 0 2 ; H R 1 8 9 5 ; 0 5 3 8 -0 5 4 J 0 5 3 5 -0 5 2 3 ? ? ? 6 6 8 P S R J 0 5 3 7 -6 9 1 0 ; N 1 5 B ; S N R 5 9 -6 9 . 1 S o u r c e i n L M C J 0 5 3 7 -6 9 9 ? ? N S 6 , 1 6 9 1 E 1 7 5 1 + 7 0 4 6 ; E T D r a ; B D 7 0 9 5 9 J 1 7 5 + 4 ? ? ? 6 6 7 0 R T e l ; H V 3 1 8 1 ; 2 0 4 -5 7 J 2 0 4 -5 4 3 ? ? ? 6 6 7 1 2 E 2 0 6 ; A X J 0 5 1 . 6 -7 3 1 S o u r c e i n M C J 0 5 1 -7 3 1 0 ? ? H M X B 9 , 1 0 6 7 2 X T E J 0 5 2 -7 2 3 S o u r c e i n S M C J 0 5 2 -7 2 0 ? ? H M X B 9 , 1 0 6 7 3 A J 0 4 3 -7 3 S o u r c e i n S M C J 0 4 2 -7 3 4 0 ? ? H M X B 9 , 1 0 6 7 4 A X J 0 4 9 . 5 -7 3 2 3 ; R J 0 4 9 . 7 -7 3 2 3 S o u r c e i n M C J 0 4 9 -7 3 2 ? ? H M X B 9 , 1 0 6 7 5 S o u r c e i n M C J 0 5 2 -7 2 3 ? ? H M X B 1 0 6 7 X M U J 0 5 6 0 5 . -7 2 2 0 S o u r c e i n M C J 0 5 6 -7 2 ? ? H M X B 1 0 6 7 C O U J 0 5 7 5 0 . 3 -7 2 0 5 6 S o u r c e i n M C J 0 5 7 -7 2 0 ? ? H M X B 1 0 6 7 8 S o u r c e i n M C J 0 5 7 -7 2 1 9 ? ? H M X B 1 0 6 7 9 A X J 0 5 7 . 4 -7 3 2 5 S o u r c e i n M C J 0 5 7 -7 3 2 5 ? ? H M X B 9 , 6 8 0 C X O U J 0 1 0 4 3 . 1 -7 2 1 3 4 S o u r c e i n M C J 0 1 -7 2 1 ? ? N S 1 0 , 1 7 , 3 2 6 8 1 S o u r c e i n M C J 0 1 -7 2 1 ? ? H M X B 1 0 6 8 2 2 E 0 1 0 1 . 5 -7 2 5 ; A X J 0 1 0 3 -7 2 S o u r c e i n M C J 0 1 3 -7 2 0 8 ? ? H M X B 9 , 6 8 3 X T E J 0 1 0 3 -7 2 8 S o u r c e i n M C J 0 1 3 -7 2 4 1 ? ? N S 1 0 6 8 4 S o u r c e i n M C J 0 1 9 -7 3 1 ? ? N S 1 0 6 8 5 P S R J 0 3 0 + 4 5 J 0 3 + 4 5 1 J 0 3 0 + 0 4 5 1 ? N S 1 6 8 P S R J 0 2 5 + 6 4 9 i n S N R 3 C 5 8 J 0 2 5 + 6 4 J 0 2 5 + 6 4 9 ? N S 1 6 8 7 P S R J 1 0 2 4 -0 7 1 9 J 1 0 2 4 -0 7 1 9 J 1 0 2 4 -0 7 1 9 ? N S 1 6 8 P S R J 1 9 -6 1 2 S N R G 2 9 2 . 2 -0 . 5 J 1 9 -6 1 2 J 1 9 -6 1 2 ? N S 1 , 2 1 6 8 9 P S R J 1 2 4 -5 9 1 S N R G 2 9 . 0 + 1 . 8 J 1 2 4 -5 9 1 J 1 2 4 -5 9 1 ? N S 1 , 9 6 9 0 P S R J 1 4 2 0 -6 0 4 8 K o k a b u r a J 1 4 2 0 -6 0 4 8 J 1 4 2 0 -6 0 4 8 ? N S 1 400 6 9 1 P S R J 1 7 4 -1 3 4 J 1 7 4 -1 3 4 J 1 7 4 -1 3 4 ? N S 1 6 9 2 PS R B 1 7 5 7 -2 4 J 1 8 0 -2 4 5 0 ? B 1 7 5 7 -2 4 N S 1 6 9 3 P S R J 1 8 4 6 -0 2 5 8 i n S N R K e s 7 5 ( G 2 9 . 7 -0 . 3 ) J 1 8 4 6 -0 2 5 8 J 1 8 4 6 -0 2 5 8 ? N S 1 , 2 0 6 9 4 P S R B 1 8 5 3 + 0 J 1 8 5 6 + 0 3 ? B 1 8 5 3 + 0 1 N S 1 6 9 5 P S R J 2 2 9 + 6 1 4 J 2 2 9 + 1 4 J 2 2 9 + 6 1 4 ? N S 1 6 9 X T E J 0 9 9 -3 1 4 J 0 9 9 -3 1 2 3 ? ? L M X B 1 2 , 2 9 6 9 7 X T E 1 7 5 1 -3 0 5 J 1 7 5 1 -3 0 7 ? ? L M X B 1 3 , 2 9 , 4 8 , 5 1 6 9 8 X T E J 1 8 0 -2 9 4 J 1 8 0 6 -2 9 2 4 ? ? L M X B 1 4 , 0 4 5 0 6 9 X T E J 1 8 4 -3 8 J 1 8 3 -3 4 6 ? ? L M X B 1 5 , 3 1 , 4 5 7 0 P S R J 0 1 1 -7 3 1 7 ; T E J 0 1 1 -7 3 2 ; ( H F P 2 0 0 ) 4 6 J 0 1 -7 3 1 6 J 0 1 1 -7 3 1 7 ? H M X B 1 6 , 3 2 7 0 1 G S 1 8 4 3 + 0 ; G i n g a J 1 8 4 5 + 5 ? B 1 8 4 3 + 0 H M X B 1 6 7 0 2 J 0 5 3 7 . 7 -7 0 3 4 ; i n L M C S o u r c e i n L M C J 0 5 3 7 -7 0 3 4 J 0 5 3 7 . 7 -7 0 3 4 ? L M X B 1 6 7 0 3 G r a n a t B 1 7 4 3 -2 9 0 J 1 7 4 6 -2 9 0 3 ? B 1 7 4 3 -2 9 0 L M X B 1 6 7 0 4 S A X J 1 7 4 7 . 0 -2 8 5 3 ; X B 1 7 4 3 -2 9 J 1 7 4 -2 8 5 J 1 7 4 7 . -2 8 5 3 ? L M X B 1 6 7 0 5 G R B 9 7 0 2 8 ; J 0 5 0 1 . 7 + 1 4 6 J 0 5 0 + J 0 5 0 . + 1 4 6 ? N S 1 6 7 0 6 P S R J 1 8 4 5 -0 4 3 4 ; P S R B 1 8 4 2 -0 4 J 1 8 4 -0 4 3 4 J 1 8 4 -0 4 3 4 B 1 8 4 2 -0 4 N S 1 6 7 0 R X J 0 3 5 6 . 5 -3 6 4 1 ; E U V E J 0 3 5 6 -3 6 . 6 ; 1 E 0 3 5 4 . 6 -3 6 5 0 J 0 3 5 6 -3 6 4 1 J 0 3 5 6 . 5 -3 6 4 1 ? L M X B 1 6 7 0 8 B 0 2 4 0 -0 2 ; A P G 3 7 ; N G C 1 0 6 8 J 0 2 4 2 -0 0 ? B 0 2 4 0 -0 2 A G N 1 6 7 0 9 E S O 4 3 4 -4 0 J 0 9 4 7 -3 0 5 6 ? B 0 9 4 5 -3 0 7 A G N 1 6 7 1 0 N G C 4 5 0 7 J 1 2 3 5 -3 9 5 4 ? B 1 2 3 2 -3 9 6 A G N 1 6 7 1 N G C 4 9 J 1 3 0 5 -4 9 2 8 ? B 1 3 0 4 -4 9 7 A G N 1 6 7 1 2 C e n A ; N G C 5 1 8 J 1 3 2 5 -4 3 0 1 ? B 1 3 2 -4 2 7 A G N 1 6 7 1 3 N G C 7 5 8 2 J 2 3 8 -4 2 2 ? B 2 3 5 -4 2 6 A G N 1 6 7 1 4 3 C 2 7 3 J 1 2 9 + 0 2 0 3 ? B 1 2 6 + 0 2 Q S O 1 6 7 1 5 S A X 1 7 4 . 7 -2 9 1 6 J 1 7 4 -2 9 1 6 J 1 7 4 . 7 -2 9 1 6 ? ? 1 6 7 1 6 G r a n a t B 7 -3 4 7 J 1 7 5 0 -3 4 1 ? B 1 7 4 7 -3 4 1 ? 1 6 7 1 J 0 1 5 3 + 7 4 2 J 0 1 5 3 + 4 2 J 0 1 5 3 + 7 4 2 ? C V 7 401 7 1 8 J 0 4 3 9 -6 8 0 9 J 0 4 3 9 -6 8 0 9 J0 4 3 9 -6 8 0 9 ? C V 7 7 1 9 V 1 4 2 5 A q l ; N A q l 1 9 5 J 1 9 5 -0 1 4 2 ? ? C V 7 7 2 0 P S R J 1 9 3 0 + 1 8 5 2 i n S N R G 5 4 . 1 + 0 3 J 1 9 3 0 + 1 8 2 ? ? N S 1 8 7 2 1 4 7 T u c C ; P S R B 0 2 1 -7 2 C ; P S R J 0 2 3 -7 2 0 4 C J 0 2 3 -7 2 0 4 J 0 2 3 -7 2 0 4 C B 0 2 1 -7 2 C N S 2 3 , 2 4 7 2 4 7 T u c D ; P S R B 0 2 1 -72 D ; P S R J 0 2 4 -7 2 0 4 D J 0 2 4 -7 2 0 4 D J 0 2 4 -7 2 0 4 D B 0 2 1 -7 2 D N S 2 3 , 4 7 2 3 4 7 T u c E ; P S R B 0 2 1 -7 2 E ; P S R J 0 2 4 -7 2 0 5 E J 0 2 4 -7 2 0 5 J 0 2 4 -7 2 0 5 E B 0 2 1 -7 2 E L M X B 2 3 , 4 7 2 4 4 7 T u c F ; P S R B 0 2 1 -7 2 F ; P S R J 0 2 4 -7 2 0 4 F J 0 2 4 -7 2 0 4 F J 0 2 4 -7 2 0 4 F B 0 2 1 -7 2 F N S 2 3 , 4 7 2 5 4 7 T u c G ; P S R B 0 2 1 -7 2 G ; J 0 4 -7 2 0 4 G J 0 2 4 -7 2 0 4 G J 0 2 4 -7 2 0 4 G B 0 2 1 -7 2 G N S 2 3 , 4 7 2 6 4 7 T u c H ; P S R B 0 2 1 -7 2 H ; P S R J 0 4 -7 2 0 4 H J 0 2 4 -7 2 0 4 H J 0 2 4 -7 2 0 4 H B 0 2 1 -7 2 H L M X B 2 3 , 4 7 2 4 7 T u c I ; P S R B 0 2 1 -7 2 I ; P S R J 0 4 -7 2 0 4 I J 0 2 4 -7 2 0 4 I J 0 2 4 -7 2 0 4 I B 0 2 1 -72 I L M X B 2 3 , 4 7 2 8 4 7 T u c J ; P S R B 0 2 1 -7 2 J ; P S R J 0 2 3 -7 2 0 3 J J 0 2 3 -7 2 0 3 J 0 2 3 -7 2 0 3 J B 0 2 1 -7 2 J L M X B 2 3 , 4 7 2 9 4 7 T u c L ; P S R B 0 2 1 -7 2 L ; P S R J 0 2 4 -7 2 0 4 L J 0 2 4 -7 2 0 4 L J 0 2 4 -7 2 0 4 L B 0 2 1 -7 2 L N S 2 3 , 4 7 3 0 4 7 T u c M ; P S R B 0 2 1 -7 2 M ; P S R J 0 3 -7 2 0 5 M J 0 2 3 -7 2 0 5 J 0 2 3 -7 2 0 5 M B 0 2 1 -7 2 M N S 2 3 , 4 7 3 1 4 7 T u c N ; P S R B 0 2 1 -7 2 N ; P S R J 0 4 -7 2 0 4 N J 0 2 4 -7 2 0 4 N J 0 2 4 -7 2 0 4 N B 0 2 1 -7 2 N N S 2 3 , 4 7 3 2 4 7 T u c O ; P S R B 0 2 1 -7 2 O ; P S R J 0 4 -7 2 0 4 O J 0 2 4 -7 2 0 4 O J 0 2 4 -7 2 0 4 O B 0 2 1 -7 2 O L M X B 2 3 , 4 7 3 4 7 T u c Q ; P S R B 0 2 1 -7 2 Q ; P S R J 0 0 2 4 -7 2 0 4 Q J 0 2 4 -7 2 0 4 Q J 0 2 4 -7 2 0 4 Q B 0 2 1 -7 2 Q L M X B 2 3 , 4 7 3 4 4 7 T u c S ; P S R B 0 2 1 -7 2 S ; P S R J 0 2 4 -7 2 0 4 S J 0 2 4 -7 2 0 4 S J 0 2 4 -7 2 0 4 S B 0 2 1 -7 2 S L M X B 2 3 , 4 7 3 5 4 7 T u c ; P R B 0 2 1 -7 2 T ; P R J 0 4 -7 2 0 4 T J 0 2 4 -7 2 0 4 T J 0 2 4 -7 2 0 4 T B 0 2 1 -7 2 T L M X B 2 3 , 4 7 3 6 4 7 T u c U ; P S R B 0 2 1 -7 2 U ; P S R J 0 4 -7 2 0 3 U J 0 2 4 -7 2 0 3 J 0 2 4 -7 2 0 3 U B 0 2 1 -7 2 U L M X B 2 3 , 4 7 3 6 3 9 7 A ; P S R B 1 7 3 6 -5 3 ; P S R J 1 4 -5 3 4 0 J 1 7 4 -5 3 4 0 J 1 7 4 -5 3 4 0 B 1 7 3 6 -5 3 L M X B 2 3 , 2 4 , 2 8 7 3 8 P S R B 2 2 4 + 6 5 ; P S R J 2 2 5 + 6 5 3 5 G u i t a r N e b u l a J 2 2 5 + 6 5 3 5 ? B 2 2 4 + 5 N S 2 7 7 3 9 P S R J 2 0 4 3 + 2 7 4 0 J 2 0 4 3 + J 2 0 4 3 + 2 ? N S 2 7 7 4 0 4 U 0 6 2 8 -2 8 ; P S R B 0 6 2 8 -2 8 ; P S R J 0 6 3 0 -2 8 3 4 J 0 6 3 -2 8 3 4 ? B 0 6 2 8 -2 8 N S 2 7 7 4 1 P S R 1 1 3 -3 6 ; P S R 1 8 1 7 -3 6 1 8 J 1 8 1 7 -3 6 1 ? B 1 8 1 3 -3 6 N S 2 7 7 4 2 1 X M U J 0 5 9 2 1 . -7 2 3 1 7 S o u r c e i n S M C J 0 5 9 -7 2 ? ? H M X B 3 2 7 4 3 1 X M U J 0 0 4 7 2 3 . 7 -7 3 1 6 S o u r c e i n S M C J 0 4 7 -7 3 1 ? ? H M X B 3 2 7 4 m a y b e : R J 5 1 . 8 -7 3 1 0 S o u r c e i n S M C J 0 5 1 -7 3 1 0 B ? ? N S 3 7 4 5 m a y b e : R J 0 5 1 . -7 3 1 0 S o u r c e i n M C J 0 5 1 -7 3 1 0 C ? ? N S 3 7 4 6 X T E J 0 5 -7 2 7 S o u r c e i n M C J 0 5 -7 2 4 2 ? ? N S 3 2 402 7 4 7 m a y b e R X J 0 5 . 4 -7 2 1 0 S o u r c e i n S M C J 0 5 -7 2 1 0 ? ? N S 3 2 7 4 8 R X J 0 5 4 . 9 -7 2 4 5 , A X J 0 5 4 . 8 -7 2 4 , C X O U J 0 5 4 5 . 6 -7 2 4 5 1 0 , X M U 4 5 . 4 -7 2 4 5 1 2 S o u r c e i n S M C J 0 5 4 -7 2 4 5 ? ? H M X B 3 2 7 4 9 S o u r c e i n M C J 0 5 3 -7 2 7 ? ? N S 3 2 7 5 0 R X J 0 5 . -7 2 3 8 S o u r c e i n M C J 0 5 -7 2 3 8 ? ? N S 32 7 5 1 X T E S M C 9 5 S o u r c e i n S M C J 0 5 3 -7 2 4 9 ? ? H M X B 3 4 7 5 2 A X J 1 8 4 5 -0 2 5 8 ; P S R 1 8 4 -0 2 5 8 , P S R 1 4 5 -0 2 5 8 i n S N R G 2 9 . 6 + 0 . 1 J 1 8 4 -0 2 5 ? ? N S 3 5 7 5 3 X T E J 1 8 5 9 + 0 8 3 J 1 8 5 9 + 0 1 5 ? ? N S 3 6 7 5 4 R J 0 4 2 0 . 0 -5 0 2 J 0 4 2 0 -5 0 2 ? ? N S 3 8 7 5 X T E J 1 5 3 -5 6 8 J 1 5 4 -5 6 4 ? ? N S 3 9 7 5 6 A J 1 7 4 0 . 2 -2 8 4 8 J 1 7 4 0 -2 8 4 7 ? ? H M X B 4 0 7 5 R X J 1 6 0 5 . 3 + 3 9 J 1 6 0 5 + 3 2 9 ? ? N S 4 1 7 5 8 R B S 1 2 3 ; R X J 1 3 0 8 4 8 . 6 + 2 1 2 7 0 8 J 1 3 0 8 + 2 2 7 ? ? N S 4 2 7 5 9 R X J 0 8 0 6 . 4 -4 1 2 3 J 0 8 0 6 -4 1 2 ? ? N S 4 3 403 B.3.2 Detailed List The following table provides data from the Detailed List of the XNAVSC. Al the data from this list is provided, except for the References section, since this information is repeated from the Simple List. Descriptions of the parameters within this table are provided in Table B-3. The actual list begins on the following page. This is the largest list of the XNAVSC. Therefore, data from a single source spans a total of six pages. The format of the layout of this list is in a column orientation. Al the rows from a column in this list are printed first with as many columns that wil fit on a page. Then the next set of rows from the columns that fit on a page is printed. This is repeated until the list is completed. A reader may wish to print out these pages and place them in a row orientation. The best approach for this would be to locate al the pages where the new headings for the columns begin and then set out the six pages for those sets of sources. For the parameter of the Catalogue J-Name, this is source name unique to the XNAVSC. For a name that is of format Jhhmm-ddmm and writen in blue ink, this name has been modified from the original citation?s J-name or was derived from the position of the source if only a B-name is known for that source. This Catalogue J-name is only created to produce a consistent naming convention for al the XNAVSC sources, and should not be used as an external name for the source. For the Galactic coordinates of Longitude (LI) and Latitude (BI), those writen in blue ink have been computed directly from the Right Ascension and Declination values. Otherwise these coordinates are from the source?s citation. 404 X-ray flux values writen in blue ink are ?derived? values from a given source?s citation. This may mean that X-ray detector photon counts were converted to energy flux. For some sources this may mean that the source was not directly observed in the ?derived? energy range, so there is no asurance that the source is visible within this X- ray range. 405 NAME and TYPE Instal Number Catalogue J-Name B-Name Object Clas Sub-Clas 1 J0534+20 B0531+21 NS RPSR SNR 2 J0835-4510 B083?45 NS RPSR SNR 3 J063+1746 B0630+17 NS RPSR 4 J1709?428 B1706?4 NS RPSR SNR 5 J1513?5908 B1509?58 NS RPSR SNR 6 J1952+3252 B1951+32 NS RPSR SNR 7 J1048?5832 B1046?58 NS RPSR 8 J1302?6350 B1259?63 NS RPSR 9 J1826?134 B1823?13 NS RPSR 10 J1803?2137 B180?21 NS RPSR SNR 1 J1932+1059 B1929+10 NS RPSR 12 J0437?4715 ? NS RPSR 13 J1824?2452 B1821?24 NS RPSR 14 J0659+1414 B0656+14 NS RPSR 15 J0540?6919 B0540?69 NS RPSR SNR 16 J2124?358 ? NS RPSR 17 J1959+2048 B1957+20 NS RPSR 18 J0953+075 B0950+08 NS RPSR 19 J1614?5047 B1610?50 NS RPSR 20 J0538+2817 ? NS RPSR 21 J1012+5307 ? NS RPSR 2 J1057?526 B105?52 NS RPSR 23 J0358+5413 B035+54 NS RPSR 24 J237+6151 B234+61 NS RPSR SNR 25 J0218+4232 ? NS RPSR 26 J0826+2637 B0823+26 NS RPSR 27 J0751+1807 ? NS RPSR 28 J0142+610 ? NS AXP 29 J0525?607 ? NS AXP 30 J1048?5937 ? NS AXP 31 J1708?408 ? NS AXP 32 J1808?2024 ? NS SGR SNR 3 J1841?0456 ? NS AXP SNR 34 J1845?0256 ? NS AXP SNR 35 J1907+0919 ? NS SGR SNR 36 J2301+5852 ? NS AXP SNR 37 J032-7348 ? HMXB 38 J049-7310 ? HMXB HMNS HMBP 406 39 J049-7250 ? HMXB HMNS APSR 40 J052-726 B050-727 HMXB 41 J050-7316 ? HMXB HMNS APSR 42 J050-7213 ? HMXB HMNS APSR 43 J051-7231 ? HMXB HMNS APSR 4 J051-7310 ? HMXB 45 J052-7319 ? HMXB HMNS HMBP 46 J052-7158 ? HMXB 47 J054-7341 B053-739 HMXB HMNS APSR 48 J056+6043 B053+604 HMXB 49 J053-726 ? HMXB HMNS APSR 50 J054-7204 ? HMXB HMNS APSR 51 J054-726 ? HMXB HMNS APSR 52 J057-7202 ? HMXB HMNS APSR 53 J058-7230 ? HMXB 54 J059-7138 ? HMXB HMNS APSR 5 J0101-7206 ? HMXB 56 J0103-7209 ? HMXB HMNS HMBP 57 J0109-744 B0103-762 HMXB 58 J0105-721 ? HMXB HMNS APSR 59 J0105-7212 ? HMXB 60 J0105-7213 ? HMXB HMNS HMBP 61 J018+6517 B014+650 HMXB HMNS APSR 62 J018+634 B015+634 HMXB HMNS APSR 63 J017-7326 B015-737 HMXB HMNS APSR 64 J017-730 ? HMXB HMNS APSR 65 J0143+6106 ? HMXB HMNS APSR 6 J0240+613 B0236+610 HMXB 67 J034+5310 B031+530 HMXB HMNS HMBP 68 J035+3102 B0352+309 HMXB HMNS APSR 69 J0419+559 ? HMXB 70 J040+431 ? HMXB HMNS APSR 71 J0501-703 ? HMXB 72 J0502-626 ? HMXB HMNS APSR 73 J0512-6717 ? HMXB 74 J0516-6916 ? HMXB 407 75 J0520-6932 ? HMXB 76 J052+3740 B0521+373 HMXB 7 J0529-656 ? HMXB HMNS APSR 78 J0531-607 B053109-609.2 HMXB HMNS APSR 79 J0531-6518 ? HMXB 80 J0532-62 B0532-64 HMXB HMNS APSR 81 J0532-6535 ? HMXB 82 J0532-651 ? HMXB 83 J0535-670 ? HMXB 84 J0535-651 B0535-68 HMXB HMNS HMBP 85 J0538+2618 B0535+262 HMXB HMNS APSR 86 J0535-6530 ? HMXB 87 J0538-6405 B0538-641 HMXB 8 J0539-694 B0540-697 HMXB 89 J0541-6936 ? HMXB 90 J0541-6832 ? HMXB 91 J054-63 B054-65 HMXB 92 J054-710 ? HMXB HMNS APSR 93 J055+2847 B056+286 HMXB 94 J0635+053 ? HMXB HMNS HMBP 95 J0648-418 ? HMXB HMNS HMBP 96 J0728-2606 B0726-260 HMXB HMNS APSR 97 J0747-5319 B0739-529 HMXB 98 J0756-6105 B0749-60 HMXB 9 J0812-314 ? HMXB HMNS APSR 10 J0835-431 B0834-430 HMXB HMNS APSR 101 J0902-403 B090-403 HMXB HMNS APSR 102 J109-5817 ? HMXB HMNS HMBP 103 J1025-5748 B1024.0-5732 HMXB HMNS APSR 104 J1030-5704 B1036-565 HMXB 105 J1037-5647 ? HMXB HMNS APSR 106 J1050-5953 B1048.1-5937 HMXB HMNS HMBP 107 J120-6154 B118-615 HMXB HMNS HMBP 108 J121-6037 B119-603 HMXB HMNS APSR 408 109 J148-6212 B145-619 HMXB HMNS APSR 10 J147-6157 B145.1-6141 HMXB HMNS APSR 11 J126-6246 B123-624 HMXB HMNS APSR 12 J1242-6012 B1239-59 HMXB HMNS HMBP 13 J1247-6038 B124-604 HMXB 14 J1249-5907 B1246-58 HMXB 15 J1242-6303 B1249-637 HMXB 16 J1239-752 B1253-761 HMXB 17 J1254-5710 B125-567 HMXB 18 J1301-6136 B1258-613 HMXB HMNS APSR 19 J1324-620 ? HMXB HMNS APSR 120 J1421-6241 B1417-624 HMXB HMNS APSR 121 J1452-5949 ? HMXB HMNS APSR 12 J1542-523 B1538-52 HMXB HMNS APSR 123 J157-5424 B153-542 HMXB HMNS APSR 124 J154-519 B155-52 HMXB 125 J170-4140 B1657-415 HMXB HMNS APSR 126 J1703-3750 B170-37 HMXB 127 J170-4157 ? HMXB HMNS HMBP 128 J1725-3624 B172-363 HMXB HMNS APSR 129 J1738-3015 ? HMXB 130 J1739-2942 ? HMXB 131 J174-2713 ? HMXB 132 J1749-2725 ? HMXB HMNS APSR 13 J1749-2638 ? HMXB HMNS APSR 134 J1810-1052 B1807-10 HMXB 135 J1820-1434 ? HMXB HMNS APSR 136 J1826-1450 ? HMXB 137 J1836-0736 B183-076 HMXB HMNS APSR 138 J1841-051 B1839-06 HMXB 139 J1841-0427 B1839-04 HMXB HMNS HMBP 140 J1845+057 B1843+09 HMXB HMNS HMBP 141 J1847-0309 B1845-03 HMXB 409 142 J1848-025 B1845-024 HMXB HMNS HMBP 143 J1847-0430 B1845.0-043 HMXB 14 J1858-024 B185-02 HMXB HMNS HMBP 145 J185-0237 ? HMXB HMNS APSR 146 J1858+0321 ? HMXB HMNS APSR 147 J1904+0310 B1901+03 HMXB 148 J1905+0902 ? HMXB HMNS APSR 149 J1909+0949 B1907+097 HMXB HMNS APSR 150 J191+0458 B1909+048 HMXB HMBH 151 J1932+5352 B1936+541 HMXB 152 J1945+2721 B1942+274 HMXB HMNS APSR 153 J1949+3012 B1947+30 HMXB 154 J1948+320 ? HMXB HMNS APSR 15 J195+3206 B1954+319 HMXB 156 J1958+3512 B1956+350 HMXB HMBH 157 J2032+3738 B2030+375 HMXB HMNS HMBP 158 J2032+4057 B2030+407 HMXB 159 J2030+4751 ? HMXB 160 J2059+4143 ? HMXB HMNS APSR 161 J2103+4545 ? HMXB HMNS APSR 162 J2139+5703 B2138+568 HMXB HMNS APSR 163 J201+5010 B202+501 HMXB 164 J207+5431 B206+543 HMXB HMNS APSR 165 J226+614 B214+589 HMXB 16 J239+616 ? HMXB 167 J04+301 B042+323 LMXB 168 J0418+3247 ? LMXB 169 J0514-402 B0512-401 LMXB LMNS XBRST 170 J0520-7157 B0521-720 LMXB LMNS ZSRC 171 J0532-6926 ? LMXB 172 J0617+0908 B0614+091 LMXB LMNS ATOL 173 J062-020 B0620-03 LMXB 410 174 J0658-0715 B0656-072 LMXB 175 J0748-6745 B0748-676 LMXB LMNS XBRST 176 J0835+518 ? LMXB LMNS XBRST 17 J0837-4253 B0836-429 LMXB LMNS XBRST 178 J0920-512 B0918-549 LMXB 179 J092-6317 B0921-630 LMXB 180 J1013-4504 B109-45 LMXB 181 J118+4802 ? LMXB LMNS ATOL 182 J126-6840 B124-684 LMXB 183 J1257-6917 B1254-690 LMXB LMNS XBRST 184 J1326-6208 B1323-619 LMXB LMNS XBRST 185 J1358-644 B1354-645 LMXB 186 J1458-3140 B145-314 LMXB LMNS XBRST 187 J1520-5710 B1516-569 LMXB LMNS ATOL 18 J1528-6152 B1524-617 LMXB 189 J1547-4740 B1543-475 LMXB LMBH 190 J1547-6234 B1543-624 LMXB 191 J150-5628 ? LMXB 192 J1601-604 B156-605 LMXB 193 J1605+251 B1603.6+260 LMXB 194 J1603-753 ? LMXB LMNS XBRST 195 J1612-525 B1608-52 LMXB LMNS ATOL 196 J1619-1538 B1617-15 LMXB LMNS ZSRC 197 J1628-491 B1624-490 LMXB 198 J1632-6727 B1627-673 LMXB LMNS APSR 19 J1634-4723 B1630-472 LMXB 20 J1636-4749 B1632-47 LMXB 201 J1640-5345 B1636-536 LMXB LMNS ATOL 202 J1645-4536 B1642-45 LMXB LMNS ZSRC 203 J1654-3950 ? LMXB 204 J1657+3520 B1656+354 LMXB LMNS APSR 205 J1702-2956 B1658-298 LMXB LMNS XBRST 206 J1702-4847 B1659-487 LMXB 411 207 J1705-3625 B1702-363 LMXB LMNS ZSRC 208 J1706-4302 B1702-429 LMXB LMNS ATOL 209 J1706+2358 B1704+240 LMXB 210 J1708-2505 B1705-250 LMXB 21 J1708-406 B1705-40 LMXB LMNS ATOL 212 J1712-4050 B1708-408 LMXB 213 J1709-2639 ? LMXB LMNS XBRST 214 J1710-2807 ? LMXB LMNS XBRST 215 J1714-3402 B171-39 LMXB 216 J1712-3738 ? LMXB LMNS XBRST 217 J1718-3210 B1715-321 LMXB LMNS XBRST 218 J1719-2501 B1716-249 LMXB LMBH 219 J1718-4029 ? LMXB LMNS XBRST 20 J1723-3739 ? LMXB LMNS XBRST 21 J1727-354 B1724-356 LMXB 22 J1727-3048 B1724-307 LMXB LMNS ATOL 23 J1731-350 B1728-37 LMXB LMNS ATOL 24 J1731-1657 B1728-169 LMXB LMNS ATOL 25 J1732-244 B1728-247 LMXB LMNS APSR 26 J173-313 B1730-312 LMXB 27 J173-323 B1730-35 LMXB LMNS XBRST 28 J173-202 B1730-20 LMXB 29 J1734-2605 B1731-260 LMXB LMNS ATOL 230 J1735-3028 B1732-304 LMXB LMNS XBRST 231 J1736-2725 B1732-273 LMXB 232 J1737-2910 B1734-292 LMXB 23 J1738-270 B1735-269 LMXB LMNS XBRST 234 J1738-427 B1735-44 LMXB LMNS ATOL 235 J1738-2829 B1735-28 LMXB 236 J1739-2943 B1736-297 LMXB 237 J1739-3059 B1737-31 LMXB 238 J1740-2818 B1737-282 LMXB 239 J1742-2746 B1739-278 LMXB 240 J1742-3030 B1739-304 LMXB 241 J1743-2926 B1740-294 LMXB 242 J1743-294 B1740.7-2942 LMXB 412 243 J174-290 B1741.2-2859 LMXB 24 J174-2921 B1741-293 LMXB LMNS XBRST 245 J1745-3213 B1741-32 LMXB 246 J1745-2854 B1741.9-2853 LMXB LMNS XBRST 247 J1745-3241 B1742-326 LMXB 248 J1745-2859 B1742.2-2857 LMXB 249 J1745-2927 B1742-294 LMXB LMNS XBRST 250 J1745-2901 B1742-289 LMXB LMNS XBRST 251 J1745-290 B1742.5-2859 LMXB 252 J1745-2846 B1742.5-2845 LMXB 253 J1745-2903 B1742.7-2902 LMXB 254 J1746-2854 B1742.8-2853 LMXB 25 J1746-2853 B1742.9-2852 LMXB 256 J1746-2931 B1742-294 LMXB LMNS XBRST 257 J1746-2851 B1742.9-2849 LMXB 258 J1746-284 B1743.1-2843 LMXB 259 J1746-2853 B1743.1-2852 LMXB 260 J1746-2853 B1743-28 LMXB LMNS XBRST 261 J1747-2959 B174-29 LMXB 262 J174-284 ? LMXB LMNS APSR 263 J1747-302 B174-30 LMXB LMNS XBRST 264 J1747-263 B174-265 LMXB LMNS ATOL 265 J1748-3607 B174-361 LMXB 26 J1745-2901 ? LMXB LMNS XBRST 267 J1748-2453 B1745-248 LMXB LMNS XBRST 268 J1748-202 B1745-203 LMXB 269 J1749-31 B1746-31 LMXB 270 J1750-325 B1746.7-324 LMXB 271 J1750-3703 B1746-370 LMXB LMNS ATOL 272 J1750-2125 B1747-214 LMXB LMNS XBRST 273 J1750-317 B1747-313 LMXB 274 J1748-2828 ? LMXB 275 J1748-2021 ? LMXB LMNS XBRST 413 276 J1752-2830 B1749-285 LMXB 27 J1750-2902 ? LMXB LMNS XBRST 278 J1752-3137 ? LMXB LMNS XBRST 279 J1758-348 B175-38 LMXB 280 J175-328 ? LMXB 281 J1801-2504 B1758-250 LMXB LMNS ZSRC 282 J1801-254 B1758-258 LMXB 283 J1801-2031 B1758-205 LMXB LMNS ATOL 284 J1806-2435 B1803-245 LMXB 285 J1806-2435 ? LMXB LMNS ATOL 286 J1808-3658 ? LMXB LMNS APSR 287 J1810-2609 ? LMXB LMNS XBRST 28 J1814-1709 B181-171 LMXB LMNS ATOL 289 J1815-1205 B1812-12 LMXB LMNS XBRST 290 J1816-1402 B1813-140 LMXB LMNS ZSRC 291 J1819-2525 ? LMXB 292 J1823-3021 B1820-303 LMXB LMNS ATOL 293 J1825-3706 B182-371 LMXB 294 J1825-00 B182-00 LMXB 295 J1829-2347 B1826-238 LMXB LMNS XBRST 296 J1835-3258 B1832-30 LMXB LMNS XBRST 297 J1839+0502 B1837+049 LMXB LMNS XBRST 298 J1849-0303 B1846-031 LMXB 29 J1853-0842 B1850-087 LMXB LMNS XBRST 30 J1856+0519 ? LMXB 301 J1858+239 ? LMXB 302 J1908+010 B1905+00 LMXB LMNS XBRST 303 J191+035 B1908+05 LMXB LMNS ATOL 304 J1915+1058 B1915+105 LMXB LMNS XBRST 305 J1918-0514 B1916-053 LMXB LMNS XBRST 306 J1920+141 B1918+146 LMXB 307 J1942-0354 B1940-04 LMXB LMNS XBRST 308 J1959+142 B1957+15 LMXB LMBH 309 J202+2514 B200+251 LMXB 310 J2012+381 ? LMXB 31 J2024+352 B2023+38 LMXB 312 J2123-0547 ? LMXB LMNS ATOL 313 J2129+1210 B2127+19 LMXB LMNS XBRST 314 J2131+4717 B2129+470 LMXB LMNS XBRST 414 315 J214+3819 B2142+380 LMXB LMNS ZSRC 316 J2320+6217 B2318+620 LMXB 317 J0720-3125 B0718-318 NS AXP 318 J1838-0301 ? NS AXP 319 J1234+3737 ? CV CV,AM 320 J1305+1801 ? CV CV,AM 321 J024-7204 ? CV CV,D 32 J0610-484 ? CV CV,D 323 J0712-3605 ? CV CV,D 324 J010+604 ? CV CV,DN 325 J0613+474 ? CV CV,DN 326 J075+20 ? CV CV,DN 327 J0807-7632 ? CV CV,DN 328 J0825+7306 ? CV CV,DN 329 J084+1252 ? CV CV,DN 30 J0901+1753 ? CV CV,DN 31 J0951+152 ? CV CV,DN 32 J106-7014 ? CV CV,DN 33 J145-0426 ? CV CV,DN 34 J164+2515 ? CV CV,DN 35 J1807+051 ? CV CV,DN 36 J207+1742 ? CV CV,DN 37 J2142+435 ? CV CV,DN 38 J214+1242 ? CV CV,DN 39 J028+5917 ? CV CV,IP 340 J0203-0243 ? CV CV,IP 341 J0206+1517 ? CV CV,IP 342 J0256+1926 ? CV CV,IP 343 J031+4354 ? CV CV,IP 34 J0350+1714 ? CV CV,IP 345 J0502+245 ? CV CV,IP 346 J0512-3241 ? CV CV,IP 347 J0529-3249 ? CV CV,IP 348 J0534-5801 ? CV CV,IP 349 J0543-4101 ? CV CV,IP 350 J058+5353 ? CV CV,IP 351 J061-8149 ? CV CV,IP 352 J0731+0956 ? CV CV,IP 353 J074-5257 ? CV CV,IP 354 J0751+144 ? CV CV,IP 35 J0757+6305 ? CV CV,IP 356 J083-248 ? CV CV,IP 357 J0859-2428 ? CV CV,IP 358 J143+7141 ? CV CV,IP 359 J1238-3845 ? CV CV,IP 415 360 J1252-2914 ? CV CV,IP 361 J1712+331 ? CV CV,IP 362 J1712-2414 ? CV CV,IP 363 J1814+4151 ? CV CV,IP 364 J185-3109 ? CV CV,IP 365 J2040-052 ? CV CV,IP 36 J217-0821 ? CV CV,IP 367 J2353-3851 ? CV CV,IP 368 J042-1321 ? CV CV,N 369 J0615+2835 ? CV CV,N 370 J0629+7104 ? CV CV,N 371 J081-3521 ? CV CV,N 372 J0932+4950 ? CV CV,N 373 J1019-0841 ? CV CV,N 374 J138+032 ? CV CV,N 375 J152-6712 ? CV CV,N 376 J159+255 ? CV CV,N 37 J162-1752 ? CV CV,N 378 J1832-2923 ? CV CV,N 379 J1848+035 ? CV CV,N 380 J1934+5107 ? CV CV,N 381 J1935-5850 ? CV CV,N 382 J2017-039 ? CV CV,N 383 J2020+2106 ? CV CV,N 384 J2042+1909 ? CV CV,N 385 J136+5154 ? CV CV,NL 386 J180+0810 ? CV CV,NL 387 J0132-654 ? CV CV,P 38 J0141-6753 ? CV CV,P 389 J0203+2959 ? CV CV,P 390 J0236-5219 ? CV CV,P 391 J0314-235 ? CV CV,P 392 J032-256 ? CV CV,P 393 J0453-4213 ? CV CV,P 394 J0515+0104 ? CV CV,P 395 J0531-4624 ? CV CV,P 396 J0542+6051 ? CV CV,P 397 J0719+657 ? CV CV,P 398 J0815-1903 ? CV CV,P 39 J0851+146 ? CV CV,P 40 J0929-2405 ? CV CV,P 401 J102-1925 ? CV CV,P 402 J1015+0904 ? CV CV,P 403 J1015-4758 ? CV CV,P 404 J1047+635 ? CV CV,P 416 405 J1051+5404 ? CV CV,P 406 J104+4503 ? CV CV,P 407 J105+2506 ? CV CV,P 408 J115+4258 ? CV CV,P 409 J117+1757 ? CV CV,P 410 J141-6410 ? CV CV,P 41 J149+2845 ? CV CV,P 412 J1307+5351 ? CV CV,P 413 J1409-4517 ? CV CV,P 414 J152+1856 ? CV CV,P 415 J1727+414 ? CV CV,P 416 J1802+1804 ? CV CV,P 417 J1816+4952 ? CV CV,P 418 J184-7418 ? CV CV,P 419 J1907+6908 ? CV CV,P 420 J1914+2456 ? CV CV,P 421 J1938-4612 ? CV CV,P 42 J205+239 ? CV CV,P 423 J208-6527 ? CV CV,P 424 J202-3954 ? CV CV,P 425 J2107-0517 ? CV CV,P 426 J211+4809 ? CV CV,P 427 J215-5840 ? CV CV,P 428 J2137-4342 ? CV CV,P 429 J2315-5910 ? CV CV,P 430 J0904-322 ? CV CV,RN 431 J0209-6318 ? CV CV,S 432 J0409-718 ? CV CV,S 43 J0810+2808 ? CV CV,S 434 J0812+6236 ? CV CV,S 435 J114-3740 ? CV CV,S 436 J1514-6505 ? CV CV,S 437 J0815-4913 ? CV CV,U 438 J0838+4838 ? CV CV,U 439 J131-5458 ? CV CV,U 40 J1949+74 ? CV CV,U 41 J1954+321 ? CV CV,U 42 J1947-420 ? CV CV,X 43 J01-128 ? CV CV,Z 44 J0104+417 ? CV CV,Z 45 J0645-1651 ? CV CV,Z 46 J0459+1926 ? CV 47 J0502+1624 ? CV 48 J053+3659 ? CV 49 J1326+4532 ? CV 417 450 J131-2940 ? CV 451 J1538+1852 ? CV 452 J1718+415 ? CV 453 J1750+0605 ? CV 454 J1846+122 ? CV 45 J2030+5237 ? CV 456 J2123+4217 ? CV 457 J0538-652 ? HMXB HMNS APSR 458 J1849-0318 ? HMXB HMNS APSR 459 J051-7159 ? LMXB ALGOL 460 J0102+8152 ? LMXB ALGOL 461 J0157+3804 ? LMXB ALGOL 462 J0241+603 ? LMXB ALGOL 463 J0248+6938 ? LMXB ALGOL 464 J0308+4057 ? LMXB ALGOL 465 J040+129 ? LMXB ALGOL 46 J0515+4624 ? LMXB ALGOL 467 J0518+346 ? LMXB ALGOL 468 J0647+6937 ? LMXB ALGOL 469 J0843+1902 ? LMXB ALGOL 470 J1045+453 ? LMXB ALGOL 471 J113-2627 ? LMXB ALGOL 472 J145+7215 ? LMXB ALGOL 473 J1249-0604 ? LMXB ALGOL 474 J1313-6409 ? LMXB ALGOL 475 J150-0831 ? LMXB ALGOL 476 J1518+3138 ? LMXB ALGOL 47 J153+6354 ? LMXB ALGOL 478 J1534+2642 ? LMXB ALGOL 479 J1639-5659 ? LMXB ALGOL 480 J1649-1540 ? LMXB ALGOL 481 J1656+5241 ? LMXB ALGOL 482 J1739-2851 ? LMXB ALGOL 483 J182-2514 ? LMXB ALGOL 484 J1852-0614 ? LMXB ALGOL 485 J1917+226 ? LMXB ALGOL 486 J2025+272 ? LMXB ALGOL 487 J2154+143 ? LMXB ALGOL 48 J232+1458 ? LMXB ALGOL 489 J174-2943 ? LMXB LMBH 490 J1849-0308 ? LMXB LMBH 491 J047+2416 ? LMXB RS CVn 492 J053-7439 ? LMXB RS CVn 493 J016+0648 ? LMXB RS CVn 494 J012+042 ? LMXB RS CVn 418 495 J012+0725 ? LMXB RS CVn 496 J0212+3018 ? LMXB RS CVn 497 J0313+4806 ? LMXB RS CVn 498 J0318-194 ? LMXB RS CVn 49 J0325+2842 ? LMXB RS CVn 50 J035+3201 ? LMXB RS CVn 501 J036+035 ? LMXB RS CVn 502 J037+259 ? LMXB RS CVn 503 J043-1039 ? LMXB RS CVn 504 J0506+5901 ? LMXB RS CVn 505 J0507-0524 ? LMXB RS CVn 506 J0516+459 ? LMXB RS CVn 507 J0528-6527 ? LMXB RS CVn 508 J0603+319 ? LMXB RS CVn 509 J0641+8216 ? LMXB RS CVn 510 J0703-054 ? LMXB RS CVn 51 J0716+7320 ? LMXB RS CVn 512 J0720-0515 ? LMXB RS CVn 513 J0802+5716 ? LMXB RS CVn 514 J0837+233 ? LMXB RS CVn 515 J0839+3147 ? LMXB RS CVn 516 J0859-2749 ? LMXB RS CVn 517 J0901+2641 ? LMXB RS CVn 518 J0909+5429 ? LMXB RS CVn 519 J1036-154 ? LMXB RS CVn 520 J130-1519 ? LMXB RS CVn 521 J136-3802 ? LMXB RS CVn 52 J140+5159 ? LMXB RS CVn 523 J147+2013 ? LMXB RS CVn 524 J1215+723 ? LMXB RS CVn 525 J125+253 ? LMXB RS CVn 526 J129+2431 ? LMXB RS CVn 527 J1301+2837 ? LMXB RS CVn 528 J1310+356 ? LMXB RS CVn 529 J1318+326 ? LMXB RS CVn 530 J134+3710 ? LMXB RS CVn 531 J1435-1802 ? LMXB RS CVn 532 J1513+3834 ? LMXB RS CVn 53 J1614+351 ? LMXB RS CVn 534 J1639+6042 ? LMXB RS CVn 535 J1645+8202 ? LMXB RS CVn 536 J1710+4857 ? LMXB RS CVn 537 J1717-656 ? LMXB RS CVn 538 J1730-339 ? LMXB RS CVn 539 J1758+1508 ? LMXB RS CVn 419 540 J1758+208 ? LMXB RS CVn 541 J1805+2126 ? LMXB RS CVn 542 J1810+3157 ? LMXB RS CVn 543 J1825+1817 ? LMXB RS CVn 54 J1921+0432 ? LMXB RS CVn 545 J1931+543 ? LMXB RS CVn 546 J1936+2753 ? LMXB RS CVn 547 J2058+3510 ? LMXB RS CVn 548 J2102+2748 ? LMXB RS CVn 549 J2121+4020 ? LMXB RS CVn 50 J2139-160 ? LMXB RS CVn 51 J20-024 ? LMXB RS CVn 52 J201+4353 ? LMXB RS CVn 53 J208+454 ? LMXB RS CVn 54 J231+5301 ? LMXB RS CVn 55 J2313+0240 ? LMXB RS CVn 56 J239+2814 ? LMXB RS CVn 57 J2349+3625 ? LMXB RS CVn 58 J235+2838 ? LMXB RS CVn 59 J0527-6921 ? LMXB LMXB-SXS 560 J0546-7108 ? LMXB LMXB-SXS 561 J058-7135 ? LMXB 562 J1656-4049 ? LMXB 563 J002+6246 ? NS RPSR SNR 564 J017+5914 B014+58 NS RPSR SNR 565 J0628+1038 ? NS RPSR SNR 56 J105-6107 ? NS RPSR SNR 567 J1617-505 ? NS RPSR SNR 568 J1623-2631 B1620-26 NS RPSR SNR 569 J1645-0317 ? NS RPSR SNR 570 J1708-409 ? NS RPSR SNR 571 J1740-3015 ? NS RPSR SNR 572 J1748-2924 ? LMXB LMNS ATOL 573 J181-1926 ? NS RPSR SNR 574 J1917+1353 ? NS RPSR SNR 575 J1939+2134 B1937+21 NS RPSR SNR 576 J1958+3232 ? HMXB HMNS APSR 57 J232+2057 ? NS RPSR SNR 578 J043-1759 ? NS 579 J1856-3754 ? NS 580 J0137+2042 ? LMXB RS CVn 581 J0247+037 ? LMXB RS CVn 582 J0743+2853 ? LMXB RS CVn 583 J105+6028 ? LMXB RS CVn 584 J1213-0904 ? LMXB RS CVn 420 585 J1239+51 ? LMXB RS CVn 586 J1416+046 ? LMXB RS CVn 587 J152+2537 ? LMXB RS CVn 58 J1523-0636 ? LMXB RS CVn 589 J1732+7413 ? LMXB RS CVn 590 J1942+1705 ? LMXB RS CVn 591 J204+4714 ? LMXB RS CVn 592 J2319+790 ? LMXB RS CVn 593 J237+4627 ? LMXB RS CVn 594 J0414+2812 ? TS 595 J0419+2749 ? TS 596 J0419+2906 ? TS 597 J0421+1932 ? TS 598 J0421+2818 ? TS 59 J0421+2826 ? TS 60 J0427+2542 ? TS 601 J0429+2632 ? TS 602 J0430+1813 ? TS 603 J0431+1706 ? TS 604 J0432+1757 ? TS 605 J0432+1801 ? TS 606 J0432+1820 ? TS 607 J043+2421 ? TS 608 J043+2421 ? TS 609 J043+2434 ? TS 610 J0434+2428 ? TS 61 J0435+2414 ? TS 612 J045+3021 ? TS 613 J045+3034 ? TS 614 J0456+3021 ? TS 615 J0503+2523 ? TS 616 J0507+3024 ? TS 617 J0535-0508 ? TS 618 J0235+034 ? WD 619 J2013+402 ? WD 620 J217+3412 ? WD 621 J037-7214 ? ?? BHC 62 J013+3039 ? ?? BHC 623 J0538-6404 ? HMXB HMBH 624 J0538-6905 ? ?? BHC 625 J1801-2547 ? ?? BHC 626 J1915+1056 ? ?? BHC 627 J1907+0918 ? ?? MGTR 628 J042+415 ? ?? BP 629 J042+416 ? ?? BP 421 630 J130+1240 B1257+12 ?? BP 631 J1537+15 B1534+12 ?? BP 632 J1748-246 B174-24A LMXB LMNS XBRST 63 J1845+050 ? ?? BP 634 J2019+2425 ? ?? BP 635 J042+353 ? ?? BY 636 J022+4729 ? ?? BY 637 J0234-4347 ? ?? BY 638 J0734+3152 ? ?? BY 639 J074+033 ? ?? BY 640 J134-0820 ? ?? BY 641 J1634+5709 ? ?? BY 642 J2045-3120 ? ?? BY 643 J2309+4757 ? ?? BY 64 J1939-0603 ? ?? CHRM 645 J130+2413 ? ?? FK 646 J0720-3146 ? ?? PCB 647 J019+2156 ? ?? SXS 648 J0513-6951 ? LMXB LMXB-SXS 649 J0543-682 ? LMXB LMXB-SXS 650 J0925-4758 ? ?? SXS 651 J1601+648 ? ?? SXS 652 J1045-5941 ? ?? VXS 653 J0654-235 ? ?? W-R 654 J2020+4354 ? ?? W-R 65 J0412-1028 ? ?? WU 656 J0943+557 ? ?? WU 657 J101+1724 ? ?? WU 658 J1503+4739 ? ?? WU 659 J2037+7535 ? ?? WU 60 J212+1708 ? ?? WU 61 J1214+149 ? ?? WUM 62 J165+3510 ? ?? WUM 63 J1805+6945 ? ?? WUM 64 J04+0932 ? ? 65 J0103-7254 ? ? 66 J013+3032 ? ? 67 J0535-0523 ? ? 68 J0537-6909 ? NS RPSR SNR 69 J1750+7045 ? ? 670 J204-543 ? ? 671 J051-7310 ? HMXB HMNS HMBP 672 J052-720 ? HMXB HMNS HMBP 673 J042-7340 ? HMXB HMNS HMBP 674 J049-7323 ? HMXB HMNS APSR 422 675 J052-723 ? HMXB HMNS HMBP 676 J056-722 ? HMXB HMNS HMBP 67 J057-7207 ? HMXB HMNS HMBP 678 J057-7219 ? HMXB HMNS HMBP 679 J057-7325 ? HMXB HMNS HMBP 680 J010-721 ? NS AXP SNR 681 J0101-721 ? HMXB HMNS HMBP 682 J0103-7208 ? HMXB HMNS APSR 683 J0103-7241 ? NS RPSR SNR 684 J019-731 ? NS RPSR SNR 685 J030+0451 ? NS RPSR SNR 686 J0205+649 ? NS RPSR SNR 687 J1024-0719 ? NS RPSR SNR 68 J119-6127 ? NS RPSR SNR 689 J124-5916 ? NS RPSR SNR 690 J1420-6048 ? NS RPSR SNR 691 J174-134 ? NS RPSR SNR 692 J180-2450 B1757-24 NS RPSR SNR 693 J1846-0258 ? NS RPSR SNR 694 J1856+013 B1853+01 NS RPSR SNR 695 J229+614 ? NS RPSR SNR 696 J0929-3123 ? LMXB LMNS APSR 697 J1751-3037 ? LMXB LMNS APSR 698 J1806-2924 ? LMXB LMNS APSR 69 J1813-346 ? LMXB LMNS APSR 70 J011-7316 ? HMXB HMNS APSR 701 J1845+051 B1843+0 HMXB HMNS HMBP 702 J0537-7034 ? LMXB 703 J1746-2903 B1743-290 LMXB 704 J1747-2852 ? LMXB 705 J0501+146 ? NS SGR XBRST 706 J1845-0434 B1842-04 NS RPSR SNR 707 J0356-3641 ? LMXB 708 J0242-00 B0240-02 AGN Seyfert 2 709 J0947-3056 B0945-307 AGN Seyfert 2 710 J1235-3954 B1232-396 AGN Seyfert 2 71 J1305-4928 B1304-497 AGN Seyfert 2 712 J1325-4301 B132-427 AGN 713 J2318-422 B2315-426 AGN Seyfert 2 714 J129+0203 B126+023 QSO 715 J174-2916 ? ? 716 J1750-3412 B1747-341 ? 717 J0153+742 ? CV CV,NL IP 718 J0439-6809 ? CV CV-SXS 719 J1905-0142 ? CV CV,N IP 423 720 J1930+1852 ? NS RPSR SNR 721 J023-7204 B021-72C NS RPSR SNR 72 J024-7204D B021-72D NS RPSR SNR 723 J024-7205 B021-72E LMXB LMNS LMBP 724 J024-7204F B021-72F NS RPSR SNR 725 J024-7204G B021-72G NS RPSR SNR 726 J024-7204H B021-72H LMXB LMNS LMBP 727 J024-7204I B021-72I LMXB LMNS LMBP 728 J023-7203 B021-72J LMXB LMNS LMBP 729 J024-7204L B021-72L NS RPSR SNR 730 J023-7205 B021-72M NS RPSR SNR 731 J024-7204N B021-72N NS RPSR SNR 732 J024-7204O B021-72O LMXB LMNS LMBP 73 J024-7204Q B021-72Q LMXB LMNS LMBP 734 J024-7204S B021-72S LMXB LMNS LMBP 735 J024-7204T B021-72T LMXB LMNS LMBP 736 J024-7203 B021-72U LMXB LMNS LMBP 737 J1740-5340 B1736-53 LMXB LMNS LMBP 738 J225+6535 B224+65 NS RPSR SNR 739 J2043+2740 ? NS RPSR SNR 740 J0630-2834 B0628-28 NS RPSR SNR 741 J1817-3618 B1813-36 NS RPSR SNR 742 J059-723 ? HMXB HMNS HMBP 743 J047-7312 ? HMXB HMNS HMBP 74 J051-7310B ? NS 745 J051-7310C ? NS 746 J05-7242 ? NS 747 J05-7210 ? NS 748 J054-7245 ? HMXB HMNS HMBP 749 J053-727 ? NS 750 J05-7238 ? NS 751 J053-7249 ? HMXB HMNS HMBP 752 J184-0257 ? NS AXP SNR 753 J1859+0815 ? NS 754 J0420-502 ? NS RPSR 75 J154-5645 ? NS 756 J1740-2847 ? HMXB HMNS HMBP 757 J1605+3249 ? NS 758 J1308+2127 ? NS 759 J0806-412 ? NS 424 POSITION RA (J200) (h:m:s) RAEror (arcsec) Dec (J200) (d:m:s) DecEror (arcsec) Gal. Longitude ("LI") (deg) Gal. Latitude ("BI") (deg) 05:34:31.973 0.0751 +2:0:52.06 0.060 184.575 -5.78427 08:35:20.67 0.29 -45:10:35.7 0.29 263.521 -2.7873 06:3:54.02 0.60 +17:46:1.5 0.49 195.139 4.2652 17:09:42.16 1.20 -4:28:56 2.9 343.096 -2.6824 15:13:5.61 1.349 -59:08:08 1.0 320.3209 -1.1617 19:52:58.298 0.135 +32:52:40.4 0.160 68.76518 2.8231 10:48:13.0 2.91 -58:32:12.6 0.120 287.4273 0.5757 13:02:47.67 0.29 -63:50:08.6 0.10 304.1836 -0.916 18:26:13.16 0.150 -13:34:47.1 0.80 18.006 -0.6912 18:03:51.35 0.450 -21:37:07.2 0.49 8.3952 0.1461 19:32:13.89 0.029 +10:59:31.9 0.069 47.38142 -3.8437 04:37:15.7102 0.029 -47:15:07.98 0.060 253.39408 -41.96394 18:24:32.083 0.0089 -24:52:10.74 0.0120 7.7968 -5.576 06:59:48.12 0.0150 +14:14:21.53 0.010 201.10763 8.25824 05:40:1.04 0.450 -69:19:5.1 0.49 279.7175 -31.5158 21:24:43.862 0.060 -3:58:43.91 0.080 10.92539 -45.43756 19:59:36.7698 0.00751 +20:48:15.1217 0.0060 59.196946 -4.697474 09:53:09.315 0.010 +07:5:36.15 0.020 28.90798 43.6962 16:14:15.4 4.497 -50:47:18 4.0 32.23 0.1734 05:38:25.06 0.60 +28:17:1 4.9 179.7182 -1.6856 10:12:3.4326 0.060 +53:07:02.6 0.010 160.34701 50.8578 10:57:58.84 0.450 -52:26:56.2 0.29 285.9839 6.6492 03:58:53.704 0.060 +54:13:13.58 0.029 148.19 0.81078 23:37:05.78 0.29 +61:51:01.8 0.10 14.2839 0.234 02:18:06.35 0.150 +42:32:17.5 0.10 139.508 -17.5268 08:26:51.309 0.029 +26:37:25.57 0.069 196.9621 31.7426 07:51:09.1582 0.0105 +18:07:38.71 0.049 202.72961 21.08587 01:42:0 15 +61:0:0 1 129.024 -1.272 05:25:5 75 -6:07:0 20 276.136 -3.251 10:48:06 15 -59:37:0 1 287.906 -0.392 17:08:46.5 13.5 -40:08:53 10 346.4801 0.0369 18:08:39 15 -20:24:39 15 9.96 -0.241 18:41:19 30 -04:56:13 3 27.3857 -0.05 18:45:53.3 1.5 -02:56:42 1 29.6786 -0.1093 19:07:14 15 +09:19:19 25 43.02 0.767 23:01:07.9 15 +58:52:46 1 109.0868 -0.95 0:32:56.1 -73:48:19. 304.7018 -43.2593 0:49:29.6 -73:10:56. 303.1273 -43.9453 425 0:49:02.5 -72:50:52. 303.1787 -4.2793 0:52:06.1 -72:26:06. 302.8615 -4.6932 0:50:4.7 -73:16:05. 303.01 -43.8601 0:50:5.8 -72:13:5. 302.986 -4.8963 0:51:47.7 -72:31:29 302.8943 -4.6035 0:51:51.4 -73:10:38. 302.898 -43.951 0:52:13.9 -73:19:13. 302.853 -43.8079 0:52:54.0 -71:58:08. 302.715 -45.1589 0:54:3.4 -73:41:04. 302.6303 -43.42 0:56:42.3 +60:43:0. 123.5764 -2.1485 0:53:5.0 -72:26:47. 302.691 -4.6806 0:54:36. -72:04:0 302.587 -45.06 0:54:56.17 -72:26:27.6 302.5608 -4.6847 0:57:48.4 -72:02:42. 302.237 -45.0747 0:58:12.7 -72:30:45. 302.2172 -4.6064 0:59:1.3 -71:38:45. 302.062 -45.4693 01:01:01.1 -72:06:57. 301.8921 -4.931 01:03:13.9 -72:09:14.0 301.657 -4.9451 01:09:06.1 -74:4:40. 301.3616 -42.329 01:05:08.9 -72:1:4. 301.4532 -4.893 01:06:15.1 -72:05:25. 301.325 -4.917 01:1:08.4 -73:16:46. 30.9714 -43.737 01:18:02.8 +65:17:19. 125.7105 2.5605 01:18:31.9 +63:4:24. 125.9237 1.0257 01:17:05.2 -73:26:35. 30.4148 -43.596 01:17:41.4 -73:30:49. 30.3697 -43.4838 01:43:32.6 +61:06:26. 129.1854 -1.1303 02:40:31.6 +61:13:45. 135.6752 1.0859 03:34:59.9 +53:10:23. 146.0521 -2.1941 03:5:23.0 +31:02:45. 163.081 -17.1364 04:19:46.0 +5:59:24. 149.1895 4.1328 04:40:59.9 +4:31:51. 159.8478 -1.2684 05:01:23.9 -70:3:3. 281.935 -34.5281 05:02:51.6 -6:26:25. 27.036 -35.4697 05:12:41.8 -67:17:23. 27.7909 -34.3419 05:16:0.1 -69:16:09. 280.0508 -3.6342 426 05:20:30.3 -69:32:04. 280.2659 -3.1926 05:2:35.2 +37:40:34. 170.0532 0.7103 05:29:48.4 -65:56:51. 275.8764 -32.8797 05:31:13. -6:07:06. 276.059 -32.718 05:31:36.1 -65:18:16. 275.0917 -32.7657 05:32:49.2 -6:2:14. 276.353 -32.5297 05:32:25.3 -65:35:09. 275.4141 -32.6524 05:32:32.6 -65:51:40.8 275.738 -32.616 05:35:05.9 -67:0:16. 27.0529 -32.2375 05:35:40.5 -6:51:53. 276.817 -32.1959 05:38:54.57 +26:18:56.8 181.45 -2.6435 05:35:53.8 -65:30:34. 275.2839 -32.3015 05:38:56.4 -64:05:01. 273.5757 -32.0819 05:39:38.7 -69:4:36. 280.2032 -31.516 05:41:2.2 -69:36:29. 280.0259 -31.3823 05:41:37.1 -68:32:32. 278.7807 -31.4689 05:4:15.5 -6:3:50. 276.462 -31.3756 05:4:06.3 -71:0:50. 281.6298 -30.992 05:5:54.7 +28:47:06. 181.2834 1.8584 06:35:17.4 +05:3:20.9 206.1475 -1.0437 06:48:04.6 -4:18:54.4 253.7053 -19.1408 07:28:53.4 -26:06:28. 240.281 -4.0509 07:47:23.5 -53:19:58. 26.3128 -13.7262 07:56:15.8 -61:05:59. 274.031 -16.2096 08:12:28.4 -31:14:51. 249.578 1.5431 08:35:53 -43:1:21.2 262.019 -1.518 09:02:06.9 -40:3:17. 263.0584 3.929 10:09:46. -58:17:32. 282.98 -1.82 10:25:56.6 -57:48:42. 284.5154 -0.2389 10:30:2.5 -57:04:39. 284.642 0.6983 10:37:35.2 -56:47:59. 285.3529 1.4326 10:50:07.9 -59:53:16. 28.2572 -0.5181 1:20:57.2 -61:54:58. 292.4984 -0.8912 1:21:15.2 -60:37:24. 292.0904 0.36 427 1:48:01.8 -62:12:29.4 295.6148 -0.2406 1:47:28.6 -61:57:14. 295.489 -0.098 12:26:37.6 -62:46:13. 30.0981 -0.0351 12:42:01.7 -60:12:05.4 301.7619 2.6489 12:47:35. -60:38:36. 302.459 2.25 12:49:36. -59:07:18. 302.696 3.749 12:42:50.4 -63:03:32. 301.9582 -0.2034 12:39:15.0 -75:2:12. 302.1439 -12.5169 12:54:37.0 -57:10:06. 303.3649 5.707 13:01:16.4 -61:36:14.2 304.1013 1.245 13:24:26.3 -62:0:53. 306.793 0.6094 14:21:12.9 -62:41:54. 313.0212 -1.5985 14:52:49.3 -59:49:18. 317.645 -0.4634 15:42:23.3 -52:23:10. 327.4195 2.1637 15:57:49.2 -54:24:52. 327.949 -0.8569 15:54:2.0 -5:19:4. 326.9767 -1.239 17:0:47.9 -41:40:23. 34.3538 0.311 17:03:56.7 -37:50:39. 347.7543 2.1737 17:0:05.3 -41:57:4. 34.045 0.2372 17:25:5. -36:24:42. 351.472 -0.547 17:38:53. -30:15:36. 358.103 0.546 17:39:30.1 -29:42:07. 358.6467 0.7305 17:4:45.4 -27:13:47. 1.3565 1.0528 17:49:10.1 -27:25:16. 1.701 0.157 17:49:12.0 -26:38:50. 2.3682 0.508 18:10:42. -10:52:0 18.6 3.932 18:20:29.5 -14:34:24. 16.4719 0.069 18:26:14.9 -14:50:29. 16.875 -1.2854 18:36:28.6 -07:36:21 24.4625 -0.1608 18:41:42. -05:51:0 26.618 -0.508 18:41:48. -04:27:0 27.874 0.1 18:45:30. +0:57:0 3.101 1.754 18:47:24. -03:09:0 29.68 -0.539 428 18:48:17.7 -02:25:13. 30.4197 -0.4046 18:47:41. -04:30:12. 28.496 -1.219 18:58:0. -02:4:0 31.245 -2.705 18:5:42. -02:37:0 31.08 -2.141 18:58:36. +03:21:0 36.729 -0.064 19:04:12. +03:10:30. 37.213 -1.387 19:05:20. +09:02:30. 42.56 1.054 19:09:37.9 +09:49:49. 43.7437 0.4761 19:1:49.5 +04:58:58.1 39.694 -2.243 19:32:52.3 +53:52:45. 85.849 15.9024 19:45:38. +27:21:38.0 63.2 1.398 19:49:35.6 +30:12:31. 6.09 2.0831 19:48:0. +32:0:0 67.475 3.282 19:5:43.3 +32:06:03. 68.397 1.926 19:58:21.68 +35:12:05.8 71.35 3.068 20:32:15.3 +37:38:15. 7.1519 -1.2418 20:32:25.7 +40:57:28. 79.8454 0.703 20:30:30.6 +47:51:46. 85.292 5.0473 20:59:0. +41:43:0 83.5 -2.724 21:03:3. +45:45:0. 87.124 -0.68 21:39:34. +57:03:36. 9.067 3.363 2:01:38.2 +50:10:04. 97.2476 -4.0413 2:07:57 +54:31:05.8 10.605 -1.107 2:26:3.1 +61:14:17. 106.381 3.1 2:39:20.90 +61:16:26.8 107.7346 2.3623 0:4:50.4 +3:01:17. 121.37 -29.829 04:18:29.9 +32:47:24. 165.4873 -12.4798 05:14:06.6 -40:02:37. 24.5096 -35.0361 05:20:29.2 -71:57:36. 283.0935 -32.6902 05:32:42.8 -69:26:18. 279.9393 -32.1547 06:17:07.3 1 +09:08:13. 1 20.874 -3.3635 06:2:4.5 -0:20:45. 209.38 -6.226 429 06:58:27. -07:15:50. 20.195 -1.756 07:48:3.8 -67:45:09. 279.9781 -19.8109 08:35:56. +51:18:36. 167.531 36.93 08:37:23. -42:53:09. 261.942 -1.17 09:20:26.8 -5:12:24. 275.8525 -3.846 09:2:34.7 -63:17:42. 281.8356 -9.398 10:13:36. -45:04:35. 275.878 9.345 1:18:10.85 +48:02:12.9 157.605 62.3205 1:26:26.7 -68:40:3. 295.306 -7.0727 12:57:37.2 -69:17:21. 303.4819 -6.424 13:26:36.1 -62:08:10. 307.0281 0.457 13:58:09.7 -64:4:05. 309.974 -2.796 14:58:2.0 -31:40:08. 32.2426 23.81 15:20:40.9 -57:10:01. 32.185 0.0375 15:28:17.2 -61:52:58. 320.3193 -4.4272 15:47:08.5 -47:40:09.4 30.9185 5.4261 15:47:54.8 -62:34:05. 321.7572 -6.364 15:50:58.78 -56:28:35.0 325.826 -1.827 16:01:02.3 -60:4:17. 324.1392 -5.9314 16:05:45.8 +25:51:45. 42.7503 46.786 16:03:54. -7:53:06. 312.429 -18.731 16:12:43.0 -52:25:23. 30.9263 -0.8505 16:19:5.1 -15:38:25. 359.0943 23.7843 16:28:02.4 -49:1:25. 34.9201 -0.256 16:32:16.8 -67:27:43. 321.7876 -13.0924 16:34:0.4 -47:23:39. 36.9081 0.2519 16:36:28. -47:49:37. 36.869 -0.346 16:40:5.5 -53:45:05. 32.915 -4.818 16:45:47.7 -45:36:40. 39.581 -0.0794 16:54:0.137 -39:50:4.90 34.98189 2.4597 16:57:49.8 +35:20:3. 58.1492 37.5231 17:02:06.3 -29:56:45. 353.8264 7.261 17:02:49.5 -48:47:23. 38.9394 -4.3267 430 17:05:4.5 -36:25:2. 349.1039 2.7486 17:06:15.3 -43:02:10. 343.865 -1.3185 17:06:34.6 +23:58:18. 45.1517 32.903 17:08:14.6 -25:05:29. 358.5875 9.0568 17:08:54.7 -4:06:02. 343.324 -2.3416 17:12:23. -40:50:36. 346.327 -0.928 17:09:30.2 -26:39:27. 357.4705 7.912 17:10:12.3 -28:07:54. 356.3571 6.92 17:14:19.2 -34:02:58. 352.0568 2.7457 17:12:34. -37:38:36. 348.935 0.928 17:18:47.4 -32:10:40. 354.127 3.064 17:19:36.9 -25:01:03. 0.1424 6.91 17:18:24.13 -40:29:30.4 347.274 -1.6512 17:23:38. -37:39:42. 350.182 -0.873 17:27:39. -35:4:04. 352.23 -0.46 17:27:3.2 -30:48:07. 356.319 2.2981 17:31:57.4 -3:50:05. 354.302 -0.1501 17:31:4.2 -16:57:42. 8.5128 9.037 17:32:02.2 -24:4:4. 1.9372 4.7948 17:3:32. -31:13:0 356.678 0.1 17:3:24.1 -3:23:16. 354.8409 -0.1583 17:3:57. -2:02:07. 4.467 5.87 17:34:13.0 -26:05:09. 1.0743 3.655 17:35:47.6 -30:28:56. 357.58 0.9897 17:36:02. -27:25:3. 0.1627 2.592 17:37:25. -29:10:48. 358.846 1.393 17:38:16. -27:0:16. 0.785 2.398 17:38:58.3 -4:27:0. 346.0543 -6.939 17:38:34. -28:29:0 359.569 1.53 17:39:3. -29:43:26. 358.634 0.71 17:39:56. -30:59:0 357.61 -0.03 17:40:57. -28:18:36. 359.95 1.201 17:42:37. -27:46:59. 0.636 1.167 17:42:4. -30:30:51. 358.328 -0.292 17:43:47. -29:26:0 359.367 0.082 17:43:54.7 -29:4:43. 359.156 -0.1054 431 17:4:25.4 -29:0:45. 359.7983 0.1834 17:4:49. -29:21:06. 359.54 -0.067 17:45:02. -32:13:38. 357.126 -1.608 17:45:01. -28:54:06. 359.961 0.131 17:45:29. -32:41:39. 356.76 -1.93 17:45:26.6 -28:59:0. 359.9396 0.084 17:45:37. -29:27:0 359.561 -0.267 17:45:37.0 -29:01:07. 359.9293 -0.0423 17:45:40.7 -29:0:1. 359.9496 -0.0457 17:45:42.9 -28:46:53. 0.143 0.0629 17:45:52.9 -29:03:2. 359.9274 -0.113 17:46:0.0 -28:54:49. 0.0626 -0.0592 17:46:04.9 -28:53:13. 0.0946 -0.0606 17:46:06.2 -29:31:06. 359.578 -0.3931 17:46:09.7 -28:51:04. 0.1343 -0.057 17:46:19.2 -28:4:07. 0.2513 -0.0264 17:46:19.5 -28:53:43. 0.152 -0.105 17:46:47. -28:53:41. 0.168 -0.196 17:47:25.7 -29:59:43. 359.293 -0.864 17:4:3.1 -28:4:29. 0.04 0.3012 17:47:25.9 -30:02:31. 359.2598 -0.912 17:47:56.0 -26:3:49. 2.2938 0.7937 17:48:13.4 -36:07:53. 354.1214 -4.192 17:45:36. -29:01:34. 359.921 -0.043 17:48:56. -24:53:40. 3.84 1.462 17:48:53.5 -20:2:02. 7.7242 3.795 17:49:50.6 -3:1:5. 356.8162 -2.9763 17:50:03.5 -32:25:43. 357.5017 -2.621 17:50:12.7 -37:03:08. 353.5309 -5.052 17:50:25.7 -21:25:21. 6.996 2.9469 17:50:45.5 -31:17:32. 358.552 -2.167 17:48:05.06 -28:28:25.8 0.6756 -0.221 17:48:53.4 -20:21:43. 7.7285 3.798 432 17:52:16. -28:30:2. 1.19 -1.028 17:50:24. -29:02:18. 0.453 -0.948 17:52:24. -31:37:42. 358.44 -2.64 17:58:40.0 1 -3:48:27. 1 357.2154 -4.8723 17:5:28.6 -32:28:39. 358.0393 -3.6314 18:01:08.2 -25:04:45. 5.072 -1.0185 18:01:12.7 -25:4:26. 4.5108 -1.3607 18:01:32.3 -20:31:4. 9.0768 1.1537 18:06:50.2 -24:35:15. 6.1407 -1.9039 18:06:51. -24:35:06. 6.14 -1.905 18:08:27.54 -36:58:4.3 35.385 -8.1483 18:10:4.5 -26:09:01. 5.1973 -3.4312 18:14:31.1 -17:09:26. 13.5158 0.108 18:15:12. -12:05:0. 18.056 2.383 18:16:01.4 -14:02:1. 16.4321 1.276 18:19:21.48 -25:25:36.0 6.7564 -4.797 18:23:40.6 -30:21:41. 2.781 -7.9139 18:25:46.8 -37:06:19. 356.8501 -1.2908 18:25:2.1 -0:0:4. 29.91 5.8191 18:29:27. -23:47:29. 9.275 -6.081 18:35:4.0 -32:58:5. 1.5395 -1.3679 18:39:56.9 +05:02:08.7 36.168 4.845 18:49:17.1 -03:03:4. 29.961 -0.9174 18:53:04.9 -08:42:20. 25.356 -4.319 18:56:39. +05:19:48. 38.269 1.272 18:58:41.58 +2:39:29.4 54.0461 8.6075 19:08:27.0 +0:10:08. 35.0246 -3.7072 19:1:16.0 +0:35:06. 35.7184 -4.143 19:15:17. +10:58:06. 45.396 -0.28 19:18:48.0 -05:14:09. 31.36 -8.4631 19:20:17. +14:41:39. 49.26 0.435 19:42:38. -03:54:0 35.301 -13.163 19:59:23.9 1 +1:42:29 1 51.3072 -9.329 20:02:49.6 +25:14:12. 63.368 -2.989 20:12:37.80 +38:1:01.1 75.385 2.2467 20:24:03.8 +3:52:04. 73.192 -2.091 21:23:14.54 -05:47:52.9 46.483 -36.194 21:29:58.3 +12:10:03. 65.013 -27.312 21:31:26.2 1 +47:17:24. 1 91.574 -3.0365 433 21:4:41.2 +38:19:18. 87.3285 -1.3163 23:20:34.1 +62:17:3. 12.5852 1.2602 07:20:24.96 -31:25:50.2 24.158 -8.1645 18:38:27.02 -03:01:14.4 28.762 1.5076 12:34:54.4 1 +37:37:43 140.2384 78.9382 13:05:43.4 1 +18:01:02 323.5429 80.3123 0:24:06.2 1 -72:04:57 305.8936 -4.882 06:10:3.6 2 -48:4:27 256.427 -26.545 07:12:32.9 1 -36:05:40 247.6826 -1.682 01:10:13.2 1 +60:04:36 125.2749 -2.7096 06:13:2.4 1 +47:4:26 16.063 13.797 07:5:05.3 1 +2:0:06 19.23 23.3948 08:07:28.6 1 -76:32:02 289.187 -2.0824 08:25:13.2 1 +73:06:40 141.3819 32.6286 08:4:27.2 1 +12:52:32 213.7396 30.8183 09:01:03.4 1 +17:53:56 210.0109 36.413 09:51:01.6 1 +1:52:30 23.698 45.19 10:06:2.3 1 -70:14:05 289.765 -1.706 1:45:21.2 1 -04:26:07 273.6054 54.6296 16:4:09.8 1 +25:15:01 4.8498 38.2364 18:07:51.8 1 +05:51:48 3.2365 12.3508 20:07:36.2 1 +17:42:15 57.5361 -7.928 21:42:42.5 1 +43:35:10 90.585 -7.1 2:14:02.5 1 +12:42:1 74.0379 -34.8276 0:28:48.9 3 +59:17:2 120.0417 -3.453 02:03:42.1 -02:43:48.6 161.3461 -60.0971 02:06:53 1 +15:17:42 1 148.527 -43.795 02:56:08.8 >15 +19:26:35 159.2495 -34.485 03:31:1.8 1 +43:54:17 150.952 -10.1041 03:50:24.5 +17:14:48.1 172.4809 -27.9384 05:02:27.4 +24:45:2.1 178.078 -10.3143 05:12:13.1 2 -32:41:39 235.6437 -34.0919 05:29:25.5 2 -32:49:05 236.7897 -30.6043 05:34:50.8 1 -58:01:42 26.4239 -32.782 05:43:20.3 1 -41:01:56 246.701 -29.7298 05:58:0.3 1 +53:53:58 159.2051 14.3163 06:1:4.07 -81:49:24.1 293.7816 -28.2401 07:31:29 1 +09:56:2 208.479 13.362 07:4:57.9 -52:57:12.9 265.7946 -13.876 07:51:17.3 1 +14:4:23 206.0609 19.7696 07:57:0.3 +63:05:56 153.4806 31.3509 08:3:06.3 -2:48:43.9 245.1894 10.0969 08:59:20 1 -24:28:56 250.253 13.83 1:43:38.34 1 +71:41:20.4 130.3043 4.456 12:38:05.0 -38:45:54.5 30.0821 24.0327 434 12:52:24.5 1 -29:14:58 303.1861 3.6218 17:12:56.1 1 +3:31:21 56.6597 34.1242 17:12:35.9 1 -24:14:41 359.864 8.7417 18:14:20.4 1 +41:51:21 69.183 24.2735 18:5:02.3 1 -31:09:49 4.958 -14.3549 20:40:09.1 1 -0:52:16 46.9325 -23.5491 2:17:5.5 1 -08:21:05 53.001 -49.1582 23:53:0.6 >15 -38:51:45 345.3585 -73.0782 04:2:38.1 1 -13:21:29 208.3127 -38.968 06:15:4 1 +28:35:08 183.574 5.562 06:29:34.1 1 +71:04:36 143.5956 23.8184 08:1:46 1 -35:21:05 252.926 -0.835 09:32:15 1 +49:50:53 168.05 45.969 10:19:56.6 1 -08:41:56 251.8735 38.7176 1:38:27 1 +03:2:07 263.493 60.525 1:52:02.4 1 -67:12:20 297.218 -4.958 15:59:30.16 +25:5:12.6 42.3738 48.1647 16:2:30.7 1 -17:52:42 357.686 21.8692 18:32:04.3 1 -29:23:13 4.4905 -9.1084 18:48:54.5 1 +0:35:03 3.1635 0.8292 19:34:36.6 1 +51:07:37 83.3796 14.5015 19:35:42.9 -59:08:21.8 37.927 -28.6252 20:17:34.2 1 -03:39:50 39.6987 -20.8014 20:20:14.8 1 +21:06:08 62.0526 -8.6028 20:42:20.3 1 +19:09:39 63.4302 -13.972 13:36:41.1 1 +51:54:49 107.0295 63.795 18:0:35.6 1 +08:10:12 34.5432 14.9895 01:32:42 >15 -65:54:32 296.307 -50.685 01:41:0.4 1 -67:53:29 295.927 -48.567 02:03:48. >15 +29:59:0 141.087 -30.325 02:36:1.6 1 -52:19:14 272.286 -58.1074 03:14:13.1 1 -2:35:42 212.9374 -57.4057 03:32:04.6 1 -25:56:57 20.4064 -54.2061 04:53:25.5 2 -42:13:41 246.7589 -39.124 05:15:41.4 1 +01:04:40 20.4843 -20.6376 05:31:35.4 1 -46:24:08 252.583 -32.665 05:42:48.9 +60:51:28 151.8343 15.6893 07:19:14 1 +65:57:48 1 150.026 27.407 08:15:06.8 1 -19:03:18 239.652 8.7131 08:51:27 >15 +1:46:58 215.73 31.92 09:29:07.1 1 -24:05:05 254.5945 19.2605 10:02:1.71 1 -19:25:37.5 1 256.975 27.9705 10:15:34.7 >15 +09:04:42 231.5895 49.0492 10:15:58.4 2 -47:58:1 27.8785 7.1952 10:47:09.9 2 +63:35:13 143.1496 48.3738 435 10:51:35.2 1 +54:04:36 153.86 5.2481 1:04:25.8 1 +45:03:14 165.826 62.1484 1:05:39.8 1 +25:06:28 21.803 6.2142 1:15:4.9 1 +42:58:23 167.4532 64.9672 1:17:16 1 +17:57:41 230.897 6.457 1:41:23 -64:10:15 295.392 -2.3 1:49:5.7 1 +28:45:08 202.536 76.3281 13:07:53.9 1 +53:51:30 17.5647 63.098 14:09:07.4 1 -45:17:16 1 316.9787 15.4546 15:52:47.3 1 +18:56:27 31.7154 47.7086 17:27:06.2 +41:14:1 6.3685 32.739 18:02:06.5 2 +18:04:43 4.149 18.7962 18:16:13.4 1 +49:52:03 7.864 25.8758 18:4:47.8 1 -74:18:3 320.374 -25.5957 19:07:06.4 +69:08:39.7 10.079 23.8575 19:14:25.7 1 +24:56:40 57.7263 6.4013 19:38:35.6 1 -46:12:57 352.4536 -27.0658 20:05:42 >15 +2:39:58 61.532 -4.92 20:08:5.8 1 -65:27:43 30.614 -32.5073 20:2:37.5 -39:54:12 1.3135 -3.8517 21:07:58.2 1 -05:17:39 4.7628 -32.638 21:1:36.5 1 +48:09:02 89.829 -0.0731 21:15:41 1 -58:40:54 37.025 -41.42 21:37:56.5 1 -43:42:14 356.706 -47.9393 23:15:18.4 -59:10:27 323.6812 -53.9096 09:04:41.5 1 -32:2:47 257.207 9.7068 02:09:50.8 1 -63:18:41 28.848 -51.6253 04:09:1.3 1 -71:17:41 284.881 -38.138 08:10:56.7 1 +28:08:3 194.084 28.8091 08:12:28.2 1 +62:36:23 153.9609 3.1365 1:14:0.2 1 -37:40:49 282.425 21.281 15:14:01.1 1 -65:05:42 1 317.25 -6.2584 08:15:19.1 1 -49:13:21 264.9296 -7.898 08:38:2.1 1 +48:38:01 170.82 37.357 13:31:19.6 1 -54:58:34 308.684 7.495 19:49:06.5 1 +7:4:23 109.9736 23.4862 19:54:40.7 1 +32:21:5 68.5096 2.2515 19:47:40.5 1 -42:0:26 357.4767 -27.7624 0:1:24.7 1 -1:28:4 90.051 -71.743 01:04:35.5 1 +41:17:58 125.5868 -21.5045 06:45:17 2 -16:51:35 27.375 -8.924 04:59:43.1 +19:26:35.2 182.0812 -13.9636 05:02:50.4 +16:24:31.7 185.081 -15.153 05:3:3.4 1 +36:59:32 171.8325 2.1451 13:26:54.3 +45:32:5 104.2808 70.2737 436 13:31:53.8 1 -29:40:59 313.392 32.3698 15:38:0.2 1 +18:52:02 29.772 50.9706 17:18:37.1 1 +41:15:50 6.1219 34.357 17:50:13.7 1 +06:05:28 31.4254 16.3759 18:46:31.3 +12:2:0.6 43.4352 6.6789 20:30:31.7 1 +52:37:51 89.139 7.8191 21:23:45.7 +42:17:52.2 87.121 -5.6898 05:38:57.9 -6:52:28.2 276.8568 -31.8734 18:49:0 60 -03:18:0 60 29.717 -0.962 0:51:46.8 -71:59:53 302.8945 -45.1302 01:02:17.9 +81:52:32.6 123.376 19.0125 01:57:46 +38:04:29.2 137.05 -2.971 02:41:23.9 +60:3:12.1 136.0486 0.5127 02:48:35.3 +69:38:02.7 132.8589 9.0527 03:08:10.1 +40:57:20.5 148.9764 -14.903 04:0:40.9 +12:29:25.8 178.3719 -29.3753 05:15:29.7 +46:24:21.9 162.1345 4.631 05:18:18.9 +3:46:04 172.7671 -2.231 06:47:28.9 +69:37:45.1 145.5089 24.9684 08:43:56.14 +19:02:03 206.9704 3.0453 10:45:20.5 +45:3:58.5 168.1404 58.9497 1:13:12.6 -26:27:54.4 27.0819 31.4294 1:45:29.4 +72:15:58.6 129.8301 43.9679 12:49:38.7 -06:04:4.3 302.181 56.789 13:13:38.1 -64:09:05 305.349 -1.3839 15:0:58.6 -08:31:07.9 348.8683 42.5109 15:18:1.4 +31:38:49.8 49.9512 57.8656 15:3:51 +63:54:24.5 9.06 4.968 15:34:40.8 +26:42:57.4 41.8713 53.743 16:39:4.7 -56:59:38.3 30.352 -6.8285 16:49:27.7 -15:40:04.3 3.7605 18.1617 16:56:18.1 +52:41:54.4 80.1976 38.4926 17:39:40.4 -28:51:1.7 359.3853 1.1503 18:2:06.9 -25:14:23.2 7.2132 -5.2624 18:52:05.9 -06:14:37.9 27.449 -2.989 19:17:40 +2:26:28.7 5.832 4.596 20:25:3.6 +27:2:09.8 67.9648 -6.079 21:54:43.4 +14:3:28.6 71.6231 -30.2096 23:32:14.8 +14:58:09 96.0102 -43.7242 17:4:02.7 -29:43:25 359.1492 -0.187 18:49:06 -03:08:0 29.87 -0.909 0:47:20.3 +24:16:01.8 121.736 -38.5951 0:53:04.9 -74:39:07.2 302.7845 -42.4758 01:16:5.12 +06:48:42.1 134.1489 -5.5041 01:2:50.7 +0:42:5.4 139.3769 -61.1496 437 01:2:56.8 +07:25:09 136.5071 -54.62 02:12:2.6 +30:18:13.4 142.9761 -29.3984 03:13:2.37 +48:06:31.3 145.923 -8.3058 03:18:03.82 -19:4:13.8 208.4792 -5.6919 03:25:35.3 +28:42:5 159.3585 -23.045 03:35:01 +32:01:02.1 158.929 -19.18 03:36:47.1 +0:35:25 184.9079 -41.5678 03:37:1.04 +25:59:27.9 163.393 -23.5724 04:43:45.8 -10:39:56 207.9846 -3.1486 05:06:12.14 +59:01:16.8 150.9514 10.8308 05:07:28.7 -05:24:02.1 205.5986 -25.5431 05:16:40.9 +45:59:29 162.5931 4.5615 05:28:4.8 -65:27:02.5 275.3032 -3.045 06:03:53.7 +31:19:41.3 179.9257 4.617 06:41:18.1 +82:16:10.1 131.5698 26.523 07:03:18.3 -05:4:10.1 219.3876 0.0148 07:16:25.2 +73:20:02.7 141.7124 27.6841 07:20:48.5 -05:15:35.6 20.9784 4.098 08:02:36.1 +57:16:28 160.327 32.0471 08:37:30.13 +23:3:41.6 201.278 3.1259 08:39:08.54 +31:47:4.5 191.7649 35.6475 08:59:42 -27:49:01 252.954 1.836 09:01:5.8 +26:41:28 19.4695 39.3083 09:09:56.2 +54:29:26.7 162.716 41.6749 10:36:01.8 -1:54:34.8 258.4084 38.9842 1:30:24.8 -15:19:19.6 275.612 43.2181 1:36:16.23 -38:02:1.4 286.928 2.4976 1:40:46.35 +51:59:53.4 146.2343 61.8145 1:47:59.14 +20:13:08.2 235.034 73.9319 12:15:41.6 +72:3:05.3 126.64 4.3168 12:25:02.3 +25:3:38.7 26.2937 83.823 12:29:41 +24:31:15 239.767 84.454 13:01:31.2 +28:37:40.5 67.4608 87.314 13:10:36.91 +35:56:05.6 9.263 80.2952 13:18:52 +3:26:18.7 81.437 81.351 13:34:47.5 +37:10:57.1 83.3268 76.408 14:35:48.5 -18:02:10.5 35.093 38.2305 15:13:32.8 +38:34:06.5 63.1589 58.2762 16:14:40.8 +3:51:27 54.654 46.1412 16:39:03.8 +60:42:01.7 90.8602 39.454 16:45:57.7 +82:02:13.9 14.962 31.0487 17:10:25.6 +48:57:57.5 75.407 36.3859 17:17:25.7 -6:56:56.4 324.906 -16.296 17:30:3.36 -3:39:15.9 354.2932 0.192 17:58:07 +15:08:17.9 40.868 18.491 438 17:58:38.5 +2:08:48.3 47.7805 21.1075 18:05:49.8 +21:26:47 47.7578 19.298 18:10:26.4 +31:57:41.5 58.659 2.0693 18:25:38.6 +18:17:39.3 46.675 13.707 19:21:48.49 +04:32:56.9 40.4638 -4.6492 19:31:13.5 +5:43:5.5 87.5128 16.8742 19:36:42.6 +27:53:03.4 62.6805 3.3751 20:58:13.4 +35:10:30.4 78.4648 -6.8658 21:02:24.9 +27:48:48 73.343 -12.29 21:21:01.5 +40:20:53.5 85.3687 -6.703 21:39:48.7 -16:0:21.6 36.8147 -4.3628 2:0:36.42 -02:4:26.9 56.2573 -42.4572 2:01:30.5 +43:53:24.6 93.406 -9.0264 2:08:39.8 +45:4:40 95.559 -8.298 23:1:10.1 +53:01:34.3 108.057 -6.9253 23:13:23.7 +02:40:21.0 80.635 -51.9658 23:39:29.8 +28:14:36.1 104.23 -32.014 23:49:40.96 +36:25:31.0 109.2831 -24.8043 23:5:03.3 +28:38:03 108.297 -32.628 05:27:53.8 -69:21:15 279.9171 -32.5863 05:46:45.1 12 -71:08:54 281.759 -30.716 0:58:36.9 -71:35:53 302.1236 -45.5189 16:56:35.98 -40:49:24.4 34.531 1.4571 0:02:54.1 +62:46:23 17.4131 0.425 01:17:38.70 +59:14:37.9 126.2831 -3.4573 06:28:40.5 1 +10:38:15 40 20.842 -0.1468 1:05:26.07 -61:07:52.1 290.4896 -0.8465 16:17:30.2 -50:5:04 32.5029 -0.275 16:23:38.228 -26:31:53.71 350.97626 15.9597 16:45:02.045 -03:17:58.35 14.1406 26.06154 17:08:46.6 -40:09:27 346.4727 0.031 17:40:3.73 -30:15:41.9 358.2945 0.2385 17:48:12 -29:24:0 359.8956 -0.721 18:1:29.2 1 -19:25:27.6 60 1.1814 -0.3479 19:17:39.71 +13:53:57.05 48.2598 0.62407 19:39:38.560084 0.0012 +21:34:59.13548 0.0014 57.50884 -0.289593 19:58:13.8 1 +32:32:58.7 1 69.0562 1.706 23:2:2.36 +20:57:03.0 96.5148 -37.31 0:43:35.37 -17:59:1.8 11.302 -80.681 18:56:35.41 -37:54:08 358.6061 -17.218 01:37:08.84 +20:42:0.4 137.1274 -40.9083 02:47:25.5 +0:37:27.5 172.81 -50.612 07:43:17.2 +28:53:03 191.1867 23.2694 10:5:43.5 +60:28:09.7 145.359 51.329 12:13:20.69 -09:04:46.9 287.3159 52.632 439 12:39:53.8 +5:1:34 126.424 61.8571 14:16:07.79 +0:46:16.1 34.0876 56.717 15:2:25.1 +25:37:34.8 39.178 56.278 15:23:26.4 -06:36:24.9 356.023 40.1052 17:32:41.21 +74:13:38.5 105.4927 31.3534 19:42:10.2 1 +17:05:15 1 53.891 -3.0263 2:04:56.61 +47:14:04.5 95.928 -6.7175 23:19:27.7 +79:0:02.8 18.4635 16.9354 23:37:3.9 +46:27:50 109.9049 -14.5309 04:14:12.92 +28:12:12.3 168.2168 -16.34 04:19:41.30 +27:49:38.8 169.3674 -15.7256 04:19:15.83 +29:06:26.9 168.358 -14.9149 04:21:59.43 +19:32:06.4 176.297 -20.868 04:21:58.85 +28:18:06.5 169.3659 -15.0323 04:21:57.41 +28:26:35.6 169.25 -14.9398 04:27:02.80 +25:42:2.3 172.1468 -15.9423 04:29:41.51 +26:32:59.8 171.89 -14.9387 04:30:03.9 +18:13:49.4 178.6093 -20.2636 04:31:27.2 +17:06:25 179.7629 -20.7147 04:32:09.28 +17:57:23.3 179.1692 -20.0514 04:32:15 +18:01:42 179.125 -19.989 04:32:14.56 +18:20:15.0 178.8682 -19.7954 04:3:34.02 +24:21:18.2 174.2137 -15.7127 04:3:34.41 +24:21:07.2 174.2171 -15.7136 04:3:13 +24:34:18 173.989 -15.63 04:34:5.45 +24:28:53.7 174.3207 -15.3952 04:35:27.37 +24:14:59.5 174.585 -15.4518 04:5:10.2 +30:21:58 172.561 -8.1958 04:5:59.38 +30:34:01.5 172.5167 -7.9328 04:56:02.2 +30:21:03 172.6949 -8.0582 05:03:06.60 +25:23:19.6 17.6504 -9.8193 05:07:49.57 +30:24:05.2 174.2042 -6.029 05:35:04.21 -05:08:13.2 208.7476 -19.3149 02:35:07 +03:4:13 165.962 -50.268 20:13:10.2 +40:02:4 7.032 3.1829 21:17:07 +34:12:24 80.352 -10.407 0:37:19.8 1 -72:14:14 304.48 -4.8495 01:3:50.9 +30:39:36.8 13.6102 -31.306 05:38:5.6 -64:04:57 273.5745 -32.0834 05:38:41.8 -69:05:14 279.493 -31.6743 18:01:0 -25:47:26.4 4.436 -1.341 19:15:1.5 +10:56:4.7 45.3656 -0.2189 19:07:21.1 2 +09:18:41 2 43.0242 0.7359 0:42:52.6 +41:15:39.7 121.2019 -21.582 0:42:5 +41:16:02.6 121.2102 -21.5759 440 13:0:02.9 +12:40:56.9 31.304 75.4141 15:37:09 +1:5:48 19.842 48.34 17:48:02.2534 0.0165 -24:46:37.7 0.5 3.83604 1.6962 18:45:36 1 +0:50:0 120 3.08 1.679 20:19:31.96 +24:25:15.4 64.746 -6.6242 0:42:48.7 +35:3:12 120.9578 -27.2853 02:2:26.03 +47:29:19.3 138.4637 -12.6202 02:34:2.57 -43:47:46.9 258.4808 -63.4143 07:34:36.3 +31:52:28 187.457 2.4762 07:4:39.5 +03:3:01 215.8567 13.4539 13:34:43.1 -08:20:56 320.9108 53.054 16:34:20.40 +57:09:42.8 86.5649 40.9126 20:45:09.9 -31:20:04 12.628 -36.8024 23:09:56.5 +47:57:30.3 105.9015 -1.5289 19:39:38.82 -06:03:49.5 32.971 -13.4715 13:30:47 +24:13:58.8 17.024 80.678 07:20:47.2 -31:46:58 24.515 -8.2534 0:19:50 1 +21:56:54 13.304 -40.32 05:13:50.8 1 -69:51:47 280.7964 -3.681 05:43:34.2 1 -68:2:2 278.564 -31.3058 09:25:46.3 1 -47:58:17 271.356 1.85 16:01:41.01 +6:48:10.1 10.287 40.9712 10:45:03.59 -59:41:04.3 287.5969 -0.6296 06:54:13.04 -23:5:42.0 234.7568 -10.0832 20:20:46 +43:54:5 81.01 4.167 04:12:08.85 -10:28:10.0 203.502 -40.0405 09:43:45.47 +5:57:09.1 158.924 45.9024 10:01:40.43 +17:24:32.7 217.7973 49.7407 15:03:45.7 +47:39:0 80.367 57.0718 20:37:18.7 +75:35:4 109.2183 20.058 21:2:04.5 +17:08:2.1 67.8703 -2.657 12:14:23.6 +1:49:21.9 271.5406 72.3975 16:5:47.8 +35:10:56.9 57.86 37.9074 18:05:36.1 +69:45:16.9 10.052 29.2747 0:4:01.32 +09:32:57.8 19.873 -53.2783 01:03:53.5 -72:54:48 301.6568 -4.1841 01:3:3.8 +30:32:12.8 13.5673 -31.4634 05:35:16.47 -05:23:23.1 209.0108 -19.3841 05:37:36.7 -69:09:41.3 279.5492 -31.7617 17:50:25.12 +70:45:36.4 101.278 30.5094 20:04:18.46 -5:43:32.3 342.1629 -32.2416 0:51:49.2 -73:10:30 302.8935 -43.9532 0:52:1 -72:20:18 302.852 -4.79 0:42:35 -73:40:30 303.789 -43.439 0:49:43.8 -73:23:02 303.109 -43.7438 441 0:52:5 -72:3:0 302.76 -4.578 0:56:05 -72:2:01 302.437 -4.757 0:57:50 -72:07:57 302.238 -4.987 0:57:36 -72:19:35 302.273 -4.794 0:57:27 -73:25:31 302.39 -43.696 01:0:43.14 -72:1:3.8 301.9301 -4.9175 01:01:21 -72:1:18 301.862 -4.919 01:03:12.8 -72:08:59 301.6573 -4.9494 01:03:13 -72:41:39 301.706 -4.406 01:19:51 -73:1:49 30.094 -43.74 0:30:27.43 +04:51:39.7 13.1412 -57.613 02:05:37.92 +64:49:42.8 130.7192 3.0845 10:24:38.7 -07:19:19.0 251.7018 40.5159 1:19:14.30 -61:27:49.5 292.1513 -0.5369 1:24:39.1 -59:16:20 292.0383 1.7515 14:20:08.24 -60:48:16.4 313.5412 0.27 17:4:29.39 -1:34:54.6 14.7939 9.1798 18:0:59.8 -24:50:57 5.2613 -0.87 18:46:24.5 -02:58:28 29.716 -0.2382 18:56:10.89 +01:13:20.6 34.5606 -0.4978 2:29:05.28 +61:14:09.3 106.6475 2.9487 09:29:18 -31:23:06 260.1 14.209 17:51:13.49 0.75 -30:37:23.4 0.6 359.1819 -1.912 18:06:59.8 -29:24:30 1.9353 -4.2726 18:13:39.03 -3:46:2.3 358.7461 -7.585 01:1:08.4 -73:16:46 30.9714 -43.737 18:45:36.9 +0:51:45 3.0359 1.688 05:37:43.0 -70:34:15 281.1905 -31.5749 17:46:20.8 -29:03:28.6 359.9787 -0.191 17:47:02.6 -28:52:58.9 0.2073 -0.2385 05:01:46.8 +1:46:51 18.9139 -17.9413 18:45:34.8 -04:34:35 28.1919 -0.785 03:56:28 -36:41:42 238.65 -49.986 02:42:40.83 -0:0:48.4 171.6457 -51.6181 09:47:40.2 -30:56:54 262.7439 17.2343 12:35:37 -39:54:19 29.64 2.865 13:05:26.1 -49:28:15 305.2681 13.374 13:25:27.62 -43:01:08.8 309.5159 19.4173 23:18:23.5 -42:2:35 348.063 -65.6928 12:29:06 +02:03:09 289.94 64.36 17:4:42 -29:16:54 359.6 -0.09 17:50:45.2 -34:12:1.7 356.0475 -3.6518 01:53:04. +74:42:4 127.04 12.35 04:39:49.7 1 -68:09:02 1 279.8683 -37.0961 19:05:26.6 1 -01:42:03 1 3.0135 -3.8913 442 19:30:30.13 +18:52:14.1 54.0962 0.2652 0:23:50.351 0.03 -72:04:31.486 0.01 305.923459 -4.892185 0:24:13.876 0.03 -72:04:43.8323 0.009 305.80632 -4.89314 0:24:1.1013 0.06 -72:05:20.131 0.03 305.83479 -4.82814 0:24:03.8519 0.03 -72:04:42.79 0.01 305.898634 -4.891679 0:24:07.956 0.015 -72:04:39.683 0.07 305.8915 -4.893 0:24:06.6989 0.0105 -72:04:06.789 0.03 305.895649 -4.90216 0:24:07.932 0.015 -72:04:39.64 0.05 305.8915 -4.893 0:23:59.4040 0.015 -72:03:58.720 0.009 305.909184 -4.902916 0:24:03.70 0.03 -72:04:56.90 0.01 305.89795 -4.879 0:23:54.485 0.045 -72:05:30.72 0.01 305.91256 -4.87672 0:24:09.1835 0.0135 -72:04:28.875 0.07 305.8908 -4.896526 0:24:04.6492 0.075 -72:04:53.751 0.03 305.896564 -4.8825 0:24:16.48 0.015 -72:04:25.149 0.07 305.8705 -4.89894 0:24:03.9 0.6 -72:04:43.4 0.6 305.8985 -4.8915 0:24:08.541 0.03 -72:04:38.91 0.02 305.89047 -4.89365 0:24:09.8325 0.075 -72:03:59.67 0.03 305.890454 -4.904673 17:40:4.589 0.06 -53:40:40.9 0.1 38.16487 -1.9671 2:25:52.36 +65:35:3.8 108.6364 6.8454 20:43:43.6 +27:40:56 70.6123 -9.1512 06:30:49.53 -28:34:43.6 236.9523 -16.757 18:17:05.76 -36:18:05.5 356.806 -9.3743 0:59:21.05 -72:23:17.1 302.0896 -4.7272 0:47:23.7 -73:12:26.9 303.373 -43.9176 0:51:51.2 7 -73:10:32 7 302.8902 -43.9527 0:51:51.2 7 -73:10:32 7 302.8902 -43.9527 0:5:21.6 -72:42:0 302.5237 -4.4251 0:5:27.9 0.6 -72:10:58 0.6 302.4967 -4.9421 0:54:5.6 0.6 -72:45:10 0.6 302.5702 -4.373 0:53:23.8 0.6 -72:27:15 0.6 302.7243 -4.673 0:5:17.9 3 -72:38:53 3 302.5285 -4.472 0:53:26.4 -72:49:15.6 302.7253 -4.3064 18:4:50.59 -02:57:58.5 29.5405 0.132 18:59:06 +08:15:0 41.146 2.0625 04:20:02.36 -50:2:49.5 258.1362 -4.385 15:4:01 -56:45:54 324.9512 -1.4612 17:40:1.6 -28:47:48 359.4938 1.0839 16:05:18.6 +32:49:19.7 52.81 47.916 13:08:48.17 +21:27:07.5 38.7309 83.0823 08:06:2.8 -41:2:3 257.4258 -4.9849 443 Distance From Earth (kpc) Galactic Plane Z-Distance (pc) Proper Motion RA-direction (arcsec/yr) Proper Motion Dec-direction (arcsec/yr) Energy Range (keV) SOFT X-RAYS Flux (photons/cm 2 /s) Flux (erg/cm 2 /s) 2.0 0.5 - 2.4 9.6E-01 1.95E-09 0.25 0.1 - 2.4 8.36E-03 1.675E-1 0.16 0.1 - 2.4 2.05E-03 4.109E-12 1.82 0.5 - 2.4 1.73E-03 3.563E-12 4.30 0.5 - 2.4 4.27E-03 8.812E-12 2.50 0.5 - 2.4 1.78E-03 3.682E-12 2.98 0.5 - 2.4 1.9E-04 4.107E-13 2.0 0.5 - 2.4 9.02E-04 1.862E-12 4.12 0.5 - 2.4 5.85E-04 1.208E-12 3.94 0.5 - 2.4 2.9E-04 6.180E-13 0.17 0.5 - 2.4 1.40E-04 2.891E-13 0.18 0.1 - 2.4 9.32E-04 1.868E-12 5.50 0.5 - 2.4 2.3E-04 4.80E-13 0.28 0.1 - 2.4 6.90E-03 1.382E-1 47.3 0.5 - 2.4 2.69E-03 5.53E-12 0.25 0.1 - 2.4 1.49E-04 2.93E-13 1.53 0.5 - 2.4 1.47E-04 3.038E-13 0.26 -0.0209 0.02946 0.1 - 2.4 6.48E-05 1.29E-13 7.26 1.50 0.5 - 2.4 9.89E-04 2.041E-12 0.52 0.1 - 2.4 2.4E-05 4.898E-14 0.50 0.1 - 2.4 4.68E-03 9.389E-12 2.07 0.5 - 2.4 8.62E-05 1.79E-13 2.46 0.5 - 2.4 4.84E-05 1.00E-13 5.70 0.1 - 2.4 7.21E-05 1.46E-13 0.38 0.1 - 2.4 1.95E-05 3.912E-14 2.02 0.1 - 2.4 4.07E-05 8.153E-14 1.5 -1 0.1 - 2 2.86E-01 5.19E-10 10.6 93 0.1 - 2 2.29E-02 4.165E-1 10 3 0.1 - 2 4.59E-02 8.356E-1 14.5 7 32 0.1 - 2 3.28E-02 5.969E-1 8.5 10 0.1 - 2 5.78E-03 1.052E-1 6.2 -108 0.1 - 2 2.03E-02 3.695E-1 60 444 65 0.1 - 2.4 6.09E-04 1.2E-12 60 0.1 ? 2 1.4E-02 2.60E-1 0.15 - 2.4 5.43E-03 1.09E-1 0.2 - 2 7.18E-03 1.31E-1 0.2 - 2 2.393E-05 - 2.393E-04 4.356E-14 - 4.356E-13 60 0.2 - 2 1.19E-05 2.16E-14 3.5 0.1 - 2.4 2.77E-03 - 8.31E-03 5.56E-12 - 1.670E-1 445 50 0.1 - 2.4 1.60E-01 3.2E-10 0.1 - 2.4 2.78E-05 5.57E-14 0.1 - 2.4 8.3E-05 1.67E-13 0.1 - 2.4 1.1E-04 2.23E-13 2.6 0.05 - 2 8.24E-02 1.5E-10 0.1 - 2.4 1.39E-03 2.78E-12 0.1 - 2.4 1.75E-03 3.5E-12 0.2 - 4.5 3.856E-03 - 3.856E-02 1.03E-1 - 1.03E-10 8.5 0.1 - 2.4 2.28E-03 4.56E-12 446 1.5 0.2 - 2 1.52E-02 2.76E-1 5.3 2.4 0.1 - 2.4 1.50E-03 3E-12 20 8.5 447 2 0.1 - 2.4 3.60E-04 7.24E-13 3.7 2.5 2.5 0.1 - 2.4 2.43E-01 4.86E-10 448 4 0.3 - 3.2 4.570E-04 1.05E-12 449 8.5 450 0.9 - 4.0 2.49E-04 7.50E-13 0.9 - 4.0 3.732E-04 - 6.469E-02 1.125E-12 - 1.951E-10 0.9 - 4.0 4.976E-04 1.50E-12 0.9 - 4.0 4.976E-04 1.50E-12 0.9 - 4.0 4.976E-04 1.50E-12 0.9 - 4.0 4.976E-04 1.50E-12 0.9 - 4.0 4.976E-04 1.50E-12 451 3 0.1 - 2.4 1.5E-01 3.108E-10 4 0.5 - 2 1.546E-02 2.90E-1 7 0.1 - 2.4 3.47E-01 6.962E-10 7 0.05 - 2 7.09E-01 1.29E-09 9.4 0.5 - 4.5 1.85E-01 5.07E-10 1 452 0.3 -43 0.1 - 2.4 8.43E-03 1.69E-1 5.2 135 0.1 - 2.4 2.50E-03 5E-12 0.832 0.1 - 4 8.65E-05 2.2E-13 0.075 0.1 - 3.5 2.46E-03 5.9E-12 4.60 0.5 - 2.5 1.19E-03 2.5E-12 0.38 0.19 0.1 - 1.2 3.75E-04 5E-13 0.1 - 2.4 1.18E-03 2.36E-12 0.075 0.1 - 3.5 1.13E-03 2.7E-12 0.125 0.2 - 4 7.47E-04 1.9E-12 0.3 1.5 - 4 4.18E-04 1.6E-12 0.1 - 0.5 8.29E-03 6E-12 0.1 - 2.4 9.90E-04 1.985E-12 0.35 0.1 - 4 6.29E-05 1.6E-13 82 0.14 0.1 - 3.5 6.67E-03 1.6E-1 0.25 0.1 - 4 1.42E-04 3.6E-13 0.20 0.08 0.1 - 3.5 6.67E-04 1.6E-12 0.125 0.1 - 4 1.14E-03 2.9E-12 0.25 0.1 - 3.5 1.0E-02 2.4E-1 0.1 - 2.4 4.39E-03 8.8E-12 0.125 0.1 - 3.5 5.42E-03 1.3E-1 0.2 0.49 0.045 1.1 0.74 0.1 - 2.4 7.54E-04 1.512E-12 0.16 0.1 - 3.5 2.71E-03 6.5E-12 0.5 0.1 - 2.4 1.05E-03 2.103E-12 0.1 - 2.4 8.98E-03 1.8E-1 0.5 0.1 - 2.4 1.28E-03 2.56E-12 0.4 0.1 - 2.4 7.57E-04 1.518E-12 1.6 0.2 - 3.5 1.67E-02 4E-1 0.25 0.15 0.1 - 2.4 2.93E-03 5.873E-12 0.1 - 2.4 2.23E-04 4.459E-13 453 0.125 0.1 - 3.5 2.71E-02 6.5E-1 0.43 0.1 - 2.4 5.9E-05 1.2E-13 0.1 - 2.4 4.74E-03 9.5E-12 1.5 0.4 0.08 0.1 - 4 2.75E-03 7E-12 0.3 0.1 - 2.4 9.05E-04 1.813E-12 0.1 - 4 2.9E-04 7.6E-13 0.18 0.2 - 4.5 7.71E-04 2.06E-12 0.83 0.1 - 2.4 3.83E-04 7.68E-13 0.7 0.1 - 3.5 5.84E-04 1.4E-12 0.15 0.1 - 3.5 9.59E-04 2.3E-12 0.136 0.1 - 2.4 3.29E-03 6.586E-12 0.1 - 2.4 2.0E-05 4E-14 1.18 0.1 - 4 8.65E-05 2.2E-13 0.2 - 4.5 5.68E-05 1.518E-13 0.38 0.1 - 3.5 3.13E-03 7.5E-12 0.6 0.2 0.1 - 4 2.01E-03 5.1E-12 1.3 0.1 - 3.5 1.67E-04 4E-13 0.81 0.2 - 4 1.18E-04 3E-13 0.345 0.2 - 4 2.24E-04 5.7E-13 0.15 0.3 0.1 - 2.4 1.38E-03 2.763E-12 0.13 0.1 - 4 3.93E-03 1E-1 0.6 0.1 - 2.4 2.69E-03 5.394E-12 0.43 0.1 - 2.4 1.1E-04 2.23E-13 0.1 0.18 - 0.5 2.76E-02 2E-1 0.52 0.05 - 2 2.79E-03 5.071E-12 0.4 0.1 - 2.4 3.49E-05 7E-14 0.5 0.1 - 2.4 1.90E-03 3.812E-12 0.3 0.1 - 2.4 3.62E-03 7.261E-12 0.19 0.1 0.1 - 2.4 9.35E-04 1.873E-12 0.14 0.5 - 4.5 6.56E-03 1.8E-1 0.1 - 2.4 1.63E-03 3.263E-12 0.1 - 2.4 2.98E-03 5.978E-12 0.1 - 2.4 5.71E-03 1.145E-1 0.1 - 4 1.57E-04 4E-13 0.1 - 0.5 4.84E-04 3.5E-13 454 0.1 - 2.4 5.53E-03 1.109E-1 0.3 0.1 - 4 2.83E-04 7.2E-13 0.216 0.05 - 2 5.41E-02 9.854E-1 0.08 0.2 - 4.5 3.54E-01 9.458E-10 0.38 0.1 - 2.4 7.3E-04 1.47E-12 0.1 - 2.4 1.6E-02 3.35E-1 0.705 630 0.1 - 2.4 9.28E-03 1.859E-1 0.086 0.1 - 4 1.57E-03 4E-12 0.142 0.25 0.1 - 2.4 6.49E-03 1.3E-1 0.1 - 2.4 1.25E-02 2.509E-1 0.1 0.1 - 0.28 7.12E-01 3.1E-10 0.1 - 2.4 4.67E-03 9.357E-12 0.3 0.1 - 2.4 3.34E-04 6.7E-13 0.4 0.215 0.1 - 2.5 4.89E-03 1E-1 0.4 0.1 - 2.4 2.76E-04 5.535E-13 0.19 0.1 - 2.4 1.65E-03 3.29E-12 0.25 0.1 - 2.4 2.57E-04 5.14E-13 1.2 0.2 - 4 1.97E-04 5E-13 0.25 0.1 - 2.4 1.90E-03 3.804E-12 2.5 0.2 - 4.5 4.61E-05 1.232E-13 0.12 0.1 - 3.5 7.51E-04 1.8E-12 0.1 0.1 - 3.5 5.84E-04 1.4E-12 0.13 0.1 - 3.5 5.0E-04 1.2E-12 0.14 0.1 - 3.5 5.25E-03 1.26E-1 0.075 0.1 - 3.5 2.75E-03 6.6E-12 0.1 - 2.4 9.24E-04 1.851E-12 0.95 0.1 - 2.4 1.58E-03 3.173E-12 0.1 0.1 - 2.4 2.82E-03 5.646E-12 0.3 0.1 - 3.5 1.67E-03 4E-12 0.2 0.1 - 4 1.06E-03 2.7E-12 0.14 0.1 - 3.5 6.67E-04 1.6E-12 0.13 0.1 - 3.5 2.92E-03 7E-12 0.2 0.1 - 3.5 2.67E-03 6.4E-12 0.08 0.1 - 3.5 4.63E-03 1.1E-1 0.1 - 2.4 2.15E-04 4.29E-13 0.1 - 2.4 3.30E-04 6.623E-13 1 0.1 - 4 4.3E-05 1.1E-13 0.1 - 2.4 7.10E-04 1.423E-12 455 0.1 - 2.4 1.5E-05 3.1E-14 0.63 0.1 - 4 9.4E-05 2.4E-13 2.8 2 - 2.4 2.0E-02 7E-1 2.3 0.1 - 2.4 9.98E-05 2E-13 0.1 - 2.4 4.40E-04 8.818E-13 50 0.2 - 4.5 1.0E+0 2.67E-09 5 0.7143 0.1 - 2.4 2.35E-05 4.7E-14 0.2083 0.1 - 2.4 1.79E-03 3.5814E-12 0.4167 0.1 - 2.4 3.75E-05 7.52E-14 0.273 0.1 - 2.4 6.10E-05 1.22E-13 0.0781 0.1 - 2.4 7.8E-03 1.5792E-1 0.0278 0.1 - 2.4 3.9E-02 7.9E-1 0.11 0.1 - 2.4 1.41E-05 2.82E-14 0.4348 0.1 - 2.4 1.41E-04 2.82E-13 0.1351 0.1 - 2.4 2.81E-05 5.64E-14 0.348 0.1 - 2.4 6.10E-05 1.22E-13 0.4762 0.1 - 2.4 1.08E-04 2.162E-13 0.2564 0.1 - 2.4 4.41E-04 8.836E-13 0.1852 0.1 - 2.4 7.97E-05 1.598E-13 0.55 0.1 - 2.4 1.08E-04 2.162E-13 0.3 - 3.5 5.30E-05 1.271E-13 0.5 0.1 - 2.4 1.08E-04 2.162E-13 0.083 0.1 - 2.4 2.98E-03 5.9784E-12 0.5 0.1 - 2.4 2.7E-04 5.546E-13 0.25 0.1 - 2.4 5.30E-04 1.062E-12 0.0263 0.1 - 2.4 2.35E-04 4.7E-13 0.167 0.1 - 2.4 8.21E-04 1.645E-12 0.0741 0.1 - 2.4 1.87E-03 3.7506E-12 0.2381 0.1 - 2.4 5.68E-04 1.1374E-12 0.5802 0.1 - 2.4 7.50E-05 1.504E-13 0.2632 0.1 - 2.4 1.08E-04 2.162E-13 1 0.1 - 2.4 2.81E-05 5.64E-14 0.348 0.1 - 2.4 9.38E-05 1.8E-13 0.3125 0.1 - 2.4 3.28E-05 6.58E-14 0.4348 0.1 - 2.4 6.24E-04 1.2502E-12 0.2 0.1 - 2.4 7.97E-05 1.598E-13 10 0.031 0.1 - 2.4 9.76E-03 1.952E-1 0.054 0.1 - 2.4 4.74E-03 9.494E-12 0.125 0.1 - 2.4 4.46E-03 8.93E-12 0.06 0.1 - 2.4 7.04E-03 1.41E-1 456 0.017 0.1 - 2.4 2.04E-02 4.089E-1 0.075 0.1 - 2.4 4.64E-03 9.306E-12 0.13 0.1 - 2.4 3.47E-03 6.956E-12 0.42 0.2 - 4.5 2.81E-04 7.5E-13 0.05 0.1 - 2.4 3.08E-02 6.1758E-1 0.048 0.1 - 2.4 1.45E-03 2.914E-12 0.036 0.1 - 2.4 1.14E-01 2.2804E-10 0.05 0.1 - 2.4 2.02E-02 4.042E-1 0.143 0.1 - 2.4 7.50E-04 1.504E-12 0.18 0.1 - 2.4 2.3E-03 4.68E-12 0.0545 0.3 - 3.5 2.80E-04 6.721E-13 0.013 0.1 - 2.4 1.18E-01 2.368E-10 0.02 0.1 - 3.5 8.34E-03 2E-1 0.2 0.1 - 2.4 1.8E-04 3.76E-13 0.074 0.1 - 2.4 1.92E-03 3.854E-12 0.38 0.1 - 2.4 6.57E-04 1.316E-12 0.25 0.1 - 2.4 3.28E-04 6.58E-13 0.525 0.1 - 2.4 5.63E-04 1.128E-12 0.038 0.1 - 2.4 6.57E-03 1.316E-1 0.3 0.1 - 2.4 7.97E-04 1.598E-12 0.395 0.1 - 2.4 4.69E-04 9.4E-13 0.05 0.1 - 2.4 8.96E-03 1.7954E-1 0.16 0.1 - 2.4 4.69E-05 9.4E-14 0.1 0.1 - 2.4 1.41E-03 2.82E-12 0.034 0.1 - 2.4 3.0E-04 6.016E-13 0.1 0.3 - 3.5 3.67E-04 8.8E-13 0.165 0.1 - 2.4 1.04E-03 2.089E-12 0.15 0.15 - 2.8 1.65E-01 3.56E-10 0.036 0.1 - 2.4 5.49E-03 1.098E-1 0.13 0.1 - 2.4 7.93E-03 1.586E-1 0.086 0.1 - 2.4 3.80E-03 7.614E-12 0.05 0.1 - 2.4 1.13E-03 2.256E-12 0.35 0.1 - 2.4 8.91E-04 1.786E-12 0.18 0.1 - 2.4 3.75E-03 7.52E-12 0.3 0.1 - 2.4 3.28E-04 6.58E-13 0.053 0.1 - 2.4 1.27E-02 2.5474E-1 0.27 0.1 - 2.4 6.58E-04 1.31816E-12 0.2 0.1 - 2.4 2.81E-04 5.64E-13 0.021 0.1 - 2.4 4.85E-02 9.7196E-1 0.18 0.1 - 2.4 2.67E-03 5.358E-12 0.071 0.1 - 2.4 6.80E-03 1.363E-1 0.31 0.1 - 2.4 1.60E-03 3.196E-12 0.039 0.1 - 2.4 2.62E-02 5.2546E-1 0.4 0.1 - 2.4 8.91E-04 1.786E-12 0.1 0.1 - 2.4 1.74E-03 3.478E-12 457 0.19 0.1 - 2.4 6.57E-04 1.316E-12 0.0417 0.1 - 2.4 8.86E-03 1.76E-1 0.285 0.1 - 2.4 7.04E-04 1.41E-12 0.315 0.1 - 2.4 7.50E-04 1.504E-12 0.1 - 2.4 6.31E-04 1.265E-12 0.302 0.1 - 2.4 7.04E-04 1.41E-12 0.39 0.1 - 2.4 3.28E-04 6.58E-13 0.063 0.1 - 2.4 5.16E-04 1.034E-12 0.046 0.1 - 2.4 1.36E-02 2.716E-1 0.029 0.1 - 2.4 4.08E-03 8.178E-12 0.25 0.1 - 2.4 1.67E-03 3.3424E-12 0.3 0.1 - 2.4 1.59E-03 3.172E-12 0.205 0.1 - 2.4 6.57E-04 1.316E-12 0.047 0.1 - 2.4 3.62E-02 7.2568E-1 0.095 0.1 - 2.4 9.38E-04 1.8E-12 0.125 0.1 - 2.4 1.14E-02 2.2936E-1 0.025 0.1 - 2.4 1.64E-03 3.29E-12 0.175 0.1 - 2.4 4.64E-03 9.306E-12 0.029 0.1 - 2.4 5.4E-02 1.09E-10 50 1.95 0.5 - 3 1.74E-04 4E-13 3 0.1 - 2.4 6.57E-04 1.316E-12 2.12 -0.13 0.1 - 2.4 1.5E-05 3.1E-14 6.56 0.1 - 2.4 2.39E-04 5.10E-13 7.0 4.5 0.6 - 2 3.61E-04 7E-13 1.8 0.1 - 2.4 4.9E-06 1E-14 2.9 1.27 0.1 - 2.4 2.74E-05 5.5E-14 3.28 0.01 0.1 - 2.4 1.15E-05 2.3E-14 7.8 4.07 0.04 0.1 - 2.4 1.32E-04 2.64E-13 3.6 -0.128 -0.486 0.1 - 2.4 4.9E-07 1E-15 0.78 0.1 - 2.4 2.9E-06 6E-15 0.2 - 4 5.90E-03 1.5E-1 0.1 - 2.4 1.82E-02 3.639E-1 0.165 0.1 - 2.4 7.03E-04 1.409E-12 0.3 - 3.5 4.84E-04 1.16E-12 0.059 0.13 0.1 - 2.4 2.14E-03 4.289E-12 458 0.09 0.1 - 2.4 7.40E-04 1.484E-12 0.4 0.18 - 2.5 5.08E-03 1.04E-1 0.3 - 3.5 1.51E-04 3.62E-13 0.3 - 3.5 1.51E-04 3.62E-13 0.08 0.1 - 2.4 1.1E-02 2.23E-1 0.15 0.18 - 2.5 1.47E-02 3E-1 0.15 0.1 - 2.4 7.30E-03 1.463E-1 0.03 0.4 - 2.8 2.1E-02 4.6E-1 0.026 0.1 - 2.4 4.90E-02 9.82E-1 0.1 - 2.4 7.50E-04 1.503E-12 0.2 - 4.5 2.69E-04 7.18E-13 0.2 - 4.5 1.15E-04 3.07E-13 0.14 0.2 - 4.5 4.48E-04 1.197E-12 0.2 - 4.5 4.30E-03 1.149E-1 0.2 - 4.5 1.79E-04 4.787E-13 0.2 - 4.5 1.15E-04 3.07E-13 0.2 - 4.5 3.20E-04 8.548E-13 0.2 - 4.5 6.6E-04 1.78E-12 0.2 - 4.5 2.18E-04 5.812E-13 0.2 - 4.5 1.6E-04 4.45E-13 0.2 - 4.5 4.61E-04 1.231E-12 0.2 - 4.5 5.63E-04 1.504E-12 0.2 - 4.5 4.86E-04 1.29E-12 0.2 - 4.5 4.86E-04 1.29E-12 0.2 - 4.5 3.3E-04 8.89E-13 0.2 - 4.5 2.94E-04 7.864E-13 0.2 - 4.5 2.43E-04 6.496E-13 0.2 - 4.5 1.28E-04 3.419E-13 0.2 - 4.5 7.17E-04 1.915E-12 0.2 - 4.5 3.3E-04 8.89E-13 0.2 - 4.5 1.41E-04 3.761E-13 0.2 - 4.5 1.02E-04 2.735E-13 0.1 - 2.4 1.69E-03 3.394E-12 0.09 0.1 - 2.4 3.69E-03 7.402E-12 0.1 - 2.4 1.82E-03 3.64E-12 68 0.1 - 2.4 1.36E-03 2.726E-12 0.1 - 2.4 5.74E-03 1.15E-1 50 0.1 - 2.4 5.94E-02 1.19E-10 0.2 - 4.5 1.17E-01 3.18E-10 10 12.5 12 0.1 - 2.4 3.49E-04 7E-13 0.2 - 4 2.36E-05 5.94E-14 0.2 - 4 1.32E-04 3.351E-13 459 0.62 0.1 - 2.4 5.49E-06 1.1E-14 0.68 0.1 - 2.4 8.8E-06 1.78E-14 0.1 - 2.4 2.02E-03 4.047E-12 5 0.91 0.1 - 2.4 8.93E-06 1.79E-14 0.0213 0.05 - 2 1.43E-02 2.612E-1 0.03 0.1 - 2.4 1.10E-03 2.21E-12 0.014 0.05 - 2 1.6E-01 3.014E-10 0.0147 0.04 - 2 1.03E-02 1.87E-1 0.06 0.15 - 4 3.74E-03 9.5E-12 0.0164 0.05 - 2 5.35E-04 9.73E-13 0.0147 0.05 - 2 1.39E-03 2.53E-12 0.08 0.05 - 2 5.94E-02 1.081E-10 0.0194 0.1 - 2.4 9.62E-03 1.928E-1 0.1 - 2.4 1.82E-03 3.647E-12 0.1 - 2.4 8.97E-04 1.797E-12 0.136 0.1 - 2.4 1.06E-03 2.123E-12 2.38 0.1 - 2.4 9.38E-03 1.8E-1 5 5 2 0.1 - 2.4 3.9E-03 8E-12 0.1 - 2.4 5.25E-03 1.052E-1 2.6 0.1 - 2.4 4.01E-04 8.038E-13 1.34 0.05 0.1 - 4 5.67E-04 1.4E-12 0.56 0.1 - 4 1.4E-03 3.67E-12 0.052 0.1 - 4 1.04E-03 2.64E-12 0.013 0.1 - 4 1.2E-03 3.09E-12 0.0238 0.1 - 4 3.78E-03 9.6E-12 0.4127 0.3 - 3.5 7.17E-05 1.72E-13 0.3 - 3.5 3.45E-04 8.28E-13 0.3 - 3.5 7.38E-05 1.7E-13 0.3 - 3.5 5.75E-05 1.38E-13 0.05 0.4 - 2.4 9.39E-04 1.894E-12 50 0.1 - 2.4 3.10E-04 6.21E-13 0.4 0.1 - 2.4 1.19E-02 2.39E-1 47.3 0.1 - 2 3.30E-04 6E-13 0.1 - 2.4 7.72E-04 1.547E-12 60 460 60 60 57 60 0.23 0.1 - 2.4 9.98E-05 2.0E-13 2.6 0.8 - 10 4.61E-03 2.0E-1 0.35 0.1 - 2.4 1.09E-05 1.12E-14 5 0.7 - 5.0 4.31E-05 2.0E-13 4.8 2 - 8 1.59E-03 9.49E-12 2 0.357 0.1 - 2.4 1.06E-05 9.23E-15 5 19 3.2 3 6 120 8 8 8 0.1 - 2.4 0.023 4.61E-1 0.1 - 2.4 0.023 4.61E-12 461 5 4.5 0.078 -0.032 0.5 - 2.5 9.92E-08 1.64E-16 4.5 0.07 -0.026 0.5 - 2.5 4.97E-07 8.23E-16 4.5 0.091 -0.039 0.5 - 2.5 9.92E-07 1.64E-15 4.5 0.06 -0.037 0.5 - 2.5 7.8E-07 1.30E-15 4.5 0.5 - 2.5 3.14E-07 5.19E-16 4.5 0.5 - 2.5 3.14E-07 5.19E-16 4.5 0.5 - 2.5 3.95E-07 6.54E-16 4.5 0.046 -0.037 0.5 - 2.5 4.97E-07 8.23E-16 4.5 0.5 - 2.5 6.26E-07 1.04E-15 4.5 0.5 - 2.5 3.14E-07 5.19E-16 4.5 0.5 - 2.5 3.95E-07 6.54E-16 4.5 0.5 - 2.5 9.92E-07 1.64E-15 4.5 0.5 - 2.5 3.14E-07 5.19E-16 4.5 0.5 - 2.5 3.95E-07 6.54E-16 4.5 0.5 - 2.5 2.49E-07 4.13E-16 4.5 0.5 - 2.5 4.97E-07 8.23E-16 2.2 -0.45 0.5 - 2.5 6.92E-06 1.37E-14 60 60 60 60 60 60 60 60 60 63 15 3.9 0.1 ? 2.4 2.6E-03 6.90E-13 8.5 1 0.1 ? 2.4 1.06E-02 9.0E-12 0.1 ? 2.4 3.51E-03 2.90E-12 0.1 ? 2.4 2.79E-03 2.90E-12 462 ENERGY Energy Range (keV) HARD X-RAYS Flux (photons/cm 2 /s) Flux (erg/cm 2 /s) Neutral Hydrogen Column Density - N H (1/cm 2 ) Photon Index (Power Law Model) - ? or ? Pulsed Fraction 2 - 10 1.54E+0 9.93E-09 3.0E+21 0.700 2 - 10 1.59E-03 1.03E-1 4.0E+20 0.100 2 - 10 1.23E-05 7.94E-14 1.30E+20 0.313 2 - 10 1.59E-04 1.03E-12 3.45E+21 2 - 10 1.62E-02 1.05E-10 1.27E+2 0.64565 2 - 10 3.15E-04 2.04E-12 3.40E+21 2 - 10 3.86E-05 2.50E-13 4.0E+21 3.60E+21 2 - 10 2.63E-03 1.70E-1 4.0E+2 2 - 10 2.75E-05 1.78E-13 1.30E+2 0.2 ? 10 1.14E-04 4.07E-13 1.0E+20 0.31623 2 - 10 6.65E-05 4.30E-13 8.0E+20 2.35 0.27542 2 - 10 1.93E-04 1.25E-12 2.90E+21 0.9800 2 - 10 3.17E-05 2.05E-13 1.70E+20 0.14791 2 - 10 5.15E-03 3.3E-1 4.60E+21 1.92 0.6700 2 - 10 1.28E-05 8.26E-14 3.50E+20 0.28184 4.50E+21 0.600 0.2 ? 10 4.81E-05 1.10E-13 2.90E+20 1.75 0.6800 2 - 10 1.24E-07 8.0E-16 6.0E+20 2 - 10 1.93E-06 1.25E-14 6.0E+19 0.75? 2 - 10 1.64E-06 1.06E-14 2.60E+20 0.14125 2 - 10 1.79E-05 1.16E-13 2.0E+20 2 - 10 6.26E-06 4.05E-14 2.0E+21 2 - 10 6.65E-05 4.30E-13 2.0E+21 0.61 0.7300 2 - 10 9.27E-07 6.0E-15 4.0E+20 1.50 2 - 10 6.63E-06 4.29E-14 4.40E+21 0.700 0.5 - 10 1.63E-03 5.97E-12 2 - 10 5.984E-04 3.872E-12 2 - 10 1.197E-04 7.74E-13 463 2 - 10 1.496E-03 - 2.693E-02 9.680E-12 - 1.742E-10 2 - 10 <2.92E-03 - 1.496E-02 <1.936E-1 - 9.680E-1 0.7 - 10 9.242E-04 3.60E-12 2 - 10 7.780E-03 5.034E-1 2 - 10 2.92E-05 - 2.693E-02 1.936E-13 - 1.742E-10 2 - 10 2 - 10 7.181E-05 - 1.406E-02 4.646E-13 - 9.09E-1 0.27 2 - 10 <2.92E-03 - 2.095E-02 <1.936E-1 - 1.35E-10 2 - 10 1.496E-02 - 3.291E-02 9.680E-1 - 2.130E-10 2 - 10 4.189E-03 2.710E-1 2 - 10 1.137E-02 7.357E-1 2 - 10 2.92E-03 1.936E-1 0.7 - 10 5.76E-04 2.25E-12 2 - 10 2.92E-04 1.936E-12 2 - 10 6.82E-03 4.453E-1 2 - 10 2.92E-04 1.936E-12 2 - 10 4.48E-02 2.904E-10 2 - 10 1.197E-02 7.74E-1 2 - 10 <5.984E-03 - 1.047E+0 <3.872E-1 - 6.76E-09 2 - 10 1.496E-03 - 1.706E-01 9.680E-12 - 1.104E-09 2 - 10 2.92E-02 1.936E-10 0.2 - 5 8.36E-04 2.32E-12 2 - 10 <1.496E-03 - 3.740E+0 <9.680E-12 - 2.420E-08 2 - 10 <2.693E-02 - 1.107E-01 <1.742E-10 - 7.163E-10 2 - 10 5.984E+0 3.872E-08 2 - 10 2.92E-03 1.936E-1 2 - 10 1.706E-02 1.104E-10 2 - 10 2.095E-04 1.35E-12 464 2 - 10 2.92E-03 1.936E-1 2 - 10 5.087E-04 3.291E-12 2 - 10 2.92E-03 1.936E-1 2 - 10 <8.97E-03 - 1.795E-01 <5.808E-1 - 1.162E-09 0.05 2 - 10 <2.92E-05 - 5.386E-01 <1.936E-13 - 3.485E-09 2 - 10 <8.97E-03 - 8.378E+0 <5.808E-1 - 5.421E-08 2 - 10 <5.087E-03 - 1.317E-01 <3.291E-1 - 8.518E-10 2 - 10 8.97E-03 - 7.480E-02 5.808E-1 - 4.840E-10 2 - 10 5.386E-03 3.485E-1 2 - 10 4.189E-04 - 1.07E-03 2.710E-12 - 6.970E-12 2 - 10 3.291E-03 2.130E-1 2 - 10 1.646E-03 1.065E-1 2 - 10 8.97E-05 5.808E-13 2 - 10 3.591E-03 - 1.406E-02 2.323E-1 - 9.09E-1 2 - 10 2.095E-03 1.35E-1 2 - 10 2.095E-03 1.35E-1 2 - 10 1.795E-03 1.162E-1 2 - 10 8.97E-02 - 8.97E-01 5.808E-10 - 5.808E-09 2 - 10 5.984E-03 - 3.291E+0 3.872E-1 - 2.130E-08 2 - 10 3.591E+0 2.323E-08 2 - 10 9.874E-03 6.389E-1 2 - 10 5.087E-04 3.291E-12 2 - 10 <2.92E-04 - 2.92E-03 <1.936E-12 - 1.936E-1 2 - 10 2.92E-04 - 2.095E-01 1.936E-12 - 1.35E-09 2 - 10 2.92E-02 - 9.36E-01 1.936E-10 - 6.040E-09 465 2 - 10 1.197E-02 - 2.92E+0 7.74E-1 - 1.936E-08 0.64 2 - 10 1.197E-02 - 1.197E-01 7.74E-1 - 7.74E-10 2 - 10 2.693E-02 - 2.92E+0 1.742E-10 - 1.936E-08 2 - 10 8.97E-03 - 4.787E-02 5.808E-1 - 3.098E-10 2 - 10 <7.181E-02 - 2.92E-01 <4.646E-10 - 1.936E-09 2 - 10 <7.181E-02 - 8.97E-01 <4.646E-10 - 5.808E-09 2 - 10 6.583E-03 4.259E-1 2 - 10 1.795E-03 1.162E-1 2 - 10 2.394E-03 1.549E-1 2 - 10 8.97E-04 - 5.984E-01 5.808E-12 - 3.872E-09 2 - 10 1.197E-03 7.74E-12 2 - 10 5.984E-03 - 1.287E-01 3.872E-1 - 8.325E-10 2 - 10 1.197E-04 7.74E-13 2 - 10 <8.97E-03 - 8.97E-02 <5.808E-1 - 5.808E-10 2 - 10 8.079E-02 5.27E-10 2 - 10 5.087E-03 3.291E-1 2 - 10 1.197E-02 - 1.257E-01 7.74E-1 - 8.131E-10 2 - 10 <3.291E-02 - 3.291E-01 <2.130E-10 - 2.130E-09 2 - 10 1.197E-03 7.74E-12 2 - 10 5.984E-04 - 1.496E-02 3.872E-12 - 9.680E-1 2 - 10 8.65E-01 7.57E-09 2 - 10 5.984E-03 3.872E-1 2 - 10 1.795E-04 1.162E-12 2 - 10 4.069E-03 2.63E-1 2 - 10 8.079E-02 5.27E-10 2 - 10 <5.984E-03 - 2.92E-01 <3.872E-1 - 1.936E-09 2 - 10 2.92E-03 1.936E-1 2 - 10 8.97E-04 5.808E-12 2 - 10 4.787E-03 - 5.984E-01 3.098E-1 - 3.872E-09 2 - 10 2.92E-03 1.936E-1 2 - 10 7.480E-03 4.840E-1 2 - 10 1.197E-03 - 9.874E-02 7.74E-12 - 6.389E-10 2 - 10 2.92E-03 1.936E-1 466 2 - 10 2.92E-03 - 1.317E-01 1.936E-1 - 8.518E-10 0.7 - 10 2.59E-01 1.01E-09 2 - 10 5.984E-03 3.872E-1 2 - 10 1.795E-02 1.162E-10 2 - 10 7.480E-02 4.840E-10 2 - 10 <5.984E-03 - 2.603E-01 <3.872E-1 - 1.684E-09 2 - 10 2.095E-03 1.35E-1 2 - 10 1.197E-02 - 8.29E-01 7.74E-1 - 5.324E-09 2 - 10 5.984E-03 - 2.92E-02 3.872E-1 - 1.936E-10 2 - 10 2.095E-03 1.35E-1 2 - 60 <1.268E-02 - 3.170E-01 <1.404E-10 - 3.509E-09 2 - 10 <2.92E-02 - 2.513E-01 <1.936E-10 - 1.626E-09 20 - 75 6.26E-02 - 1.230E-01 3.594E-09 - 7.054E-09 2 - 10 <4.48E-03 - 2.394E-01 <2.904E-1 - 1.549E-09 2 - 10 7.032E-01 - 3.950E+0 4.50E-09 - 2.56E-08 2 - 10 <1.496E-03 - 4.189E+0 <9.680E-12 - 2.710E-08 2 - 10 2.693E-01 - 1.287E+0 1.742E-09 - 8.325E-09 2 - 10 1.197E-04 7.74E-13 2 - 10 9.575E-01 6.195E-09 2 - 10 5.984E-02 3.872E-10 2 - 10 <1.795E-02 - 2.92E-01 <1.162E-10 - 1.936E-09 2 - 10 2.095E-03 1.35E-1 2 - 10 1.795E-03 - 1.646E-02 1.162E-1 - 1.065E-10 2 - 10 1.496E-03 9.680E-12 2 - 10 4.787E-02 3.098E-10 2 - 10 1.496E-03 - 1.646E-01 9.680E-12 - 1.065E-09 20 - 30 2.246E+01 2.03E-06 2 - 10 8.97E-03 - 1.795E-02 5.808E-1 - 1.162E-10 2 - 10 2.693E-02 - 1.317E-01 1.742E-10 - 8.518E-10 2 - 10 1.496E-03 9.680E-12 2 - 10 1.496E-01 9.680E-10 2 - 10 5.984E-05 - 1.496E+02 3.872E-13 - 9.680E-07 467 2 - 10 5.984E-02 - 2.394E-01 3.872E-10 - 1.549E-09 2 - 10 2.92E-04 - 1.795E-01 1.936E-12 - 1.162E-09 2 - 10 <1.795E-02 <1.162E-10 2 - 10 2.92E-03 - 1.646E-01 1.936E-1 - 1.065E-09 2 - 10 2.92E-02 1.936E-10 2 - 10 8.97E-03 5.808E-1 1 - 10 3.940E+0 1.74E-08 2 - 12 1.40E-01 9.68E-10 2 - 10 <1.197E-02 - 8.97E+0 <7.74E-1 - 5.808E-08 2 - 10 7.48E-02 4.840E-10 2 - 10 2.095E-02 1.35E-10 2 - 10 1.496E-02 - 3.591E-01 9.680E-1 - 2.323E-09 2 - 10 2.92E-04 - 5.984E+01 1.936E-12 - 3.872E-07 2 - 10 1.496E-02 - 8.97E+0 9.680E-1 - 5.808E-08 2 - 10 <1.496E-02 - 2.843E+0 <9.680E-1 - 1.839E-08 2 - 10 <2.92E-03 - 4.48E+01 <1.936E-1 - 2.904E-07 2 - 10 1.047E-01 6.76E-10 2 - 10 1.795E+0 - 2.095E+01 1.162E-08 - 1.35E-07 2 - 10 4.787E-02 3.098E-10 2 - 10 4.787E-01 3.098E-09 2 - 10 <2.92E-03 - 2.92E-01 <1.936E-1 - 1.936E-09 2 - 10 4.189E+01 2.710E-07 2 - 10 1.646E-01 1.065E-09 2 - 10 7.480E-02 4.840E-10 2 - 10 <5.984E-03 - 4.189E+0 <3.872E-1 - 2.710E-08 2 - 10 3.890E-02 2.517E-10 2 - 10 6.583E-01 4.259E-09 2 - 10 1.496E+0 9.680E-09 2 - 12 5.61E+0 3.87E-08 2 - 10 4.48E-02 - 1.496E-01 2.904E-10 - 9.680E-10 2 - 10 <1.496E-02 - 2.394E-01 <9.680E-1 - 1.549E-09 2 - 10 4.48E-03 - 2.693E+0 2.904E-1 - 1.742E-08 468 2 - 10 2.469E+0 1.597E-08 2 - 10 1.346E-01 8.712E-10 2 - 10 <1.496E-03 - 3.291E-02 <9.680E-12 - 2.130E-10 2 - 10 <5.984E-03 - 1.07E+01 <3.872E-1 - 6.970E-08 2 - 10 2.92E-02 - 8.378E-01 1.936E-10 - 5.421E-09 2 - 10 9.575E-02 6.195E-10 2 - 10 4.48E-01 2.904E-09 2 - 10 5.984E-03 3.872E-1 2 - 10 4.787E-02 - 3.890E-01 3.098E-10 - 2.517E-09 2 - 9 9.26E-02 5.760E-10 2 - 10 8.378E-02 5.421E-10 20 - 10 4.51E+0 2.90E-07 2 - 10 4.189E+0 2.710E-08 2 - 10 2.095E-01 1.35E-09 2 - 10 9.575E-02 6.195E-10 2 - 10 4.48E-02 2.904E-10 2 - 10 4.48E-01 2.904E-09 2 - 10 8.97E-01 5.808E-09 2 - 10 2.92E-01 1.936E-09 2 - 10 2.693E+0 1.742E-08 2 - 10 <2.92E-04 - 5.984E-01 <1.936E-12 - 3.872E-09 2 - 10 <2.92E-02 - 3.890E-01 <1.936E-10 - 2.517E-09 2 - 10 <2.92E-02 - 3.291E-01 <1.936E-10 - 2.130E-09 2 - 10 2.92E-02 1.936E-10 2 - 10 <1.496E-02 - 1.496E-01 <9.680E-1 - 9.680E-10 2 - 10 1.017E-02 6.582E-1 2 - 10 2.92E-02 1.936E-10 2 - 10 4.787E-01 3.098E-09 2 - 10 <1.197E-03 - 1.691E+0 <7.74E-12 - 1.094E-08 2 - 10 5.984E-03 3.872E-1 2 - 10 7.780E-02 5.034E-10 2 - 10 8.97E-03 5.808E-1 2 - 60 1.09E+01 1.21E-07 2 - 10 2.693E-02 1.742E-10 2 - 10 8.97E-02 5.808E-10 2 - 10 1.197E-02 - 8.97E-02 7.74E-1 - 5.808E-10 469 2 - 10 <4.48E-03 - 8.97E-01 <2.904E-1 - 5.808E-09 2 - 10 <1.496E-02 - 7.780E-02 <9.680E-1 - 5.034E-10 2 - 10 <5.984E-03 - 2.304E+0 <3.872E-1 - 1.491E-08 2 - 10 2.095E-02 1.35E-10 2 - 10 <5.984E-03 - 8.97E-03 <3.872E-1 - 5.808E-1 2 - 10 1.346E-01 8.712E-10 2 - 10 <2.693E-02 - 5.984E+0 <1.742E-10 - 3.872E-08 2 - 10 2.92E-03 - 1.496E-02 1.936E-1 - 9.680E-1 2 - 10 1.795E-01 - 5.386E-01 1.162E-09 - 3.485E-09 2 - 10 1.496E-03 - 3.591E-02 9.680E-12 - 2.323E-10 2 - 10 <2.92E-03 - 1.197E-01 <1.936E-1 - 7.74E-10 2 - 10 1.795E-02 1.162E-10 8 - 20 6.95E+0 1.365E-07 2 - 10 1.197E-02 7.74E-1 2 - 10 1.197E+0 7.74E-09 2 - 10 <7.480E-02 - 8.29E-01 <4.840E-10 - 5.324E-09 3 - 10 8.215E-04 - 4.107E-03 6.76E-12 - 3.38E-1 2 - 10 2.92E-04 - 3.291E-01 1.936E-12 - 2.130E-09 2 - 10 2.92E-04 - 5.386E-01 1.936E-12 - 3.485E-09 2 - 10 8.079E-02 5.27E-10 2 - 10 2.92E-04 1.936E-12 2 - 10 9.575E-02 6.195E-10 2 - 10 2.095E-01 1.35E-09 2 - 10 4.48E-03 - 5.984E-02 2.904E-1 - 3.872E-10 2 - 10 1.915E+0 1.239E-08 2 - 10 8.97E-02 5.808E-10 470 2 - 10 1.795E-01 1.162E-09 2 - 10 3.890E-01 2.517E-09 2 - 26 4.85E+0 4.30E-08 2 - 10 2.92E-01 1.936E-09 2 - 12 6.31E-01 4.36E-09 2 - 10 3.740E+0 2.420E-08 2 - 10 5.984E-02 3.872E-10 2 - 10 2.095E+0 1.35E-08 2 - 10 5.984E-03 - 2.92E+0 3.872E-1 - 1.936E-08 2 - 12 1.54E+0 1.07E-08 2 - 10 3.291E-01 2.130E-09 1.2E+21 2.2 0.041 2 - 10 4.787E-02 3.098E-10 2 - 10 1.047E+0 6.76E-09 2 - 10 4.48E-02 2.904E-10 2 - 10 2.095E+0 1.35E-08 2 - 12 3.504E-03 - 4.55E+01 2.420E-1 - 3.146E-07 2 - 10 7.480E-01 4.840E-09 2 - 10 2.92E-02 - 7.480E-02 1.936E-10 - 4.840E-10 2 - 10 7.480E-02 - 1.85E-01 4.840E-10 - 1.20E-09 2 - 10 8.97E-02 5.808E-10 2 - 10 6.732E-01 4.356E-09 2 - 10 8.97E-01 5.808E-09 2 - 10 2.095E-02 1.35E-10 2 - 10 2.095E-01 1.35E-09 2 - 10 1.795E+0 1.162E-08 2 - 10 2.92E-02 1.936E-10 2 - 10 <2.92E-04 - 3.890E+0 <1.936E-12 - 2.517E-08 2 - 10 8.97E-01 5.808E-09 2 - 10 7.480E-02 4.840E-10 2 - 10 <1.496E-02 - 1.346E-01 <9.680E-1 - 8.712E-10 2 - 10 <1.496E-01 <9.680E-10 2 - 10 8.97E-02 5.808E-10 2 - 10 <1.496E-03 - 3.291E+01 <9.680E-12 - 2.130E-07 2 - 10 4.787E-01 3.098E-09 2 - 10 1.197E-03 - 5.984E+01 7.74E-12 - 3.872E-07 2 - 10 3.291E-01 2.130E-09 2 - 10 1.795E-02 1.162E-10 2 - 10 2.693E-02 1.742E-10 471 2 - 10 1.346E+0 8.712E-09 2 - 10 7.181E-03 4.646E-1 2 - 10 1.14E-02 7.4E-1 0.5 - 25 4.43E-03 2.168E-1 2 - 20 4.65E-04 3.8E-12 2 - 20 7.34E-04 6E-12 2 - 20 4.89E-05 4E-13 2 - 20 2.13E-03 1.74E-1 2 - 20 1.10E-04 9E-13 2 - 20 3.91E-04 3.2E-12 2 - 10 1.30E-02 8.4E-1 2 - 20 4.7E-04 3.9E-12 2 - 10 2.94E-03 1.9E-1 0.5 - 25 6.27E-04 3E-12 2 - 10 4.02E-03 2.6E-1 2 - 10 6.18E-03 4E-1 2 - 10 7.73E-05 5E-13 2 - 10 2.78E-03 1.8E-1 2 - 10 4.64E-03 3.0E-1 2 - 10 4.3E-03 2.8E-1 0.5 - 25 3.94E-03 1.816E-1 2 - 10 3.09E-03 2E-1 1 - 20 7.32E-03 4E-1 2 - 10 3.25E-03 2.1E-1 472 2 - 10 2.01E-02 1.3E-10 2 - 10 7.73E-05 5E-13 2 - 10 9.27E-03 6E-1 2 - 10 4.64E-04 3E-12 2 - 10 4.3E-03 2.8E-1 0.5 - 25 4.43E-03 2.168E-1 0.5 - 25 3.94E-03 1.816E-1 2 - 10 5.56E-03 3.6E-1 2 - 10 6.65E-03 4.3E-1 2 - 10 2.16E-04 1.4E-12 473 2 - 10 6.18E-04 4E-12 2 - 10 3.40E-03 2.2E-1 2 - 6 6.03E-04 3.2E-12 2 - 10 2.63E-03 1.7E-1 2 - 10 3.56E-03 2.3E-1 2 - 10 6.18E-04 4E-12 2 - 10 4.3E-04 2.8E-12 2 - 10 3.56E-03 2.3E-1 2 - 20 5.87E-04 4.8E-12 0.4 0.26 2 - 20 9.29E-04 7.6E-12 474 20 - 10 2.21E-02 1.41E-09 1 - 10 1.41E-05 1.12E-13 2 - 10 3.09E-05 2E-13 475 476 2 - 10 6.18E-06 4E-14 2 - 10 1.24E-05 8E-14 2 - 10 1.48E-05 9.6E-14 0.1 2 - 10 6.57E-07 4.25E-15 2.57E+21 3.90E+21 2 - 10 1.0E-04 6.47E-13 8.5E+21 2 - 10 1.37E-03 8.86E-12 6.80E+21 0.8 - 10 4.19E-02 1.7E-10 0.3 2 - 10 1.90E-03 1.23E-1 1.38E+2 2 - 10 4.9E-05 4.10E-13 2.10E+2 1.21 0.86 2 - 10 4.28E-01 2.7E-09 2 - 10 9.24E-02 5.98E-10 477 10 - 20 1.5E-02 3.43E-10 2 - 10 7.73E-01 5.0E-09 2 - 10 1.98E-03 1.28E-1 0.4 0.5 478 2 - 10 6.86E-02 4.4E-10 0.07 2 - 10 2.47E-05 1.6E-13 2 - 10 6.18E-05 4E-13 2 - 10 1.62E-02 1.05E-10 0.5 - 12 4.12E-03 1.6E-1 3 - 12 1.51E-01 1.34E-09 2 - 10 7.93E-05 5.13E-13 6.90E+21 479 0.2 - 10 1.69E-04 6.04E-13 3.0E+20 2.85 0.3 2 - 10 1.96E-05 1.27E-13 2.15E+21 2 - 10 2.32E-03 1.50E-1 3.0E+21 2 - 10 1.37E-06 8.86E-15 2.0E+20 2 - 10 7.3E-05 4.74E-13 1.50E+2 0? 2 - 10 1.70E-03 1.10E-1 3.17E+21 1.60 2 - 10 7.26E-04 4.70E-12 2.20E+2 1.60 2 - 10 9.95E-07 6.4E-15 1.0E+20 2 - 10 1.2E-04 7.90E-13 3.50E+2 2 - 10 6.03E-03 3.90E-1 4.70E+2 2 - 10 1.86E-04 1.20E-12 2.57E+21 2 - 10 2.01E-04 1.30E-12 6.30E+21 2 - 10 1.05E-02 7.10E-1 1.0E+2 1.70 0.05 2 - 10 1.81E-01 1.17E-09 9.8E+21 1.4 0.05 2 - 10 1.18E-01 8.29E-10 6.30E+21 1.96 0.075 0.5 - 10 9.97E-02 3.6E-10 0.12 2 - 10 1.98E-02 1.28E-10 2 - 10 4.76E-02 3.08E-10 2 - 10 4.0E-04 2.59E-12 2 - 10 1.56E-02 1.01E-10 2 - 10 1.4E+01 9.32E-08 2 - 10 3.20E-04 2.05E-12 2 - 10 2.40E-03 1.5E-1 2 - 10 7.60E-03 4.92E-1 2 - 10 4.0E-03 2.59E-1 2 - 10 4.0E-03 2.59E-1 2 - 10 2.50E-02 1.62E-10 2 - 10 8.0E-03 5.18E-1 40 - 80 1.01E-03 8.97E-1 2 - 10 6.64E-03 4.30E-1 2 - 10 1.76E-03 1.14E-1 480 2 - 10 2.16E-04 1.70E-12 0.27 1.0E+21 1.5 0.2 ? 10 3.30E-06 1.41E-14 1.73 0.2 ? 10 2.26E-06 1.10E-14 1.5 0.2 ? 10 2.17E-05 5.37E-14 2.73 0.2 ? 10 4.24E-07 1.51E-15 0.2 ? 6 2.5E-04 7.89E-13 9.0E+20 1.10 0.50 0.2 ? 6 1.04E-03 3.48E-12 2.30E+21 0.74 0.47 2 ? 15 1.14E-03 8.50E-12 1.0E+21 2.0 2 ? 15 9.21E-04 6.90E-12 1.0E+21 2.0 0.5 ? 10 2.80E-04 9.98E-13 0.5 ? 10 1.89E-04 6.73E-13 2 ? 10 5.75E-03 4.51E-1 1.82E+2 1.41 0.80 1.0E+23 2 ? 10 3.12E-02 2.0E-10 1.70E+20 2 ? 10 1.92E-02 1.23E-10 0.6 2 ? 10 3.76E-04 3.47E-12 3.16E+2 0.70 1.10E+20 1.0E+20 2.50E+20 481 STABILITY Pulse Width (50%) (s) Pulse Width (10%) (s) Magnetic Field (Gaus) Transient Characteristics Stability Code Timing Stability 1.67E-03 3.79E+12 S Gl 3.38E+12 S Gl 1.63E+12 S 3.13E+12 S Gl 1.54E+13 S 4.86E+1 S Gl 3.48E+12 S 3.3E+1 S Bi 2.79E+12 S Gl 4.29E+12 S Gl 5.18E+1 S 5.81E+08 S Bi 5.50E-05 2.25E+09 S 4.6E+12 S 4.97E+12 S 4.68E+08 S 1.67E+08 S Bi 2.4E+1 S 1.08E+13 S 7.3E+1 S 2.81E+08 S Bi 1.08E+12 S 8.39E+1 S Gl 9.86E+12 S 3.50E-04 4.23E+08 S Bi 9.64E+1 S 1.69E+08 S Bi 2.60E+14 6.30E+14 9.50E+14 8.0E+14 1.40E+15 8.07E+14 1.20E+14 Bi Bi 482 T Bi T Bi T Bi T Bi T Bi T Bi T Bi T Bi T Bi Bi T Bi T Bi T Bi T Bi Bi T Bi T Bi Bi T Bi T Bi Bi T Bi T Bi T Bi Bi T Bi T Bi Bi T Bi T Bi T Bi T Bi Bi T Bi Bi T Bi 483 T Bi Bi T Bi T Bi Bi Bi Bi Bi T Bi T Bi T Bi Bi Bi Bi Bi Bi Bi T Bi Bi Bi Bi T Bi Bi Bi T Bi T Bi Bi T Bi T Bi Bi T Bi 3.81E+14 Bi T Bi 2.40E+12 Bi 484 T Bi Bi T Bi Bi T Bi T Bi Bi Bi Bi T Bi T Bi T Bi T Bi Bi T Bi Bi Bi Bi Bi T Bi T Bi Bi Bi T Bi T Bi T Bi T Bi Bi T Bi T Bi T Bi T Bi T Bi 485 T Bi T Bi T Bi T Bi T Bi T Bi T Bi 2.10E+12 T Bi Bi Bi T Bi T Bi T Bi Bi Bi T Bi Bi Bi T Bi T Bi T Bi Bi T Bi Bi T Bi T Bi T Bi Bi, Bu Bi Bi 1.70E+08 Bi T Bi 486 T Bi T Bi, Bu T Bi, Bu T Bi, Bu Bi Bi T Bi T Bi T Bi Bi, Bu Bi, Bu T Bi T Bi, Bu T Bi T Bi T Bi Bi T Bi Bi Bi T Bi, Bu T Bi 2.35E+09 Bi Bi 3.0E+12 Bi T Bi Bi 5.50E+08 Bi Bi. Zsrc T Bi Bi T Bi, Bu T Bi 487 Bi Bi Bi T Bi Bi Bi T Bi, Bu T Bi, Bu T Bi T Bi, Bu Bi, Bu T Bi Bi, Bu T Bi, Bu Bi Bi 4.50E+08 Bi Bi Bi T Bi T Bi, Bu T Bi 2.30E+08 T Bi, Bu Bi, Bu T Bi Bi Bi, Bu Bi T Bi Bi T Bi Bi T Bi Bi T Bi Bi 488 Bi T Bi, Bu T Bi T Bi, Bu Bi Bi T Bi, Bu T Bi, Bu Bi Bi Bi Bi Bi Bi, Bu Bi Bi Bi T Bi, Bu Bi T Bi, Bu Bi, Bu Bi T Bi T Bi, Bu T Bi, Bu T Bi Bi Bi Bi T Bi, Bu Bi T Bi T Bi, Bu 489 T Bi T Bi, Bu Bi, Bu Bi T Bi 2.18E+09 Bi Bi Bi T Bi T Bi 4.0E+08 T Bi, Bu T Bi, Bu Bi Bi, Bu 2.38E+09 Bi T Bi 6.19E+08 Bi Bi Bi T Bi, Bu Bi, Bu Bi, Bu T Bi Bi, Bu T Bi T Bi Bi, Bu 2.10E+08 T Bi T Bi, Bu Bi, Bu T Bi Bi, Bu 1.0E+08 Bi T Bi T Bi T Bi T Bi Bi, Bu Bi, Bu 490 Bi Bi 1.0E+14 1.01E+03 T T 1.90E+06 T 3.0E+05 3.0E+05 S 8.0E+12 491 6.0E+05 T 1.0E+05 7.0E+12 6.80E+13 2.30E+12 T 3.80E+13 3.60E+13 1.90E+13 492 4.40E+13 3.0E+13 2.30E+13 2.45E+13 1.0E+08 5.60E+13 6.70E+13 T 493 1.0E+1 T Bi T Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi 494 Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi 495 Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi Bi 7.76E+1 5.50E+12 1.0E+12 6.31E+12 3.02E+09 8.32E+1 1.70E+13 1.76E+08 Bi 2.0E+12 1.20E+12 2.10E-05 4.07E+08 T Bi 1.29E+08 Bi Bi Bi Bi Bi 496 Bi Bi Bi Bi Bi Bi Bi Bi Bi T Bi 2.0E+14 Bi Bi 497 4.60E+10 Bi 9.5E+09 Bi Bi, Bu Bi 1.0E+08 Bi Bi Bi T 1.0E+12 Bi Bi Bi T Bi 498 Bi Bi Bi Bi Bi Bi T Bi T 4.47E+08 3.60E+12 4.10E+13 1.0E+13 2.40E+12 4.80E+13 Gl? 4.07E+12 T Bi T Bi 0.015 T Bi T Bi T Bi T Bi Bi Bi T Bi, Bu T Bu Bi 499 1.0E+13 S 4.0E+08 8.0E+08 8.0E+08 Bi 7.0E+08 7.0E+08 5.0E+08 Bi 6.0E+08 Bi 2.0E+08 Bi 7.0E+08 3.0E+08 5.0E+08 7.0E+08 Bi 7.0E+08 Bi Bi 2.20E+09 Bi 9.0E+08 Bi Bi Bi Bi Bi? Bi? T Bi? Bi Bi? Bi? T Bi 8.0E+14 T Bi 500 PERIODICITY Pulse Period (s) Pulse Period Deriv. (s/s) Pulse Period 2ndDeriv. (s/s/s) Epoch (MJD) Characteristic Age (t c = P/2Pdot) (yrs) Binary Orbit Period (d) Other Period 0.034 4.2096E-13 -2.79E-25 48743.000 1.256E+03 ? 0.08929 1.2468E-13 49672.000 1.132E+04 ? 0.23709 1.097E-14 -1.47236E-26 43946.000 3.420E+05 ? 0.10245 9.304E-14 4861.300 1.746E+04 ? 0.15023 1.5402E-12 -1.3164E-23 4835.000 1.52E+03 ? 0.03953 5.85E-15 4705.180 1.074E+05 ? 0.12365 9.592E-14 48658.000 2.042E+04 ? 0.0476 2.27E-15 4950.000 3.327E+05 1236.72359 ? 0.10145 7.495E-14 48650.000 2.143E+04 ? 0.1361 1.3432E-13 4870.000 1.578E+04 ? 0.2651 1.16E-15 48381.000 3.105E+06 ? 0.0575 2E-20 4825.000 1.60E+09 5.741042329 ? 0.0305 1.60E-18 47953.500 2.92E+07 ? 0.38487 5.503E-14 48423.000 1.109E+05 ? 0.05037 4.7906E-13 -1.7347E-25 48256.000 1.67E+03 ? 0.0493 1.08E-20 4913.000 7.30E+09 ? 0.016 1.2E-20 48196.000 1.510E+09 0.38196639 ? 0.253065 2.30E-16 52403.000 1.741E+07 ? 0.2316 4.9254E-13 48658.000 7.47E+03 ? 0.14315 3.6E-15 4944.36720 6.194E+05 ? 0.0525 1.4E-20 4920.000 5.702E+09 0.604672713 ? 0.1971 5.83E-15 4355.61720 5.358E+05 ? 0.15638 4.39E-15 48382.000 5.636E+05 ? 0.49524 1.9191E-13 48419.000 4.093E+04 ? 0.0232 8E-20 49150.60860 4.909E+08 2.0285 ? 0.5306 1.72E-15 48383.000 4.920E+06 ? 0.0347 8E-21 49301.000 6.87E+09 0.26314268 ? 8.680590 2.34E-12 5.83E+04 8.1000 6.497690 2.2E-1 4.645E+03 10.99427 1.9237E-1 9.059E+03 7.476510 2.8E-1 4.231E+03 1.765730 4.13E-1 4.510E+03 6.971300 5.159130 1.09E-10 7.49E+02 6.9789485 4.83E-13 2.264E+05 9.1321 501 74.676 323.2 0.059 91.1 5.00 8.8163 3.0E-10 15.3 -1.26E-08 2.374 46.63 5.792 169.3 58.969 2.708 280.4 2.7632 304 345.2 3.343 31.0294 1008 0.483 3.6145107 5.90E-1 1.013 0.716 0.162 2.07 1404.2 1.102 4.4 1.427 835 24.167 202.5 4.0635 502 69.5 13.7 1.058 13.502932 8.07E-06 0.058 10.042 0.069 0.696 103.29 -6.0E-08 4.625 0.071 0.176 96.08 0.038 13.1789 0.065 103.2 1.438 31.851 3.33 12.327396 4.583 283 0.373 93.5 5.625 0.061 862 6.498 2.200E-1 4.64E+03 405 4.81793 0.087 503 293.464 7.813 298 0.235 697.63 3.20E-07 1.73 191 272.267 5.542 170.84 17.6 1.75 437.4 529 0.15 9.3 1.275 38 0.43 0.142 714.5 413 20.38 4.45 1.242 152.26 11.194 3.30E-09 81.1 29.5 6.9713 504 94.8 10.042 361 0.254 21 89.17 437.649 5.0E-07 0.349 0.546 15.8 3.33 18.7 1.45 - 2.92 0.208 41.8 1.917 0.08 198 4.583 358.61 0.528 6.2 392 10.917 0.213 0.340 0.0305 5.200 0.323 505 0.159 9.08 0.171 0.43 0.164 0.12 0.629 16.60 1.123 1.540 0.379 0.07 0.0323 0.78 0.875 7.7 0.029 0.0345 0.158 2.620 1.24 1.70 0.296 0.618 506 0.91 - 0.9375 0.521 0.054 0.613 0.0276 0.175 14 14.167 0.038 0.194 507 0.467 1.834 0.238 0.515 508 0.18125 0.0303 0.0249392 4.35E-18 0.084 24.70 0.0327 0.0363 0.08 0.232 0.9375 0.014 0.0364 0.792 0.035 0.387 0.34 6.475 0.248 0.713 0.218259 509 9.842 8.3915 1.0E-16 5.479 -4.4363E-1 1028.7325 -3.20E-12 0.0127 0.032386 120.2 0.23193 8460 0.1016667 21.83 0.07365 0.18280 0.17690 0.07492 0.28984 0.3048 30 0.3800 160 0.1640 0.06312 0.18267 24 0.25816 745.8 0.285314 27.8682 0.056667 6 0.27512973 0.3708333 323.2 0.250 0.02917 1020 0.1375 206.298 0.25256 351.341 -2.70E-1 1.9680 54.635 0.5218 3726 0.4145833 863.5 0.14375 191? 0.290 718 0.25830 1920 0.5830 269.5 1040.4 0.12720 913.2 0.1347486 0.1500 834.3 0.2917 0.05625 157.5 0.25 3108 0.0732 529.31 0.16538 214 0.248148148 510 4021.62 4.54E-1 0.06823 4847.7312 0.6151 927 0.14208 63.63032 4.0E-13 0.2098 745.506 2.30E-1 0.1402323 3.076735 4.0E-14 0.416667 1254.451 2.20E-1 0.20206 5246 250 0.23910 120 0.16280 0.1390 0.06143 0.41830 0.24507 0.0582 0.05923 27.50 1.2340 5.714 3682.8 0.138154 0.146 0.198096 0.23 0.51420 0.214165 0.196713 0.07845 0.05405 275 0.07890 276 0.08020 4861.2? 0.05627 0.15860 5702.4 0.07080 0.3542 0.09268 1202.4 3.30E-09 0.13842 0.68207 0.069747 0.08710 0.14125 0.07429 0.0547 4086 0.2060 240 511 0.07948 0.07975 13.9 0.07909 347.6 0.08050 538.14192 0.062363 0.131516 0.06260 0.05340278 0.07049 0.078709 0.0832837 0.078504167 0.128927 0.0627 0.07265625 567.7 0.097189 0.1545252 0.108333 78.0176 0.08682 0.139613 0.0769444 0.07541667 5360 0.1434 0.074813 14.07 0.074271 25.703 2.76E-06 0.86924 0.07635 0.06250 0.06360 0.19393 0.26810 0.61016 0.15198 240 0.2163 0.7650 35.7 0.209893 0.21450 0.32125 0.36410 512 0.1370 0.1584328 0.20583 0.16 0.297645 0.08125 0.069212 5.01E-10 16.680 94.9 242.18 0.87092 2.49310 1.01050 0.68470 1.19520 2.86730 3.95295 1.2473 4.13470 0.7130 9.48530 3.06320 6.95340 1.35740 1.31 2.47870 2.32730 3.4520 2.80680 17.359 4.42510 0.6140 1.1980 3.12676 3.27549 3.8210 4.476 1.520 14.26 0.7181 17.7692 241747.2 0.86105 493.184 513 1057968 127308.96 68292 4.700 56235.424 1456.4 1.3260 245462.4 163296 2712960 70588 8.1700 8.8200 69120 104.023 4460 912384 51241.248 0.59307 52768.384 416707.2 21.20812 878083.2 87564 10.170 186957.792 286848 3.19860 71657.568 41384.736 0.4790 271710.72 2.300 1.0430 7.32825 475200 50800 70848 0.96160 3.5830 314702.496 413960.54 4.800 1614962.8 2.61321 926394.624 657169.632 10975.68 1.1400 3999.168 39.4809 23848 27.5384 145298.8 1.68170 2674918.08 342316.8 514 685670.4 7598.8 248918.4 8.8076 0.873712 9404985.6 345459.2 54530.752 5978.8 0.6981 3.24347 2574 79549.6 9.208 438394.896 171350.208 1.9832 5439.52 341712 526348.8 2080 6.7240 0.39262 0.4268 38.2 -6.51E-09 7.84825 0.241 0.10143723 5.84E-15 0.2875 1.05E-13 0.063191253 1.58E-14 0.06938 1.40E-13 0.01075761 9.7E-19 -2.30E-27 47187.50415 191.43 0.38768791 1.78E-15 40621.54 10.0759 0.60643258 4.6E-1 48673 0.034 0.06467 4.40E-14 2400 0.194626341 7.20E-15 42301.5 0.0157807 1.05E-19 -3.78E-32 52328 721 0.048 4.0E-21 7.600 2.6300 19.6045 7.4920 898560 515 7.1 0.3417 9.6300 1.130 272160 905.90 0.465069102 24.43 2.76 4654368 20.5212 ? d 2.96 ? 51.075 ? 487296 65640 241920 13747.2 565056 7340 62080 23280 28940 10454 34920 313632 62080 39740 238464 708480 570240 103680 257472 406080 603936 43200 490691.52 4.2319 0.71 821 0.17193 9149760 10.00 1.70491 2.75960 5.161297854 1.23E-10 76.923 3.01856 516 0.062 3.30E-20 6.540 0.037 2.42E-18 0.4200 0.01563148 -1.90E-20 48270 0.07564617 29.5056 -2.80493E-08 0.0393 2.0E-21 2.1700 0.46543 1.5610 0.81428 2.7800 3.9600 1.26840 4.865 3.03 20.6 2.4029 4003.2 1.26245 0.6042 0.76278 1.04360 3.500 54 5148576 85.1 3.760 290 0.32150 0.3364 0.28410 0.2678158 0.2783152 0.45789 0.4080 0.3580 0.358 3602.016 86400 3.45310 15.42 0.0161475 5.12E-14 500 1207872 387 172.4 4.782 0.087 75.5 517 82.4 140.1 152.1 564.83 101.4 8.02 2.57E-1 45 343 6.848 2.165 0.0487 1.0E-20 0.06568 1.93E-13 5380 0.0516 2.9E-21 0.40764 4.02E-12 3.59E-23 5173 1606 0.13531 7.45E-13 290 0.06818 8.32E-14 0.0407 7.13E-21 0.1249 1.28E-13 0.324818968 7.10E-12 5191.0878 723 0.2674 2.08E-13 0.05162 7.80E-14 0.0540232 2.69E-18 52396 0.03026326 0.0297171 1.58E-18 0.029459 0.05245943 0.027829236 0.0318148 0.178125 31 29.5 0.1403 0.258 518 0.13685047 7.51E-13 5280 290 0.0575678 -4.985E-20 0.05357573 -3.30E-21 0.03536329 9.852E-20 2.25684818 0.02623579 6.451E-20 0.04040379 -4.215E-20 0.03210341 -1.620E-21 2.3576965 0.0348492 -4.590E-20 0.2979249 0.0210634 -9.787E-21 0.12064939 0.04346168 -1.219E-19 0.0367643 -3.832E-20 0.03053954 -2.186E-20 0.0264343 3.032E-20 0.135974304 0.0403181 3.410E-20 1.18908405 0.075848 2.947E-19 1.12617678 0.04342827 9.524E-20 0.429105683 0.03650329 1.68E-19 51749.71082 1.35405939 0.683 0.096 1.24 0.387 201.9 51834.63 263 51832.684 16.5718 1.26E-08 25.4904 -1.95E-08 18.37 34.08 503.6 138.04 701.6 95.2 6.97 9.801 52859.78 2.69 27.12 729 519 B.3.3 2?10 keV Energy List The following table provides al the data in the 2?10 keV Energy List of the XNAVSC. To reduce the overal size of this table, only the Installation Number, the J- name, and the converted 2?10 keV X-ray Flux columns are provided for this list, as al other columns are repeated in the other lists. The first page of this table provides the headings of each column of the table. Descriptions of the parameters within this table are provided in Table B-4. For the parameter of the Catalogue J-Name, this is source name unique to the XNAVSC. For a name that is of format Jhhmm-ddmm and writen in blue ink, this name has been modified from the original citation?s J-name or was derived from the position of the source if only a B-name is known for that source. This Catalogue J-Name is only created to produce a consistent naming convention for al the XNAVSC sources, and should not be used as an external name for the source. X-ray flux values writen in blue ink are ?derived? values from a given source?s citation. This may mean that X-ray detector photon counts were converted to energy flux. For some sources this may mean that the source was not directly observed in the ?derived? energy range, so there is no asurance that the source is visible within this X- ray range. 520 2-10 keV X-ray Instal Number Catalogue J-Name Energy Range (keV) Flux (photons/cm 2 /s) Flux (erg/cm 2 /s) 1 J0534+20 2 - 10 1.54E+0 9.93E-09 2 J0835-4510 2 - 10 1.59E-03 1.03E-1 3 J063+1746 2 - 10 1.23E-05 7.94E-14 4 J1709?428 2 - 10 1.59E-04 1.03E-12 5 J1513?5908 2 - 10 1.62E-02 1.05E-10 6 J1952+3252 2 - 10 3.15E-04 2.04E-12 7 J1048?5832 2 - 10 3.86E-05 2.50E-13 8 J1302?6350 2 - 10 5.10E-04 3.30E-12 9 J1826?134 2 - 10 2.63E-03 1.70E-1 10 J1803?2137 2 - 10 2.75E-05 1.78E-13 1 J1932+1059 2 ? 10 4.30E-05 2.78E-13 12 J0437?4715 2 - 10 6.65E-05 4.30E-13 13 J1824?2452 2 - 10 1.93E-04 1.25E-12 14 J0659+1414 2 - 10 3.17E-05 2.05E-13 15 J0540?6919 2 - 10 5.15E-03 3.3E-1 16 J2124?358 2 - 10 1.28E-05 8.26E-14 17 J1959+2048 2 - 10 8.31E-05 5.38E-13 18 J0953+075 2 - 10 9.60E-06 6.53E-14 19 J1614?5047 20 J0538+2817 2 - 10 1.24E-07 8.0E-16 21 J1012+5307 2 - 10 1.93E-06 1.25E-14 2 J1057?526 2 - 10 1.64E-06 1.06E-14 23 J0358+5413 2 - 10 1.79E-05 1.16E-13 24 J237+6151 2 - 10 6.26E-06 4.05E-14 25 J0218+4232 2 - 10 6.65E-05 4.30E-13 26 J0826+2637 2 - 10 9.27E-07 6.0E-15 27 J0751+1807 2 - 10 6.63E-06 4.29E-14 28 J0142+610 2 - 10 1.73E-01 1.12E-09 29 J0525?607 30 J1048?5937 2 - 10 1.39E-02 8.98E-1 31 J1708?408 2 - 10 2.78E-02 1.80E-10 32 J1808?2024 2 - 10 6.35E-04 4.1E-12 3 J1841?0456 2 - 10 1.9E-02 1.29E-10 34 J1845?0256 2 - 10 3.50E-03 2.27E-1 35 J1907+0919 36 J2301+5852 2 - 10 1.23E-02 7.96E-1 37 J032-7348 2 - 10 5.98E-04 3.87E-12 38 J049-7310 2 - 10 1.20E-04 7.74E-13 39 J049-7250 2 - 10 1.50E-03 9.68E-12 40 J052-726 2 - 10 2.9E-03 1.94E-1 41 J050-7316 2 - 10 3.91E-04 2.53E-12 521 42 J050-7213 2 - 10 7.78E-03 5.03E-1 43 J051-7231 2 - 10 2.9E-05 1.94E-13 4 J051-7310 45 J052-7319 2 - 10 1.41E-02 9.10E-1 46 J052-7158 2 - 10 2.93E-03 1.90E-1 47 J054-7341 2 - 10 2.9E-03 1.94E-1 48 J056+6043 2 - 10 1.50E-02 9.68E-1 49 J053-726 2 - 10 4.19E-03 2.71E-1 50 J054-7204 2 - 10 1.14E-02 7.36E-1 51 J054-726 2 - 10 2.9E-03 1.94E-1 52 J057-7202 2 - 10 2.4E-04 1.58E-12 53 J058-7230 54 J059-7138 2 - 10 4.35E-03 2.82E-1 5 J0101-7206 2 - 10 2.9E-04 1.94E-12 56 J0103-7209 2 - 10 1.45E-05 9.38E-14 57 J0109-744 2 - 10 6.8E-03 4.45E-1 58 J0105-721 2 - 10 2.9E-04 1.94E-12 59 J0105-7212 2 - 10 7.21E-06 4.67E-14 60 J0105-7213 2 - 10 4.49E-02 2.90E-10 61 J018+6517 2 - 10 1.20E-02 7.74E-1 62 J018+634 2 - 10 5.98E-03 3.87E-1 63 J017-7326 2 - 10 1.50E-03 9.68E-12 64 J017-730 2 - 10 2.9E-02 1.94E-10 65 J0143+6106 2 - 10 1.50E-03 9.70E-12 6 J0240+613 2 - 10 3.48E-04 2.25E-12 67 J034+5310 2 - 10 1.50E-03 9.68E-12 68 J035+3102 2 - 10 2.69E-02 1.74E-10 69 J0419+559 2 - 10 5.98E+0 3.87E-08 70 J040+431 2 - 10 2.9E-03 1.94E-1 71 J0501-703 72 J0502-626 2 - 10 1.71E-02 1.10E-10 73 J0512-6717 74 J0516-6916 2 - 10 2.10E-04 1.36E-12 75 J0520-6932 76 J052+3740 2 - 10 2.9E-03 1.94E-1 7 J0529-656 2 - 10 5.09E-04 3.29E-12 78 J0531-607 2 - 10 2.9E-03 1.94E-1 79 J0531-6518 80 J0532-62 2 - 10 8.98E-03 5.81E-1 81 J0532-6535 2 - 10 1.50E-05 9.71E-14 82 J0532-651 2 - 10 4.50E-05 2.91E-13 83 J0535-670 2 - 10 5.9E-05 3.8E-13 84 J0535-651 2 - 10 2.9E-05 1.94E-13 85 J0538+2618 2 - 10 8.98E-03 5.81E-1 86 J0535-6530 2 - 10 7.51E-04 4.86E-12 522 87 J0538-6405 2 - 10 5.09E-03 3.29E-1 8 J0539-694 2 - 10 8.98E-03 5.81E-1 89 J0541-6936 90 J0541-6832 91 J054-63 2 - 10 5.39E-03 3.49E-1 92 J054-710 2 - 10 4.19E-04 2.71E-12 93 J055+2847 2 - 10 3.29E-03 2.13E-1 94 J0635+053 2 - 10 1.65E-03 1.07E-1 95 J0648-418 2 - 10 8.98E-05 5.81E-13 96 J0728-2606 2 - 10 3.59E-03 2.32E-1 97 J0747-5319 2 - 10 2.10E-03 1.36E-1 98 J0756-6105 2 - 10 2.10E-03 1.36E-1 9 J0812-314 2 - 10 1.80E-03 1.16E-1 10 J0835-431 2 - 10 8.98E-02 5.81E-10 101 J0902-403 2 - 10 5.98E-03 3.87E-1 102 J109-5817 2 - 10 3.59E+0 2.32E-08 103 J1025-5748 2 - 10 1.65E-03 1.07E-1 104 J1030-5704 2 - 10 9.87E-03 6.39E-1 105 J1037-5647 2 - 10 5.09E-04 3.29E-12 106 J1050-5953 2 - 10 2.9E-04 1.94E-12 107 J120-6154 2 - 10 2.9E-04 1.94E-12 108 J121-6037 2 - 10 2.9E-02 1.94E-10 109 J148-6212 2 - 10 1.20E-02 7.74E-1 10 J147-6157 2 - 10 1.20E-02 7.74E-1 11 J126-6246 2 - 10 2.69E-02 1.74E-10 12 J1242-6012 2 - 10 8.98E-03 5.81E-1 13 J1247-6038 2 - 10 7.18E-02 4.65E-10 14 J1249-5907 2 - 10 7.18E-02 4.65E-10 15 J1242-6303 2 - 10 6.58E-03 4.26E-1 16 J1239-752 2 - 10 1.80E-03 1.16E-1 17 J1254-5710 2 - 10 2.39E-03 1.5E-1 18 J1301-6136 2 - 10 8.98E-04 5.81E-12 19 J1324-620 2 - 10 1.20E-03 7.74E-12 120 J1421-6241 2 - 10 5.98E-03 3.87E-1 121 J1452-5949 2 - 10 1.20E-04 7.74E-13 12 J1542-523 2 - 10 8.98E-03 5.81E-1 123 J157-5424 2 - 10 8.08E-02 5.23E-10 124 J154-519 2 - 10 5.09E-03 3.29E-1 125 J170-4140 2 - 10 1.20E-02 7.74E-1 126 J1703-3750 2 - 10 3.29E-02 2.13E-10 127 J170-4157 2 - 10 1.20E-03 7.74E-12 128 J1725-3624 2 - 10 5.98E-04 3.87E-12 129 J1738-3015 2 - 10 8.65E-01 7.57E-09 130 J1739-2942 2 - 10 5.98E-03 3.87E-1 131 J174-2713 2 - 10 1.80E-04 1.16E-12 523 132 J1749-2725 2 - 10 4.07E-03 2.63E-1 13 J1749-2638 2 - 10 8.08E-02 5.23E-10 134 J1810-1052 2 - 10 5.98E-03 3.87E-1 135 J1820-1434 2 - 10 2.9E-03 1.94E-1 136 J1826-1450 2 - 10 8.98E-04 5.81E-12 137 J1836-0736 2 - 10 4.79E-03 3.10E-1 138 J1841-051 2 - 10 2.9E-03 1.94E-1 139 J1841-0427 2 - 10 7.48E-03 4.84E-1 140 J1845+057 2 - 10 1.20E-03 7.74E-12 141 J1847-0309 2 - 10 2.9E-03 1.94E-1 142 J1848-025 2 - 10 2.9E-03 1.94E-1 143 J1847-0430 2 - 10 1.10E-01 7.1E-10 14 J1858-024 2 - 10 5.98E-03 3.87E-1 145 J185-0237 2 - 10 1.80E-02 1.16E-10 146 J1858+0321 2 - 10 7.48E-02 4.84E-10 147 J1904+0310 2 - 10 5.98E-03 3.87E-1 148 J1905+0902 2 - 10 2.10E-03 1.36E-1 149 J1909+0949 2 - 10 1.20E-02 7.74E-1 150 J191+0458 2 - 10 5.98E-03 3.87E-1 151 J1932+5352 2 - 10 2.10E-03 1.36E-1 152 J1945+2721 2 - 10 1.06E-02 6.84E-1 153 J1949+3012 2 - 10 2.9E-02 1.94E-10 154 J1948+320 2 - 10 7.31E-01 4.73E-09 15 J195+3206 2 - 10 4.49E-03 2.90E-1 156 J1958+3512 2 - 10 7.03E-01 4.5E-09 157 J2032+3738 2 - 10 1.50E-03 9.68E-12 158 J2032+4057 2 - 10 2.69E-01 1.74E-09 159 J2030+4751 2 - 10 1.20E-04 7.74E-13 160 J2059+4143 2 - 10 9.58E-01 6.20E-09 161 J2103+4545 2 - 10 5.98E-02 3.87E-10 162 J2139+5703 2 - 10 1.80E-02 1.16E-10 163 J201+5010 2 - 10 2.10E-03 1.36E-1 164 J207+5431 2 - 10 1.80E-03 1.16E-1 165 J226+614 2 - 10 1.50E-03 9.68E-12 16 J239+616 2 - 10 4.79E-02 3.10E-10 167 J04+301 2 - 10 1.50E-03 9.68E-12 168 J0418+3247 2 - 10 2.09E+02 1.35E-06 169 J0514-402 2 - 10 8.98E-03 5.81E-1 170 J0520-7157 2 - 10 2.69E-02 1.74E-10 171 J0532-6926 2 - 10 1.50E-03 9.68E-12 172 J0617+0908 2 - 10 1.50E-01 9.68E-10 173 J062-020 2 - 10 5.98E-05 3.87E-13 174 J0658-0715 2 - 10 5.98E-02 3.87E-10 175 J0748-6745 2 - 10 2.9E-04 1.94E-12 176 J0835+518 2 - 10 1.80E-02 1.16E-10 524 17 J0837-4253 2 - 10 2.9E-03 1.94E-1 178 J0920-512 2 - 10 2.9E-02 1.94E-10 179 J092-6317 2 - 10 8.98E-03 5.81E-1 180 J1013-4504 2 - 10 2.01E+0 1.30E-08 181 J118+4802 2 - 10 1.35E-01 8.70E-10 182 J126-6840 2 - 10 1.20E-02 7.74E-1 183 J1257-6917 2 - 10 7.48E-02 4.84E-10 184 J1326-6208 2 - 10 2.10E-02 1.36E-10 185 J1358-644 2 - 10 1.50E-02 9.68E-1 186 J1458-3140 2 - 10 2.9E-04 1.94E-12 187 J1520-5710 2 - 10 1.50E-02 9.68E-1 18 J1528-6152 2 - 10 1.50E-02 9.68E-1 189 J1547-4740 2 - 10 2.9E-03 1.94E-1 190 J1547-6234 2 - 10 1.05E-01 6.78E-10 191 J150-5628 2 - 10 1.80E+0 1.16E-08 192 J1601-604 2 - 10 4.79E-02 3.10E-10 193 J1605+251 2 - 10 2.16E-04 1.40E-12 194 J1603-753 2 - 10 4.79E-01 3.10E-09 195 J1612-525 2 - 10 2.9E-03 1.94E-1 196 J1619-1538 2 - 10 4.19E+01 2.71E-07 197 J1628-491 2 - 10 1.65E-01 1.07E-09 198 J1632-6727 2 - 10 7.48E-02 4.84E-10 19 J1634-4723 2 - 10 5.98E-03 3.87E-1 20 J1636-4749 2 - 10 3.89E-02 2.52E-10 201 J1640-5345 2 - 10 6.58E-01 4.26E-09 202 J1645-4536 2 - 10 1.50E+0 9.68E-09 203 J1654-3950 2 - 10 5.39E+0 3.49E-08 204 J1657+3520 2 - 10 4.49E-02 2.90E-10 205 J1702-2956 2 - 10 1.50E-02 9.68E-1 206 J1702-4847 2 - 10 4.49E-03 2.90E-1 207 J1705-3625 2 - 10 2.47E+0 1.60E-08 208 J1706-4302 2 - 10 1.35E-01 8.71E-10 209 J1706+2358 2 - 10 1.50E-03 9.68E-12 210 J1708-2505 2 - 10 5.98E-03 3.87E-1 21 J1708-406 2 - 10 2.9E-02 1.94E-10 212 J1712-4050 2 - 10 9.58E-02 6.20E-10 213 J1709-2639 2 - 10 4.49E-01 2.90E-09 214 J1710-2807 2 - 10 5.98E-03 3.87E-1 215 J1714-3402 2 - 10 4.79E-02 3.10E-10 216 J1712-3738 2 - 10 9.52E-02 6.16E-10 217 J1718-3210 2 - 10 8.38E-02 5.42E-10 218 J1719-2501 2 - 10 4.89E+01 3.16E-07 219 J1718-4029 2 - 10 4.19E+0 2.71E-08 20 J1723-3739 2 - 10 2.10E-01 1.36E-09 21 J1727-354 2 - 10 9.58E-02 6.20E-10 525 22 J1727-3048 2 - 10 4.49E-02 2.90E-10 23 J1731-350 2 - 10 4.49E-01 2.90E-09 24 J1731-1657 2 - 10 8.98E-01 5.81E-09 25 J1732-244 2 - 10 2.9E-01 1.94E-09 26 J173-313 2 - 10 2.69E+0 1.74E-08 27 J173-323 2 - 10 2.9E-04 1.94E-12 28 J173-202 2 - 10 2.9E-02 1.94E-10 29 J1734-2605 2 - 10 2.9E-02 1.94E-10 230 J1735-3028 2 - 10 2.9E-02 1.94E-10 231 J1736-2725 2 - 10 1.50E-02 9.68E-1 232 J1737-2910 2 - 10 1.02E-02 6.58E-1 23 J1738-270 2 - 10 2.9E-02 1.94E-10 234 J1738-427 2 - 10 4.79E-01 3.10E-09 235 J1738-2829 2 - 10 1.20E-03 7.74E-12 236 J1739-2943 2 - 10 5.98E-03 3.87E-1 237 J1739-3059 2 - 10 7.78E-02 5.03E-10 238 J1740-2818 2 - 10 8.98E-03 5.81E-1 239 J1742-2746 2 - 10 9.08E+0 5.8E-08 240 J1742-3030 2 - 10 2.69E-02 1.74E-10 241 J1743-2926 2 - 10 8.98E-02 5.81E-10 242 J1743-294 2 - 10 1.20E-02 7.74E-1 243 J174-290 2 - 10 4.49E-03 2.90E-1 24 J174-2921 2 - 10 1.50E-02 9.68E-1 245 J1745-3213 2 - 10 5.98E-03 3.87E-1 246 J1745-2854 2 - 10 2.10E-02 1.36E-10 247 J1745-3241 2 - 10 5.98E-03 3.87E-1 248 J1745-2859 2 - 10 1.45E-04 9.39E-13 249 J1745-2927 2 - 10 1.35E-01 8.71E-10 250 J1745-2901 2 - 10 2.69E-02 1.74E-10 251 J1745-290 2 - 10 2.9E-03 1.94E-1 252 J1745-2846 2 - 10 2.18E-04 1.41E-12 253 J1745-2903 2 - 10 2.90E-04 1.8E-12 254 J1746-2854 2 - 10 2.90E-04 1.8E-12 25 J1746-2853 2 - 10 2.90E-04 1.8E-12 256 J1746-2931 2 - 10 1.80E-01 1.16E-09 257 J1746-2851 2 - 10 2.90E-04 1.8E-12 258 J1746-284 2 - 10 1.50E-03 9.68E-12 259 J1746-2853 2 - 10 2.90E-04 1.8E-12 260 J1746-2853 2 - 10 2.9E-03 1.94E-1 261 J1747-2959 2 - 10 1.80E-02 1.16E-10 262 J174-284 2 - 10 3.80E+01 2.46E-07 263 J1747-302 2 - 10 1.20E-02 7.74E-1 264 J1747-263 2 - 10 1.20E+0 7.74E-09 265 J1748-3607 2 - 10 7.48E-02 4.84E-10 26 J1745-2901 2 - 10 1.39E-03 9.0E-12 526 267 J1748-2453 2 - 10 2.9E-04 1.94E-12 268 J1748-202 2 - 10 2.9E-04 1.94E-12 269 J1749-31 2 - 10 8.08E-02 5.23E-10 270 J1750-325 2 - 10 2.9E-04 1.94E-12 271 J1750-3703 2 - 10 9.58E-02 6.20E-10 272 J1750-2125 2 - 10 2.10E-01 1.36E-09 273 J1750-317 2 - 10 4.49E-03 2.90E-1 274 J1748-2828 2 - 10 1.92E+0 1.24E-08 275 J1748-2021 2 - 10 8.98E-02 5.81E-10 276 J1752-2830 2 - 10 1.80E-01 1.16E-09 27 J1750-2902 2 - 10 3.89E-01 2.52E-09 278 J1752-3137 2 - 10 4.2E+0 2.73E-08 279 J1758-348 2 - 10 2.9E-01 1.94E-09 280 J175-328 2 - 10 6.06E-01 3.92E-09 281 J1801-2504 2 - 10 3.74E+0 2.42E-08 282 J1801-254 2 - 10 5.98E-02 3.87E-10 283 J1801-2031 2 - 10 2.10E+0 1.36E-08 284 J1806-2435 2 - 10 5.98E-03 3.87E-1 285 J1806-2435 2 - 10 1.48E+0 9.57E-09 286 J1808-3658 2 - 10 3.29E-01 2.13E-09 287 J1810-2609 2 - 10 4.79E-02 3.10E-10 28 J1814-1709 2 - 10 1.05E+0 6.78E-09 289 J1815-1205 2 - 10 4.49E-02 2.90E-10 290 J1816-1402 2 - 10 2.10E+0 1.36E-08 291 J1819-2525 2 - 10 3.37E-03 2.18E-1 292 J1823-3021 2 - 10 7.48E-01 4.84E-09 293 J1825-3706 2 - 10 2.9E-02 1.94E-10 294 J1825-00 2 - 10 7.48E-02 4.84E-10 295 J1829-2347 2 - 10 8.98E-02 5.81E-10 296 J1835-3258 2 - 10 9.86E-03 6.38E-1 297 J1839+0502 2 - 10 6.73E-01 4.36E-09 298 J1849-0303 2 - 10 8.98E-01 5.81E-09 29 J1853-0842 2 - 10 2.10E-02 1.36E-10 30 J1856+0519 2 - 10 2.10E-01 1.36E-09 301 J1858+239 2 - 10 1.80E+0 1.16E-08 302 J1908+010 2 - 10 2.9E-02 1.94E-10 303 J191+035 2 - 10 2.9E-04 1.94E-12 304 J1915+1058 2 - 10 8.98E-01 5.81E-09 305 J1918-0514 2 - 10 7.48E-02 4.84E-10 306 J1920+141 2 - 10 1.50E-02 9.68E-1 307 J1942-0354 2 - 10 1.50E-01 9.68E-10 308 J1959+142 2 - 10 8.98E-02 5.81E-10 309 J202+2514 2 - 10 1.50E-03 9.68E-12 310 J2012+381 2 - 10 4.79E-01 3.10E-09 31 J2024+352 2 - 10 1.20E-03 7.74E-12 527 312 J2123-0547 2 - 10 3.29E-01 2.13E-09 313 J2129+1210 2 - 10 1.80E-02 1.16E-10 314 J2131+4717 2 - 10 2.69E-02 1.74E-10 315 J214+3819 2 - 10 1.35E+0 8.71E-09 316 J2320+6217 2 - 10 7.18E-03 4.65E-1 317 J0720-3125 2 - 10 4.5E-03 2.95E-1 318 J1838-0301 2 - 10 1.35E-03 8.73E-12 319 J1234+3737 2 - 10 3.81E-05 2.46E-13 320 J1305+1801 2 - 10 1.13E-03 7.30E-12 321 J024-7204 2 - 10 6.57E-04 4.25E-12 32 J0610-484 2 - 10 1.14E-02 7.40E-1 323 J0712-3605 2 - 10 1.63E-03 1.06E-1 324 J010+604 2 - 10 4.14E-04 2.68E-12 325 J0613+474 2 - 10 6.37E-04 4.12E-12 326 J075+20 2 - 10 6.54E-04 4.23E-12 327 J0807-7632 2 - 10 4.36E-05 2.82E-13 328 J0825+7306 2 - 10 1.90E-03 1.23E-1 329 J084+1252 2 - 10 1.0E-01 6.47E-10 30 J0901+1753 2 - 10 5.35E-04 3.46E-12 31 J0951+152 2 - 10 2.7E-05 1.79E-13 32 J106-7014 2 - 10 9.80E-05 6.34E-13 33 J145-0426 2 - 10 3.06E-03 1.98E-1 34 J164+2515 2 - 10 3.49E-04 2.26E-12 35 J1807+051 2 - 10 1.30E-02 8.40E-1 36 J207+1742 2 - 10 4.25E-04 2.75E-12 37 J2142+435 2 - 10 5.02E-04 3.25E-12 38 J214+1242 2 - 10 2.94E-03 1.90E-1 39 J028+5917 2 - 10 2.37E-03 1.53E-1 340 J0203-0243 2 - 10 2.31E-04 1.50E-12 341 J0206+1517 2 - 10 2.49E-03 1.61E-1 342 J0256+1926 2 - 10 4.02E-03 2.60E-1 343 J031+4354 2 - 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10 5.94E-04 3.84E-12 637 J0234-4347 2 - 10 1.01E-01 6.51E-10 638 J0734+3152 2 - 10 6.24E-03 4.04E-1 639 J074+033 2 - 10 1.65E-03 1.07E-1 640 J134-0820 2 - 10 3.24E-04 2.10E-12 641 J1634+5709 2 - 10 8.42E-04 5.45E-12 642 J2045-3120 2 - 10 3.60E-02 2.3E-10 643 J2309+4757 2 - 10 5.20E-03 3.36E-1 64 J1939-0603 2 - 10 9.83E-04 6.36E-12 645 J130+2413 2 - 10 4.84E-04 3.13E-12 646 J0720-3146 2 - 10 5.72E-04 3.70E-12 647 J019+2156 2 - 10 5.07E-03 3.28E-1 648 J0513-6951 2 - 10 2.47E-05 1.60E-13 649 J0543-682 2 - 10 6.18E-05 4.0E-13 650 J0925-4758 2 - 10 2.16E-03 1.39E-1 651 J1601+648 2 - 10 2.84E-03 1.83E-1 652 J1045-5941 2 - 10 1.62E-02 1.05E-10 653 J0654-235 2 - 10 2.17E-04 1.40E-12 654 J2020+4354 2 - 10 1.58E-03 1.02E-1 65 J0412-1028 2 - 10 2.50E-04 1.62E-12 656 J0943+557 2 - 10 6.34E-04 4.10E-12 657 J101+1724 2 - 10 4.58E-04 2.96E-12 658 J1503+4739 2 - 10 5.37E-04 3.48E-12 659 J2037+7535 2 - 10 1.6E-03 1.08E-1 60 J212+1708 2 - 10 3.29E-05 2.13E-13 61 J1214+149 2 - 10 1.58E-04 1.02E-12 62 J165+3510 2 - 10 3.39E-05 2.19E-13 63 J1805+6945 2 - 10 2.64E-05 1.71E-13 64 J04+0932 2 - 10 5.10E-04 3.30E-12 65 J0103-7254 2 - 10 2.39E-01 1.5E-09 66 J013+3032 2 - 10 1.67E-04 1.08E-12 67 J0535-0523 2 - 10 6.43E-03 4.16E-1 68 J0537-6909 2 - 10 7.93E-05 5.13E-13 69 J1750+7045 2 - 10 4.17E-04 2.70E-12 670 J204-543 671 J051-7310 535 672 J052-720 673 J042-7340 674 J049-7323 675 J052-723 676 J056-722 67 J057-7207 678 J057-7219 679 J057-7325 680 J010-721 2 - 10 6.37E-05 4.12E-13 681 J0101-721 682 J0103-7208 683 J0103-7241 684 J019-731 685 J030+0451 2 - 10 1.96E-05 1.27E-13 686 J0205+649 2 - 10 2.32E-03 1.50E-1 687 J1024-0719 2 - 10 1.37E-06 8.86E-15 68 J119-6127 2 - 10 7.3E-05 4.74E-13 689 J124-5916 2 - 10 1.70E-03 1.10E-1 690 J1420-6048 2 - 10 7.26E-04 4.70E-12 691 J174-134 2 - 10 9.95E-07 6.4E-15 692 J180-2450 2 - 10 1.2E-04 7.90E-13 693 J1846-0258 2 - 10 6.03E-03 3.90E-1 694 J1856+013 2 - 10 1.86E-04 1.20E-12 695 J229+614 2 - 10 2.01E-04 1.30E-12 696 J0929-3123 2 - 10 1.05E-02 7.10E-1 697 J1751-3037 2 - 10 1.81E-01 1.17E-09 698 J1806-2924 2 - 10 1.18E-01 8.29E-10 69 J1813-346 2 - 10 3.8E-02 2.51E-10 70 J011-7316 2 - 10 1.98E-02 1.28E-10 701 J1845+051 2 - 10 4.76E-02 3.08E-10 702 J0537-7034 2 - 10 1.24E-02 8.04E-1 703 J1746-2903 2 - 10 4.0E-04 2.59E-12 704 J1747-2852 2 - 10 1.56E-02 1.01E-10 705 J0501+146 2 - 10 1.4E+01 9.32E-08 706 J1845-0434 2 - 10 3.20E-04 2.05E-12 707 J0356-3641 2 - 10 1.24E-03 8.04E-12 708 J0242-00 2 - 10 2.40E-03 1.5E-1 709 J0947-3056 2 - 10 7.60E-03 4.92E-1 710 J1235-3954 2 - 10 4.0E-03 2.59E-1 71 J1305-4928 2 - 10 4.0E-03 2.59E-1 712 J1325-4301 2 - 10 2.50E-02 1.62E-10 713 J2318-422 2 - 10 8.0E-03 5.18E-1 714 J129+0203 2 - 10 3.54E-02 2.29E-10 715 J174-2916 2 - 10 6.64E-03 4.30E-1 716 J1750-3412 2 - 10 1.76E-03 1.14E-1 536 717 J0153+742 718 J0439-6809 719 J1905-0142 720 J1930+1852 2 - 10 2.16E-04 1.70E-12 721 J023-7204 2 - 10 2.71E-08 1.75E-16 72 J024-7204D 2 - 10 1.36E-07 8.78E-16 723 J024-7205 2 - 10 2.71E-07 1.75E-15 724 J024-7204F 2 - 10 2.16E-07 1.39E-15 725 J024-7204G 2 - 10 8.58E-08 5.54E-16 726 J024-7204H 2 - 10 8.58E-08 5.54E-16 727 J024-7204I 2 - 10 1.08E-07 6.97E-16 728 J023-7203 2 - 10 1.36E-07 8.78E-16 729 J024-7204L 2 - 10 1.71E-07 1.1E-15 730 J023-7205 2 - 10 8.58E-08 5.54E-16 731 J024-7204N 2 - 10 1.08E-07 6.97E-16 732 J024-7204O 2 - 10 2.71E-07 1.75E-15 73 J024-7204Q 2 - 10 8.58E-08 5.54E-16 734 J024-7204S 2 - 10 1.08E-07 6.97E-16 735 J024-7204T 2 - 10 6.82E-08 4.40E-16 736 J024-7203 2 - 10 1.36E-07 8.78E-16 737 J1740-5340 2 - 10 4.64E-06 3.34E-14 738 J225+6535 2 - 10 1.57E-06 1.08E-14 739 J2043+2740 2 - 10 1.23E-06 8.96E-15 740 J0630-2834 2 - 10 4.49E-06 2.5E-14 741 J1817-3618 2 - 10 1.60E-07 1.03E-15 742 J059-723 2 - 10 1.43E-04 1.12E-12 743 J047-7312 2 - 10 7.70E-04 6.51E-12 74 J051-7310B 2 - 10 1.05E-03 6.78E-12 745 J051-7310C 2 - 10 8.49E-04 5.50E-12 746 J05-7242 747 J05-7210 748 J054-7245 2 - 10 1.05E-04 6.72E-13 749 J053-727 750 J05-7238 2 - 10 7.08E-05 4.53E-13 751 J053-7249 2 ? 10 5.75E-03 4.51E-1 752 J184-0257 753 J1859+0815 2 ? 10 3.12E-02 2.0E-10 754 J0420-502 2 - 10 1.7E-04 1.13E-12 75 J154-5645 2 ? 10 1.92E-02 1.23E-10 756 J1740-2847 2 ? 10 3.76E-04 3.47E-12 757 J1605+3249 2 - 10 8.41E-04 5.31E-12 758 J1308+2127 2 - 10 2.6E-04 1.68E-12 759 J0806-412 2 - 10 3.21E-04 2.03E-12 537 B.4 Catalogue Specific References The reference articles and databases utilized specificaly by the XNAVSC are provided in Table B-5. There are a total of 54 references used within this catalogue. These reference numbers are those that pertain specificaly to the XNAVSC and are not to be confused with the numbers of the references used for this disertation. Table B-5. XNAVSC References. XNAVSC Reference Number Reference Citation [1] Becker, W., and Tr?mper, J., "The X-ray luminosity of rotation-powered neutron stars," Astronomy and Astrophysics, Vol. 326, October 197, p. 682-691. [2] Liu, Q. Z., van Paradijs, J., and van den Heuvel, E. P. J., "A catalogue of low-mas X-ray binaries," Astronomy and Astrophysics, Vol. 368, March 201, p. 1021-1054. [3] Liu, Q. Z., van Paradijs, J., and van den Heuvel, E. P. J., "A catalogue of high-mas X-ray binaries," Astronomy and Astrophysics Suplement Series, Vol. 147, November 200, p. 25-49. [4] ATNF, "ATNF Pulsar Catalogue," [online database], Australian Telescope National Facility, URL: htp:/ww.atnf.csiro.au/research/pulsar/psrcat/ [cited 2 December 203]. [5] Princeton, "Princeton University Pulsar Group Pulsar Catalog," [online database], Princeton University, URL: htp:/pulsar.princeton.edu/pulsar/catalog.shtml [cited 4 May 203]. [6] Kim, Y. H., X-ray Source Tables, Sadleback Colege, 202 (unpublished). [7] Riter, H., and Kolb, U., "Catalogue of cataclysmic binaries, low-mas X-ray binaries and related objects (Sixth edition)," Astronomy and Astrophysics Suplement Series, Vol. 129, April 198, p. 83-85. [8] Singh, K. P., Drake, S. A., and White, N. E., "RS CVn Versus Algol-Type Binaries: A Comparative Study of Their X-Ray Emision," Astronomical Journal, Vol. 11, No. 6, June 196, pg. 2415. [9] Meregheti, S., "The Zo of X-ray Pulsars," Frontier Objects in Astrophysics and Particle Physics, Vulcano Workshop, Italian Physical Society, Eds. F. Giovaneli and G. Manochi, Vulcano, Italy, 21-27 May 200, pg. 239. [10] Corbet, R., Coe, M., Edge, W., Laycock, S., Markwardt, C., and Marshal, F. E., "X-ray Pulsars in the SC," [online database], URL: htp:/lheaww.gsfc.nasa.gov/users/corbet/pulsars/ [cited 30 October 204]. [1] Posenti, A., Ceruti, R., Colpi, M., and Meregheti, S., "Re-examining the X-ray versus spin-down luminosity corelation of rotation powered pulsars," Astronomy and Astrophysics, Vol. 387, June 202, p. 93-102. [12] Remilard, R. A., Swank, J., and Strohmayer, T., "XTE J0929-314," International Astronomical Union Circular, Vol. 7893, May 202, pg. 1. [13] Markwardt, C. B., and Swank, J. H., "XTE J1751-305," International Astronomical Union Circular, Vol. 7867, April 202, pg. 1. [14] Markwardt, C. B., Juda, M., and Swank, J. H., "XTE J1807-294," International Astronomical Union Circular, Vol. 8095, March 203, pg. 2. [15] Kraus, M. I., Dulighan, A., Chakrabarty, D., van Kerkwijk, M. H., and Markwardt, C. B., "XTE J1814-38," International Astronomical Union Circular, Vol. 8154, June 203, pg. 3. 538 [16] Meliani, M. T., "A Catalogue of X-ray sources in the sky region betwen delta = -73deg. and delta = +27 deg," Publications of the Astronomical Society of Australia, Vol. 16, August 199, p. 175-205. [17] Lamb, R. C., Prince, T. A., Macomb, D. J., and Majid, W. A., "CXOU J01043.1-72134," International Astronomical Union Circular, Vol. 820, October 203, pg. 1. [18] Camilo, F., Lorimer, D. R., Bhat, N. D. R., Gothelf, E. V., Halpern, J. P., Wang, Q. D., Lu, F. J., and Mirabal, N., "Discovery of a 136 Milisecond Radio and X-Ray Pulsar in Supernova Remnant G54.1+0.3," Astrophysical Journal, Vol. 574, July 202, p. L71-L74. [19] Camilo, F., Manchester, R. N., Gaensler, B. M., Lorimer, D. R., and Sarkisian, J., "PSR J124-5916: Discovery of a Young Energetic Pulsar in the Supernova Remnant G292.0+1.8," Astrophysical Journal, Vol. 567, March 202, p. L71-L75. [20] Meregheti, S., Bandiera, R., Bochino, F., and Israel, G. L., "BepoSAX Observations of the Young Pulsar in the Kes 75 Supernova Remnant," Astrophysical Journal, Vol. 574, August 202, p. 873-878. [21] Pivovarof, M. J., Kaspi, V. M., Camilo, F., Gaensler, B. M., and Crawford, F., "X-Ray Observations of the New Pulsar-Supernova Remnant System PSR J119-6127 and Supernova Remnant G292.2-0.5," Astrophysical Journal, Vol. 54, June 201, p. 161-172. [2] Becker, W., and Tr?mper, J., "The X-ray emision properties of milisecond pulsars," Astronomy and Astrophysics, Vol. 341, January 199, p. 803-817. [23] Grindlay, J. E., Camilo, F., Heinke, C. O., Edmonds, P. D., Cohn, H., and Luger, P., "Chandra Study of a Complete Sample of Milisecond Pulsars in 47 Tucanae and NGC 6397," Astrophysical Journal, Vol. 581, December 202, p. 470-484. [24] Freire, P. C., Camilo, F., Lorimer, D. R., Lyne, A. G., Manchester, R. N., and D'Amico, N., "Timing the milisecond pulsars in 47 Tucanae," Monthly Notices of the Royal Astronomical Society, Vol. 326, September 201, p. 901-915. [25] Kuiper, L., and Hermsen, W., "X-ray and Gama-ray Observations of Milisecond Pulsars," X-ray and Gama-ray Astrophysics of Galactic Sources, 8 December 203. [26] Nicastro, L., Cusumano, G., L?hmer, O., Kramer, M., Kuiper, L., Hermsen, W., Mineo, T., and Becker, W., "BepoSAX Observation of PSR B1937+21," Astronomy and Astrophysics, Vol. 413, January 204, p. 1065-1072. [27] Zavlin, V. E., and Pavlov, G. G., "X-Ray Emision from the Old Pulsar B0950+08," Astrophysical Journal, Vol. 616, November 204, p. 452-462. [28] D'Amico, N., Posenti, A., Manchester, R. N., Sarkisian, J., Lyne, A. G., and Camilo, F., "An Eclipsing Milisecond Pulsar with a Posible Main-Sequence Companion in NGC 6397," Astrophysical Journal, Vol. 561, November 201, p. L89-L92. [29] Galoway, D. K., Chakrabarty, D., Morgan, E. H., and Remilard, R. A., "Discovery of a High-Latitude Acreting Milisecond Pulsar in an Ultracompact Binary," Astrophysical Journal, Vol. 576, September 202, p. L137-L140. [30] Markwardt, C. B., Smith, E., and Swank, J. H., "XTE J1807-294," International Astronomical Union Circular, Vol. 8080, February 203, pg. 2. [31] Markwardt, C. B., and Swank, J. H., "XTE J1814-38," International Astronomical Union Circular, Vol. 814, June 203, pg. 1. [32] Majid, W. A., Lamb, R. C., and Macomb, D. J., "X-Ray Pulsars in the Smal Magelanic Cloud," Astrophysical Journal, Vol. 609, July 204, p. 13-143. [3] Lamb, R. C., Macomb, D. J., Prince, T. A., and Majid, W. A., "Discovery of 16.6 and 25.5 Second Pulsations from the Smal Magelanic Cloud," Astrophysical Journal, Vol. 567, March 202, p. L129-L132. [34] Laycock, S., Corbet, R. H. D., Perodin, D., Coe, M. J., Marshal, F. E., and Markwardt, C., "Discovery of a new transient X-ray pulsar in the Smal agelanic Cloud," Astronomy and Astrophysics, Vol. 385, April 202, p. 464-470. [35] Gaensler, B. M., Gothelf, E. V., and Vasisht, G., "A New Supernova Remnant Coincident with the Slow X-Ray Pulsar AX J1845-0258," Astrophysical Journal, Vol. 526, November 199, p. L37-L40. [36] Marshal, F. E., in 't Zand, J. J. M., Strohmayer, T., and Markwardt, C. B., "XTE J1859+083," International Astronomical Union Circular, Vol. 7240, August 199, pg. 2. 539 [37] Lamb, R. C., Prince, T. A., Macomb, D. J., and Finger, M. H., "RX J052.1-7319," International Astronomical Union Circular, Vol. 7081, January 199, pg. 4. [38] Haberl, F., Pietsch, W., and Motch, C., "RX J0420.0-502: an isolated neutron star candidate with evidence for 2.7 s X-ray pulsations," Astronomy and Astrophysics, Vol. 351, November 199, p. L53-L57. [39] Takeshima, T., Marshal, F. E., and in 't Zand, J., "XTE J1543-568," International Astronomical Union Circular, Vol. 7369, February 200, pg. 2. [40] Sakano, M., and Koyama, K., "AX J1740.2-2848," International Astronomical Union Circular, Vol. 7364, February 200, pg. 2. [41] Motch, C., Haberl, F., Zickgraf, F. J., Hasinger, G., and Schwope, A. D., "The isolated neutron star candidate RX J1605.3+3249," Astronomy and Astrophysics, Vol. 351, November 199, p. 17-184. [42] Schwope, A. D., Hasinger, G., Schwarz, R., Haberl, F., and Schmidt, M., "The isolated neutron star candidate RBS123 (1RXS J130848.6+212708)," Astronomy and Astrophysics, Vol. 341, January 199, p. L51-L54. [43] Haberl, F., Motch, C., and Pietsch, W., "Isolated Neutron Stars in the ROSAT Survey," Astronomische Nachrichten, Vol. 319, January 198, pg. 97. [4] Campana, S., Ravasio, M., Israel, G. L., Mangano, V., and Beloni, T., "XM-Newton Observation of the 5.25 ilisecond Transient Pulsar XTE J1807-294 in Outburst," Astrophysical Journal, Vol. 594, September 203, p. L39-L42. [45] Strohmayer, T. E., Markwardt, C. B., Swank, J. H., and in't Zand, J., "X-Ray Bursts from the Acreting Milisecond Pulsar XTE J1814-38," Astrophysical Journal, Vol. 596, October 203, p. L67-L70. [46] Chakrabarty, D., and Morgan, E. H., "The two-hour orbit of a binary milisecond X-ray pulsar," Nature, Vol. 394, 23 July 198, p. 346-348. [47] Wijnands, R., "An XM-Newton Observation during the 200 Outburst of SAX J1808.4- 3658," Astrophysical Journal, Vol. 58, May 203, p. 425-429. [48] Markwardt, C. B., Swank, J. H., Strohmayer, T. E., in 't Zand, J. J. M., and Marshal, F. E., "Discovery of a Second Milisecond Acreting Pulsar: XTE J1751-305," Astrophysical Journal, Vol. 575, August 202, p. L21-L24. [49] Karet, P., Marshal, H. L., Aldcroft, T. L., Graesle, D. E., Karovska, M., Muray, S. S., Rots, A. H., Schulz, N. S., and Seward, F. D., "Chandra Observations of the Young Pulsar PSR B0540-69," Astrophysical Journal, Vol. 546, January 201, p. 159-167. [50] Kirsch, M. G. F., Mukerje, K., Breitfelner, M. G., Djavidnia, S., Freyberg, M. J., Kendziora, E., and Smith, M. J. S., "Studies of orbital parameters and pulse profile of the acreting milisecond pulsar XTE J1807-294," Astronomy and Astrophysics, Vol. 423, August 204, p. L9-L12. [51] Miler, J. M., Wijnands, R., M?ndez, M., Kendziora, E., Tiengo, A., van der Klis, M., Chakrabarty, D., Gaensler, B. ., and Lewin, W. H. G., "XM-Newton Spectroscopy of the Acretion-driven Milisecond X-Ray Pulsar XTE J1751-305 in Outburst," Astrophysical Journal, Vol. 583, February 203, p. L9-L102. [52] Wijnands, R., and van der Klis, M., "A milisecond pulsar in an X-ray binary system," Nature, Vol. 394, 23 July 198, p. 34-346. [53] White, N. E., and Zhang, W., "Milisecond X-Ray Pulsars in Low-mas X-Ray Binaries," Astrophysical Journal, Vol. 490, November 197, pg. L87. [54] Nice, D. J., and Thorset, S. E., "Pulsar PSR 174-24A - Timing, eclipses, and the evolution of neutron star binaries," Astrophysical Journal, Vol. 397, September 192, p. 249-259. 540 Apendix C TOA Observations and Spacecraft Orbit Data C.1 ARGOS Barycentered and Non-Barycentered TOAs Information is provided on several observations of the Crab Pulsar made by the USA experiment on ARGOS. A discussion is provided on how to create phase diference measurements using an observation at the vehicle where position is unknown. Table C-1 provides a list of Crab Pulsar observations, as wel as the TOA for each observation measured by transfering the photon arival times to the SB using the ARGOS navigation information. Table C-2 provides the measured TOAs for the same observations but asuming the position of the spacecraft is located at the geocenter. No spacecraft navigation information is used to produce these geocenter-based TOAs, only Earth position relative to SB and the recorded arival time of photons at the spacecraft. The table also provides measured TOAs for this set of observations at ARGOS, where no time transfer at al is used to correct the photon arival times. The TOAs listed in these tables were created by comparing the folded profile to the standard template profile of the Crab Pulsar. 541 Table C-1. Crab Pulsar Observations by USA on ARGOS. Observation Number Observation Date Duration (s) SB Barycentered TOA (MJD) Expected Eror (10 -6 s) 1 199 Nov 28 13:13:14.67 1209.635954 51510.56987267372 3.73 2 199 Dec 18 12:38:56.03 382.659762 51530.53426842310 1.25 3 199 Dec 19 08:54:05.78 483.57335 51531.372976203982 9.98 4 200 Jan 03 13:29:45.06 381.74501 51546.56843761956 14.5 5 200 Jan 03 15:09:48.94 462.948790 51546.637924843878 10.13 6 200 Jan 03 16:50:0.20 48.67547 51546.707502185379 13.92 Table C-2. Geocenter-Based TOAs and ARGOS-Based TOAs. Observation Number Geocenter to SB TOA (MJD) Expected Eror (10 -6 s) No Time Transfer TOA (MJD) Expected Eror (10 -6 s) 1 51510.5698466872 1.14 51510.51607240106 25.62 2 51530.534242540 34.9 51530.52784013696 17.81 3 51531.372974026506 7.93 51531.371643466494 15.98 4 51546.56843401846 17.32 51546.563075878172 41.62 5 51546.6379249412712 24.02 51546.632593182410 6.14 6 51546.7075018385294 37.95 51546.702138708969 29.60 The data in Table C-1 and Table C-2 provide information on TOAs created using diferent asumptions of detector location. It can be sen that these TOAs have large expected erors, which would result in large position estimate erors. This may be a result of the pulse template being defined for the SB and not at either the geocenter or the ARGOS positions. The TOAs for the geocenter are known to be in eror since the pulses were detected on the vehicle and not at Earth-center, so these values must be corrected for this offset eror. Since this eror is related directly to the offset of the vehicle position with respect to Earth, determining this diference provides the desired position. Below is a series of steps that corrects the above information to determine acurate position. - Compute geocenter to SB TOA using SB template: GE - Using pulsar template model, determine any phase fraction betwen TOA and integer cycle: !=" G #ound E 542 - Determine number of cycles, such as: o Asume N GEO =0 o Use spacecraft near Earth: N GEO =?1 o Use other methods within disertation to determine ambiguous cycles - Correct geocenter-based TOA to SB TOA: TOA SSB ! GEO coretd =TA GEO "N+# GEO () P - Using non-time transfered profile on spacecraft determine TOA at spacecraft: SC =MJD0 NoBary # NoBary - Determine delta-time from these measurements and compare to position: dt SC = ? n! /E GE cretd " SC () ? n! E Improved results for the above were found when modifying the spacecraft TOA by: SC =MJD0 NoBary !"# NoBary +$ GEO P () This is not completely understood at this time, but may be related to methods of determining the geocenter-based TOA. Table C-3 provides data used to correct the TOAs for the above observations. The values of the unknown cycles, N, were chosen by hand for these single pulsar examples. An actual system would have to determine these using the methods described in this disertation. Using the known location of Earth at the TOA time, the diference of these two arival times can be compared to determine the phase diference betwen the two locations. Since ARGOS navigation provides this data directly, this can be compared to 543 the computed results. Table C-4 provides this data, along with the measured Doppler efect ? n!v E () , which indicates amount of smearing of pulse profile at spacecraft and potential quality of phase diference measurement. The table shows that Doppler efect can afect the measured results. However, observation #4 shows very large Doppler, but fairly smal erors. Observation #3 provides the best results and has the least expected eror in al the TOA measurements of Table C-1 and Table C-2. The TOAs with large expected eror may contribute to the erors computed in Table C-4. The least confident algorithm is the expresion for the TOA SC , since Earth position is known wel, and TOA GE coretd compared wel with the true TOA values from Table C-1. Additional research should be completed to determine the correct computation of this value. Barycentered pulse timing models were used in these tests. In future work, creating models that exist at the geocenter and using an inertial frame origin at geocenter may reduce erors and computations. Table C-3. Corrected TOAs and Integer Cycles. Observation Number Cycles T GEO coretd (MJD) TOA SC (MJD) 1 -1 51510.569872404 51510.516071616 2 -1 51530.534268298 51530.5278432857 3 -1 51531.3729761945 51531.3716434235 4 -1 51546.5684376143 51546.56307617072 5 0 51546.6379248415 51546.6325964142 6 -1 51546.70750218459 51546.7021389849 Table C-4. Comparison of Measured and Actual Phase Diferences. Observation Number Dopler Efect (km/s) !" mas !" ruth Phase Eror Range Eror (km) 1 1.37 -0.413535276084 -0.32839378530425 0.085 85 2 -1.4 -0.313727346821 -0.4293876182579 -0.16 -161 3 0.126 -0.418673125163 -0.4197469432832 0.008 -9 4 -4.74 -1.069151353274 -1.062342726745 0.069 69 5 -4.78 -0.398706872268 -0.0176753121523 38 3828 6 -4.7 -0.9482050191436 -0.90815067628982 0.040 402 544 C.2 Spacecraft Orbit Data The Two-Line Element (TLE) sets provided by NORAD were used to determine spacecraft orbit information for various sections of this disertation [97]. The TLE sets used during the disertation analysis are provided below. ARGOS 1 25634U 99008A 99360.46769266 .00000242 00000-0 13979-3 0 2228 2 25634 98.7653 305.9904 0010182 97.0149 263.2181 14.17835610 43356 LAGEOS-1 1 08820U 76039A 03365.88757026 -.00000010 00000-0 10000-3 0 248 2 08820 109.8375 249.2939 0044229 259.2681 100.3073 6.38664526389689 GPS Block IA-16 PRN-01 1 22231U 92079A 04341.32034493 -.00000065 +00000-0 +00000-0 0 01957 2 22231 056.2538 046.2019 0061186 264.6021 094.7448 02.00570114088222 DirecTV 2 (DBS 2) 1 23192U 94047A 05002.12423223 -.00000093 +00000-0 +10000-3 0 06272 2 23192 000.0210 096.9411 0001908 193.3646 115.4913 01.00271524048246 Orbit information of the LRO?s planned mision was provided by Dave Folta and Mark Beckman of NASA GSFC. This data is preliminary information for a mision planned to be launched and orbit the Moon in 2008. Below is the first epoch in the data file, which provides ECI position and velocity information of the vehicle in its orbit about the Moon. 545 LRO Time: 1 Jun 2008 12:00:00.000 Position (m): 280653.751729 192906.946167 116373.703572 Velocity (m/s): 0.130996 1.297566 -0.995554 546 Apendix D State Dynamics and Kalman Filter Equations D.1 State Dynamics and Observations The following sections provide a description of a system of equations representing time-varying state variables x= ! t () x 1 , 23, "x n {} , where x is the vector of individual states, x i . The time-dependent dynamics of this system ay be represented as linear or non-linear based upon the physical nature of the system. Equations for both types of systems are discused. For systems where the chosen state variables are represented as the whole value states, dynamics necesary to describe the propagation of the erors within the states is also presented. External observations that are used to correct estimated values of the whole value states, as wel as determine any erors asociated with these states, are presented. A summary of al the dynamics of the states, their erors, and their observations is provided at the end of this section [65, 189]. D.1.1 Linear System Equations D.1.1.1 State Dynamics Given a set of states, , which are the whole value of each state that vary linearly with time, the dynamics over time can be represented as follows [39, 65, 176], !x () =At () +Btu () N! () (D.1) 547 In Eq. (D.1), !x=dt () dt represents the first time derivative of each state. Higher order derivatives can be included in the system by continualy introducing state variables that represent the first order derivative of another variable, such that only first order equations are represented. An example of this is the aceleration of a body. The position of the body is typicaly of interest, and position can be chosen as a state variable. In order to expres the dynamics of a body, its aceleration in an inertial frame relating the motion of the body to the external forces is required. If velocity is introduced as a second set of state variables, then the first time derivative of velocity is aceleration, and the first time derivative of position is velocity. Thus, choosing position and velocity as the state variables, the full motion of the body can be represented as a first order system of equations. The remaining terms in Eq. (D.1) are as follows. At () is the matrix that linearly maps the dynamics of the state variables, !x , with each state. The ut () vector is the control input vector, determined by the system?s available control parameters, and Bt () is the matrix that maps these input variables into the state dynamics. The ! vector is the random forcing function, or noise, which may be afecting the system, and N () is the matrix that maps this noise into the state variables. Eq. (D.1) represents the full linear dynamics of the whole value states. This system of equations can be integrated, either analyticaly or numericaly, to determine the solution of the states with respect to time. 548 D.1.1.2 Observations If external observations, or measurements, are provided and are observable, the relationship of this observation vector, yt () , to the state variables can be represented as, yt () =Cx+DuMt () !+"t () (D.2) In this equation, is the matrix that linearly maps the states into the observations, the Dt () matrix maps the control input vector into the observations, t () maps the state noise into the observations, and the vector !t () is the measurement noise asociated with each observation. The linear system represented by Eqs. (D.1) and (D.2) describes the full dynamics and observations of a system. With these two equations, a system is said to be in state- space form. D.1.1.3 State Erors If a system includes erors asociated with the estimated values, whether known or unknown, then the state erors can also be represented by the dynamics and observations equations. Asuming the state vector x () is the true value of the states, then the estimated values of these states are represented using the symbol, !x () , a tilde over the state. The erors of the estimated states with respect to the true state values are then writen as !x () . Since the erors are asumed smal, they relate estimates to the true values in a linear fashion as in, x () =!+x () (D.3) (Note that some texts and articles use capital ?x?, X , to represent whole value states, and smal ?x? to represent the eror-states. This can get confusing when writing these 549 equations by hand, or when reading some smal fonts. To avoid confusion, xt () wil refer to the whole value states, and an explicit !xt () wil be used to represent the eror in the states.) D.1.1.3.1 Eror-State Dynamics Taking the derivative of Eq. (D.3) with respect to time yields, !xt () ="+!xt () (D.4) The dynamics of the erors within the states can be found by substituting Eq. (D.4) into Eq. (D.1), such that, !xt () =At" () ! xt# $ % & +t () xBt () u+Nt () ' (D.5) In many operational cases, the term in brackets may be estimated as zero, and the eror- states equation reduces to, ! " (D.6) D.1.1.3.2 Eror-State Observations In order to proces observations using eror-states, a measurement residual is introduced that is the diference of observation and whole value states as, z () =y!C () x (D.7) Therefore, using Eq. (D.2) the full measurement residual equation is, zt () Dut () +Mt () "t (D.8) By using the estimated and eror-states, this measurement residual equation can be writen as, zt () =y!Ct () x "+Dut () Mt# () +$t (D.9) 550 D.1.2 Non-Linear System Equations The previous section presented algorithms that represent systems where the states vary linearly with respect to their dynamics and observations. For many real-world systems however, this relationships is actualy non-linear, and cannot be acurately represented by the state-space form of Eqs. (D.1) and (D.2). This is often the case when the dynamics is a function of the states in a complex manner [ex. !x j = i 2 , j cosx i () ]. This section provides method to represent these non-linear systems in forms that can be solved without the use of complicated non-linear techniques [98]. Asume the non-linear system can be represented by the state vector and input control vector as, !xt () = " ft () ,ut () +! () (D.10) In this equation, ! f is a non-linear function of the state vector and control input vector, and perhaps time. The second term in Eq. (D.10) is the noise asociated with the state dynamics. To begin the eror-state analysis, asume that there is zero control input, u0 , and the noise is negligible, ! () "0 . Using the estimated state vector and the eror-states as in Eq. (D.4), the non-linear dynamics of Eq. (D.10) can be expanded in Taylor series form about the estimated state as he ollowing, !x="+! # f"x () f !+ 1 2 " # fx () ! 2 +H.OT (D.11) In this equation, H.O.T. refers to higher-order terms within the Taylor series expansion that can be combined together or ignored with aceptable truncation eror. Terms of second order and higher can be expresed [160], 551 1 2! f"x () 2 +H.OT= 1 ! 2 f i x jk " jk 3 f i jkm x jk +# (D.12) Asuming second and higher-order terms are al represented as ! , the eror-state dynamics for a non-linear system can then be writen from Eqs. (D.11) as, !x= "f# () + (D.13) To further solve the eror-state dynamics, introduce the eror-state dynamics matrix, F , refered to as the Jacobian matrix, as F () = !"x (D.14) such that the eror-state dynamics from Eq. (D.13) is represented as, !x=Ft () +" (D.15) To find the solution to Eq. (D.15) and the relationship of the F matrix, first asume no noise, !=0 , and a solution of the form, !x="t 0 () (D.16) In this expresion, the state transition matrix, , represents the dynamics of the eror- states from 0 . Using Eqs. (D.13) through (D.16), this dynamics can be represented as, !t, 0 () t, 0 () ! # Ft, 0 (D.17) Here the time derivative of the initial eror-states is asumed smal !x"0 () . The eror- state-transition matrix can then be represented from Eq. (D.17) as, 552 ! t, 0 () =Ft () , 0 () I (D.18) Other important identities for the state-transition matrix are, , 0 () = "1 0 , () k+1k+k0 ) (D.19) D.1.2.1 Truncated Eror Terms In the above analysis, higher-order Taylor series terms, as wel as the noise, of each state was asumed zero during the dynamics. For some systems this asumption can produce truncation eror, which can be potentialy significant. Asuming these higher order terms are constant over smal time steps, !" , their solution from Eq. (D.13) becomes, !x H.OT ="# (D.20) A more general expresion for these terms can be expresed as [213], " t 0 # ,$dt (D.21) The term ! is refered to as the proces noise and represents the uncertainty in the eror- state dynamics. D.1.2.2 Eror-State Dynamics The full dynamics of the eror-states can be expresed in linear form using Eqs. (D.13) through (D.21) as, !x () =F+LtuGt" () (D.22) The matrix L () represents the mapping of the control input variables into the dynamics of the eror-states, in which case, 553 Lt () = !f"x u (D.23) In this equation, matrix Gt () has been added for completenes, specificaly for situations where proces noise is connected to diferent states. D.1.2.3 Eror-State Discrete Dynamics The above algorithms are sufficient for continuous systems, where time varies continuously from one time point to the next. In many systems, especialy real-time operating systems, discrete time points are utilized for procesing loops. For these discrete time-step systems, the dynamics and observations must be valid from one time point to another. Using the second identity in Eq. (D.19), the eror-state dynamics can be writen in a common form used in discrete time systems, !xt k+1 () ="t k+1 , () !xt k ( (D.24) Given the eror-state vector estimate a time point t k , Eq. (D.24) can be used to determine the dynamics betwen k in order to compute the eror-state vector estimate at time point t k+1 . By similarly determining the discrete time dynamics of the remaining terms in Eq. (D.22), the following equation represents the full dynamics of the eror-state in discrete time, !x k+1 =" k+1 , () k # k+1 t () k $t k+1 ,% k (D.25) In Eq. (D.25), a notation simplification is used for !x k = k . k+1 , and ! k+1 , () are the discrete time representations of the continuous matrices G and L from t k , respectively. 554 For a non-linear system the state-transition matrix is determined using numerical integration of its dynamics from Eq. (D.18). However, in the cases where the system is near-linear approximations to the integration can be made to the dynamics when the Jacobian matrix F can be considered constant over the integration interval !t= k+1 "t such that !t k+1 , () =e F"t #I+t 1 2! F"t [] 2 + 3! t [] 3 (D.26) Use of Eq. (D.26) must be carefully considered to insure valid results from this approximation. D.1.2.4 Measurement Using Eror-States Similar to the state dynamics, the observations may also have a non-linear relationship with the whole-value states and the control input vector. Thus the measurement may have the following representation, yt ( = ! hxt () ,ut () +! () (D.27) In this equation, ! h is a non-linear function of the state vector and control input vector, and perhaps time. The measurement noise asociated with each observation is represented as ! . Using the estimated and eror-states as in Eq. (D.3), the measurement of Eq. (D.27) can be represented using Taylor series expansion as, yt () = ! h"x+ () 1 2! h"x () 2 +H.OT#t () (D.28) Using the representation of the measurement diference as in Eq. (D.7) and only the first order terms from Eq. (D.28) yields, 555 zt () =y!h"x () ! #+$t () (D.29) Thus, a new matrix of measurement partial derivatives can be introduced as, H!x () = " h (D.30) The measurement diference can therefore be writen as, zt () =H!x+"t () (D.31) This measurement diference, , is often refered to as the measurement residual. This can be represented in discrete form as, k+1k1k (D.32) 556 D.1.3 Dynamics Summary This section provides a summary of the state-space form of the above dynamics and observations, for both linear and non-linear systems. The terms that are continuous functions of time have their t () dropped for simplicity. Linear Systems Whole Value States !x=A+BuN y=Cx+DuM" Eror-States !x=A" ! # $ % & +xBuN' zCDuM( Non-Linear Systems Whole Value States !x= " f,ut () + yh! Eror-States FLuG H Discrete Systems !x=F"t, 0 () !x k+1k+1k #t k+1 , () u k $t k+1 , () % k zH& 557 D.2 Kalman Filter Equations This section describes the procesing algorithms of the Kalman filter. This type of filter can be used to blend the dynamics of a set of variables with their observations in a recursive, or repeated sequentialy, manner. Based upon the dynamics and the estimated knowledge of acuracy within the system, an optimal gain can be determined that is used to generate corrections to the state variables [29, 65, 91, 213, 221, 237]. A discussion on probability and statistics that is needed for the Kalman filter equation derivations is presented first. The discrete Kalman filter is presented next, and then the continuous Kalman filter algorithms follow. Subsets of each form are presented, which depend on the known dynamics of the system. It is interesting to note that the discrete form of the Kalman filter was developed prior to the continuous form, whereas most analytical proceses are developed in the reverse order. This is because for many practical applications only the discrete form is realy applicable. The continuous form is presented here for completenes. The spacecraft navigation Kalman filter, discussed within the disertation, utilizes the discrete form of the filter. D.2.1 Random Variables and Statistics Take X to be a random variable, a variable that can take on a random set of values. The value of this variable is recorded for N diferent samples. The sample average, or sample mean, of this random variable is expresed as [29], X= 1 + 23 !+X N = 1 i i (D.33) 558 Here the over-bar of the variable represents this average, or mean. For an infinite number (or large amount) of samples, the random variable could have n possible realizable values of x 1 , 23 !,x n . For each sample there is an asociated probability, p i , that it wil be chosen, such that over N trials there is an expected occurrence of each value of p 1 Nx ?s, 2 ?s, etc. With these values of the random variable and their probabilities, the sample average can be expresed as, X= p 1 Nx+ 2 p 3 Nx+! n N (D.34) Based on this equation, the expected value of X is can be found using the expectation operator, E , as X=Expected value of X () ! p i x =1 n " N i i=1 Dscret Form f x () dx #$ % Contnuous & ' ( ) (D.35) In the continuous form of the expectation in Eq. (D.35), f x () is known as the probability density function of X . Important properties of this function are [29], i)f x () is a non-negative function dx !" # =1 (D.36) The expectation operator, E , is refered to as the first moment of X , and represents the mean value of X . The mean expected squared value, or second moment, of is defined as [65], EX 2 () ! 1 N X i 2 i= " Discret Form xf () dx #$ % Contnuous & ' (D.37) 559 The square root of EX 2 () in Eq. (D.37) is refered to as the root mean square (RMS) of X . In discrete form, this is expresed as RMSX () =E 2 () ! 1 N X i 2 i= " (D.38) The variance of a random variable is the second moment about the mean, or a measure of dispersion (or deviation) of X about its mean [29], Varince of X=! 2 "E#X () () 2 $ % & ' (D.39) This can be expanded in terms of the expectations as, ! X 2 "E# () () 2 $ % & ' =EX 2 () # () $ % & ' 2 +EX () $ % & ' 2 = 2 () (D.40) The expresion for variance can therefore also be writen as, Varince of X=! 2 " 1 N X i 2 i= # $ i i=1 N % & ' ( ) * 2 Discret Form xE () () $+ , f x dxContnuous - . / 0 (D.41) The standard deviation of the random variable X is defined as the square root of the variance, or, ! X "Vrinc of X=! 2 (D.42) From their definitions, a relationship exists betwen the root mean square of X and its variance. From Eqs. (D.38) and (D.40), the relationship for the root mean square is the square of the sum of the variance and the mean value squared, or, RMS(X)=E 2 () X 2 () !E () " # $ % 2 ) +X () " # $ % 2 &+ (D.43) 560 D.2.2 Covariance Matrix The above representations can also be implemented when investigating the statistics of two or more random variables. The covariance betwen two random variables X and Y is the product of their deviations from their mean values as, Covariance of Xnd Y=! X 2 E" () () YE () () # $ % & X (D.44) If x is now a vector of several random variables, the mean vector, m , of this set of variables is the mean of each element as, Ex () =m (D.45) The covariance of this vector is a matrix of covariances betwen each element in the vector. This covariance matrix, P , is represented as, P=E! () () Ex () () T " # $ % =! () x T " # $ % (D.46) The covariance can also be used to represent the eror of an estimated vector of state variables relative to their true state values [65]. The covariance matrix can be writen in this case as, !x () T " # $ % ! () T " # $ % E& () T " # $ % (D.47) The covariance matrix in the form of Eq. (D.47) represents the estimates of the erors within each state, and can be used to determine how el each sate has been determined. The variance of each specific state variable within the vector x is provided along the diagonal of the covariance matrix. The standard deviation of the variances of x are from P as, d devx () =! 1 , 23 , n {} =diagP () (D.48) 561 The covariance matrix is a symmetric matrix, since ! xy = . Therefore, for al instances P= T . The covariance matrix is asociated with the states that are defined in a specified reference frame. To transform the covariance matrix into another reference frame use, P b =T a b (D.49) In Eq. (D.49), the transformation matrix transforms vectors in frame a into frame b b=T a () . D.2.3 Discrete Kalman Filter Equations Based upon the statistics discused above, the Kalman filter algorithms are presented below. The discrete form of the blending routines is presented through the development of the dynamics and measurement procesing algorithms. D.2.3.1 Covariance Dynamics Given that the covariance matrix represents the eror estimates of each state, as in Eq. (D.47), the propagation of this matrix presents the eror estimates of each state over time. Asuming there is no control input u=0 () , for the discrete form of the dynamics equation, Eq. (D.25), the covariance matrix at time k+1 can be found from, P k+1 ! =E"x () T # $ % & =E' k "x+( k ) () k "x+( k () T # $ % & kk TT ' k ' T kk #% & k "x k # $ % & T $ (D.50) The minus superscript ! () is utilized to represent the update to the covariance matrix due to time propagation only (a priori), and prior to any measurement update, which is 562 described below. In Eq. (D.50) the symbols from Eq. (D.25) have been simplified as ! k =t k+1 , () and ! k =t k+1 , () . The expectations of the eror-states and the noise are represented as, P k =E!x k T " # $ % (D.51) Q kk (D.52) The Q matrix is refered to as the proces noise matrix for the system, and is related to how wel the dynamics of the state variables are known. High proces noise is interpreted by the filter as poor knowledge of the dynamics. The noise of the individual states, ! , is asumed to be uncorrelated with respect to time (white noise). The noise is also asumed to be uncorrelated with respect to the states such that, E!x k " T # $ % & =0 (D.53) Using the terms from Eqs. (D.51)?(D.53), the dynamics of the covariance matrix from Eq. (D.50) becomes, P k+1k Q T (D.54) D.2.3.2 Measurement Update A similar approach as the covariance dynamics can be applied to the procesing of the filter?s covariance matrix estimate of state erors due to external observations, or measurements. The primary contribution of R. Kalman?s work was the computation of the optimal gain used to produce the best estimate of the new eror-states after a measurement update [91]. A simple derivation of the measurement update algorithms is presented below for both linear and non-linear systems. 563 D.2.3.2.1 Linear System Asuming zero control input, u=0 , and state noise is not observable, a measurement as in Eq. (D.2) can be represented in discrete time as, y k+1 =C k x +1 ! k (D.55) Using the estimated state, a gain, K , can be chosen that can be applied to the diference of the observation and the state-based estimate of the observation in order to correct erors within the estimate of the state. This is represented using Eq. (D.55) as, !x k+1 =K k+1 y!C k+1 x () K k+1 " (D.56) Here the plus superscript + () is used to represent the state estimates after the measurement update (a posteriori). This equation can also be represented using the measurement and eror-state expresion of Eq. (D.9) as, !x k+1 =K k+1 z=!x k+1k C +1 "x k ! K k+1 # (D.57) Using this measurement update for the estimated states, the update to the covariance matrix can be determined. The updated form of the eror estimate can be expresed as, !x k+1 ="! k+1 (D.58) The new covariance is generated based upon this eror estimate of Eq. (D.58) as, P k+1 =E!x k+1 () k T " # $ % =Ex k+1 &! () k+1 !x T " # $ % (D.59) Substituting the updated eror estimate from Eq. (D.56) and the measurement from Eq. (D.55) into this covariance update equation yields, 564 P k+1 =E x k+1 !K k+1 C"x k+1 ! # $ % & ' ( ) ! k K +1 C k "x +1 ! 1 # $ % & ' ( ) T * , - . / " k+1k+1k ! k+k+k1 ! 1 T , / (D.60) Working the expectation operator through this equation, as was done in Eq. (D.50), and asuming the a priori state-erors are uncorrelated with respect to measurement noise such that E!x k+1 " # T () =0 , yields the final relationship for a measurement update to the covariance matrix, P k+1 IK k+1 C () P k+1 ! I k+1 () T K k+1 R k+1 T (D.61) The measurement noise covariance matrix, R , is the expectation of the measurement noise, as R=E!! " # $ % & (D.62) This measurement noise is often asumed to be white noise, with zero mean, or () 0 (D.63) To determine the optimal gain for this proces, the trace of the covariance matrix of Eq. (D.61) is diferentiated with respect to the variable gain, k+1 [29, 91], as in, dtraceP k+1 () ! " # $ K =%2C k+1 P % () T 2K k+1 CP k+1 %T R k+1 () =0 (D.64) Solving this expresion yields the optimal gain as K k+1 op =P k1 ! C + T k1+ ! k1 T R k+ () !1 (D.65) This gain is often refered to as the Kalman gain. Substituting this gain back into Eq. (D.61) yields thre alternative update equations, 565 P k+1 = ! k+1 C T k+1 P ! k1 T R k+ () !1 C k P +1 (D.66) or, k + K k opt kkk () K opt T (D.67) or, P k+1 =I!K k+1 opt CP k+1 ! (D.68) The Eq. (D.68) is the most commonly used expresion for the covariance measurement update, however, al of Eqs. (D.66)?(D.68) can be used with the optimal Kalman gain. An alternative form, refered to as the Joseph?s form [65] can be used with either the optimal gain or any sub-optimal gain. This form is exactly Eq. (D.61) with any selected gain. Some filter designers also choose to implement additional terms with the system such that the memory of older measurements fades over time alowing newer measurements to be considered with equal weight. These fading memory filters help avoid ignoring important current measurements [65]. With properly modeled state dynamics and measurements, the Kalman filter should converge upon a solution after time propagation and measurement updates. However, due to poorly modeled state dynamics, or significantly high proces noise, a Kalman filter solution to the state-eror estimates can diverge away from the true solution. Proper consideration of true state dynamics, including any significant perturbation efects from nominal dynamics, as wel as true measurement models, must be maintained to reduce or eliminate the chance of filter divergence. 566 If litle or no proces noise is used with the system, procesing many high quality measurements R!smal () wil drive the covariance estimate to smal values. Very smal valued covariance estimates and low measurement noise produces a smal matrix within the parentheses of Eq. (D.65), which produces an unreliable computation of the optimal gain matrix of Eq. (D.64). This often results in les and les consideration, or weight, given to future measurements. Designing Kalman filters and selecting its parameters are often a trade-off betwen exact modeling of the dynamics and acurate representation of the proces and measurement noise while asuring al measurements are considered with the system. Some filter designers often choose to retain higher proces noise terms to avoid this isue of driving the covariance estimates to very smal values. Numerical stability of the Kalman filter equations can be a concern due to the calculation of the matrix inverse in Eq. (D.65). Several alternative forms of determining the covariance matrix, P , and the Kalman gain, K , have been developed that improve the overal stability of the Kalman filter proces. These methods primarily involve factoring these matrices into decomposed forms and procesing the filter on these new matrices. The Cholesky decomposition method creates a new matrix that is the square root of the covariance matrix [29, 65] P= T ;P (D.69) Routines for time propagation and measurement update proces the covariance square root matrix S , instead of P . Alternatively, Bierman proposes a factorization into a unit- diagonal upper-triangular matrix U , and a diagonal matrix D , such that [26], U (D.70) 567 The Kalman filter routines are writen for these factored matrices, instead of the full covariance matrix, in order to maintain numerical stability. D.2.3.2.2 Non-Linear System For a system that has non-linear dynamics or measurements, the Kalman filter routines are modified slightly from the linear case. This type of filter that takes into acount the non-linear efects is refered to as an Extended Kalman filter. The discrete form of the covariance dynamics has the same form as the linear case, as, P k+1 ! =" k T # k Q T (D.71) However, the filter measurement equations change slightly due to the diferent observation matrix, H , for a non-linear system. The state update equation (a posteriori) becomes from Eq. (D.32) and (D.57) !x k+1 =K k+1 z=!x k+1k H +1 "x k ! K k+1 # (D.72) The optimal Kalman gain also changes to, k+1 opt =P k1 ! H + T k1+ ! k1 R k+ () !1 (D.73) This changes the covariance update equation from Eq. (D.68) to P k+1 =I! k+1 opt ( P k+1 ! (D.74) The Joseph?s form of this update becomes, k+1 I k () k IK k () k K k+1 T (D.75) 568 D.2.4 Continuous Kalman Filter Equations The continuous form of the Kalman filter routines is diferent from the discrete form, primarily through the realization of the time propagation routines. These are presented below for both the linear and non-linear systems. D.2.4.1.1 Linear System The continuous form of the time propagation for the covariance matrix of a linear system is refered to as the linear variance equation [65]. This is represented as, ! Pt () =At () +Pt () T NtQ () t T ;Pt 0 () = (D.76) The Kalman gain is determined to be, Kt () =Ct () T R !1 (D.77) The measurement equation of the covariance is a blend of the Eqs. (D.76) and (D.77), ! Pt () =At () +Pt () T NtQ () t T C T R !1 (D.78) This is refered to as the matrix Ricatti equation. D.2.4.1.2 Non-Linear System For a continuous non-linear system, the Kalman filter equations are changed from Eqs. (D.76)-(D.78) due to the diferent dynamics and observations matrices. For time propagation, the covariance update is [65], ! P () =F () +Pt () T GtQ () T ;Pt 0 = (D.79) The Kalman gain equation becomes, K () =tH () T Rt !1 (D.80) The measurement equation for the non-linear system case is then, 569 ! Pt () =Ft () +Pt () T GtQ () t T HR !1 (D.81) D.2.5 Measurement Testing Although most observations, or measurements, are asumed valid, spurious or eroneous measurements may occur due to sensor malfunction or data procesing isues. If these eroneous measurements are improperly tagged with a measurement noise that appears to show optimistic performance, the procesing of these eroneous measurements through the Kalman filter can severely impact the filter?s performance. It is prudent to test individual measurements prior to their incorporation into the filter to avoid these negative situations. A method to test an individual measurement is to use the filter?s estimate of its performance to evaluate a measurement. If the filter ?believes? it is performing wel, by having reduced covariance values, out-lying measurements that are many times the filter?s own estimate of its performance can be ignored. The innovations of the filter are determined from the optimal Kalman gain calculations of Eqs. (D.65) or (D.73). This innovations term, ! , for the non-linear case is, ! k+1 =H k P +1 " k T R k+1 (D.82) Asuming there are N individual states and M measurements, for a specific individual measurement z i as, 570 z= 1 2 ! i M" # # $ % & & ;z i () (D.83) An individual measurement from Eq. (D.32) can be represented as, z i =H,1:N () !x Nx1 (D.84) In Eq. (D.84), the i th row of the measurement matrix H is used. A test of this individual measurement compared to the innovations can be made such that if the following is true the measurement is valid; otherwise it is marked as invalid and not procesed through the filter, z i !m" i (D.85) The innovations for this measurement are the i th diagonal element from Eq. (D.82) as ! i = k+1 i, () . The scalar m is the proportional value of the innovations chosen as an aceptable value for the test. As long as the measurement is m -times les than the filter?s innovations, the filter can proces this measurement. Typical values of are 3, 4, or 5. Since the value of z i is often refered to as the measurement residual, Eq. (D.85) is refered to as the measurement residual test. 571 D.2.6 Kalman Filter Algorithm Summary This section provides a summary of the algorithms used by Kalman filters for both linear and non-linear systems. These routines asume zero control input u=0 () . The terms that are continuous functions of time have their t () dropped for simplicity. Linear Kalman Filter Discrete Form Time Propagation ! t k , 0 () =At () k ,t 0 () State Transition Matrix x +1 " ! ;x! Whole Value State Estimate P k T #Q T Eror-Covariance Measurement Update z k yC k+1 Measurement Residual +1 "T R k+1 Innovations If m Measurement Residual Test K k+1 opt =P k1 ! C + T " k1 () ! Optimal Kalman Gain k+1 =I! k+1 opt () P k+1 ! Eror Covariance Update !x opt z Whole Value State Update End Continuous Form Time Propagation " A; 0 () x Whole Value State ! NQ;t 0 () = Eror-Covariance Measurement Update T R Kalman Gain ! " xy-Cx [] Whole Value State T - T R - Eror-Covariance 572 Non-Linear Kalman Filter Discrete Form Time Propagation ! " x k+1 = # f! k ,t () Whole Value State Estimate F= !f"x k+1 ,t () State Jacobian Matrix Near-Linear x + Eror-State Estimate ! k =I+F"t 1 2! t [] 2 + 3! F"t [] 3 State Transition Matrix Full Non-Linear (Extended) k 0 Eror-State Estimate ! t, 0 () =Ft, 0 () ;t 0 , () =I State Transition Matrix P k+1k T k Q T Eror-Covariance Measurement Update z k+1 yH k+1 !x Measurement Residual P "T R k+1 Innovations If m Measurement Residual Test K k+1 opt P k1 ! H + T k1 () ! Optimal Kalman Gain P 1k opt ) P k1 Eror Covariance Update Near-Linear x opt z k1k+ x 1 " ) Eror-State Update Full Non-Linear (Extended) k opt Eror-State Update !x k+1 ="x k+1 Whole Value State Update End 573 Continuous Form Time Propagation ! " x= # f,t () Whole Value State F= !f"x,t () State Jacobian Matrix !x=F Eror-State ! PF+ T GQ T ;Pt 0 () = Eror-Covariance Measurement Update H= !h"x,t () Measurement Matrix KH T R !1 Kalman Gain ! " x= # f,t () +Ky-H!x [] Whole Value State ! TT R !1 Eror-Covariance D.2.7 Error Measures Several methods exist to determine the statistical measure of the magnitude of the filter states as they vary in time. Several of these are discussed below. From the Kalman filter itself, the filter?s covariance matrix provides the statistical estimate measured for each state. This value helps determine how wel the filter has determined its solution. However, unles these values have zero mean, this value does not fully represent eror from truth. If the true values of filter states are known, and the filter estimates are diferenced from these values, then the RMS of these state diferences can be computed over diferent durations of the filter operation [11]. Computing the RMS value provides additional information about the filter?s performance, since the RMS includes the mean value of this truth minus state diference. If the mean value of this diference is non-zero, this information is represented within the RMS value. 574 D.2.7.1 Mean Radial Spherical Eror The mean radial spherical eror (MRSE) represents the radius of a sphere within which the computed eror betwen a measured quantity and its expected value should reside. The probability that the eror lies in this sphere is 61% [133]. A covariance matrix of the erors can be asembled by determining the variance of each state eror during the filter?s operation as, ! "x 2 #E$"x () () 2 % & ' ( =Ex 2 () $" () % & ' ( 2 = 2 () (D.86) The covariance matrix, P !x , is based upon the variances and covariances of al the eror states combined together. If only the thre position states are considered, the 3x3 sub- matrix from the covariance matrix can be produced. The eigenvalues of this covariance sub-matrix are the squares of each of the thre primary eror axes in space, and can be labeled as, ! 1 2 ,and 3 2 . The MRSE is the norm-2 magnitude of these eigenvalues, or SE=! 1 + 3 (D.87) 575 Apendix E X-ray Detectors E.1 Detector Types Variable celestial sources that produce X-ray emisions have been detected by a variety of methods on previous spacecraft misions. These detectors are designed using the principles of measuring the energy that is released when the X-ray energy photons collide with atoms within the detector material. The amount of energy released is considered proportional to the number of photons detected. Two-dimensional arays within the detectors have been used to asist in the determination of where the photon entered the detector grid. Several types of detectors are described below, along with their atributes and limitations [59]. Some types are beter for source image detection due to their acurate photon position determination within the grid. Others are more beneficial for pulse timing due to their acurate photon arival determination. 576 ? Proportional Counters. Description: These photon counting devices are typicaly windowed chambers filed with an inert gas. Low and high electric fields are produced within the gas using electrodes. Asembling a mesh of electrodes alows two-dimensional position determination of the photon arival. As an X-ray photon enters the gas chamber, they may interact with the gas molecules releasing a photoelectron. This photoelectron is then multiplied many times when it is near the anode wire and ionized gas. The magnitude of the number of electron-positive ion pairs produced is proportional to the X-ray photon energy. Collimators may be added in front of the detector window to reject X-ray background photons [59]. Limitations: Gas proportional counters are limited due to the lifetime of the gas and damage to the anode wires within the chambers. Timing: Microsecond-level photon arival timing is possible. Timing is limited by the positive ion mobility and anode-cathode spacing. Figure E-1. Gas proportional counter X-ray detector diagram. 577 ? Microchannel Plates Description: These devices are composed of tightly packed individual channels. The channels are typicaly glas tubes, about 10 m in diameter. As an X-ray photon enters the device they interact with the channel plate glas and electrodes via the photoelectric efect. The electrons produced in this interaction are then detected on a position sensitive plate. The device provides distortionles imaging with very high spatial resolution. Z-plate (chevrons) configurations are used to suppres ion fedback and channel electrons onto the read-out electronics [59]. Limitations: The channel plates can be complex to manufacture. The plates also require very low presure or vacuum to be efective (10 -5 Torr). Timing: Nanosecond-level photon arival timing is possible. Figure E-2. Microchannel plate X-ray detector diagram [59]. 578 ? Scintilators Description: These devices are composed of crystals or similar materials. As an X-ray photon enters the device X-ray energy is converted to visible light. This light is used to excite electrons. These devices have been typicaly used in baloon-supported telescopes in the hard X-ray range of 20?200 keV [59]. Limitations: This type of device is more eficient at higher X-ray energy. Timing: Unsure. Figure E-3. Scintilator X-ray detector diagram [59]. 579 ? Calorimeters Description: These devices are composed of super-cooled solid mater. As X-ray photons enter the absorbent solid material, the temperature pulse induced in the material is measured. The amount of temperature rise is dependent on the energy of the photons. The material must be kept near 0? K. The types of devices can detect a single photon [59]. Limitations: Due to the required cryo-cooling, the detector power usage is high and must utilize a significant amount of supporting electronics and hardware. The absorber is typicaly very smal, on the order of 1-m 3 , so the detector area is smal. This requires optics in order to increase the efective area. Timing: Nanosecond-level or lower photon arival timing is possible. Figure E-4. Calorimeter X-ray detector diagram. 580 ? Charge-Coupled Device (CD) Semiconductors Description: These devices are of an aray of individual pixels composed of charge-coupled semiconductors. The metal-oxide-silicon capacitors are charge by the energy of ariving X-ray photons. These capacitors are periodicaly read and cleared by electronics. Due to the pixel aray configuration, these devices provide a high quality imaging capability. The aray of pixels alows good two- dimensional positioning of ariving photons [59]. Limitations: Each time a pixel is read, deep depletion is required to clear the remaining energy. Some devices may require backlit ilumination. Timing: Microsecond-level photon arival timing is possible. Timing is limited by the read-out electronics and the deep depletion methods. Figure E-5. CD semiconductor X-ray detector diagram. 581 ? Solid State Semiconductors Description: These devices are solid-state semiconductors that are asumed non- calorimetric and non-scintilation types. They are composed of a volume of semi- conducting material separated by doping of other mater. X-ray photons interact with the atoms of the semiconductor and electron-hole pairs are created. The multiplication of these pairs alows a measure of the X-ray energy of the ariving photons [59]. Limitations: These devices are limited by the purity of the material used. Achieving low X-ray energies are dificult, and may require cooling. Timing: Microsecond-level photon arival timing is possible. Figure E-6. Solid state semiconductor X-ray detector diagram. Table E-1 through Table E-3 provide a comparison of the characteristics of the various X-ray detector types. Each type has advantages and limitations, and these design trade-offs have been typicaly chosen based upon the requirements of a specific X-ray astronomy mision. 582 Table E-1. Characteristics Of Detector Types (Part A). Characteristic Detector Type Technology State (Manufacturing) Power Usage Mas Quantum Eficiency Detector Size Proportional Gas Counters Mature High (40 kg) Large (100s cm 2 ) Microchanel Plates Mature Medium (10s Wats) Soft X-rays: Low (~20%) Hard X-rays: Med (~40%) Scintilators Fairly New Soft X-rays: Low (~25%) Hard X-rays: High (~90%) Calorimeters New (1980s) High (10s Wats) High (95%) Smal (0.01 cm 2 ) CD Semiconductor New (1980s) Low Soft X-rays: Low (~25%) Hard X-rays: High (~90%) Solid State Semiconductor New (late 1980s) Low (1 W per 10 cm 2 ) High (80%) Large (100s cm 2 ) Table E-2. Characteristics Of Detector Types (Part B). Characteristic Detector Type Spatial Resolution Energy Range Energy Resolution Photon Timing Proportional Gas Counters Soft X-rays: God (0.1-20 keV) Hard X-rays: Por (> 20 keV) Medium Medium (~ ?s) Microchanel Plates High (~30 m) Soft X-rays: God (0.1-10 keV) Por Very God (< ns, maybe 10 ps) Scintilators Medium Soft X-rays: Por (0.1-20 keV) Hard X-rays: God (> 20 keV) Medium Calorimeters High (3 eV @ 6 keV) Very God (< ns) CD Semiconductor High (~15 m) Por (~1 keV) Por (> ms) Solid State Semiconductor Hard X-rays: God (2-10 keV) Medium (~ ?s) 583 Table E-3. Characteristics Of Detector Types (Part C). Characteristic Detector Type Imaging Capable Active Coling Required Optics Required Background Rejection Proportional Gas Counters Yes No No (colimator) High Microchanel Plates Yes No (but neds vacum) No (Lobster-eye Optics) God Scintilators Yes Medium (Strongly temperature dependent) No God Calorimeters Por (Cant be packed close together due to heat) Yes Yes (Detector very smal) CD Semiconductor Yes Some (180? K) No Solid State Semiconductor Yes No E.2 Conceptual Detector System Designs X-ray detector systems are wel known and have succesfully flown on many orbital misions, as shown in Chapter 2. Various detectors, such as the one used by the USA experiment, are gas-filed proportional counters with collimators used to sense the arival of X-ray photons. Newer semiconductor sensor technology, such as those based on silicon, can be used as detectors situated at the base of a collimated container. A coded- aperture mask or focusing X-ray optics may be used to help image the X-ray sources within the field of view. To improve navigation performance with several simultaneous measurements, multiple detectors, either within the same sensor unit or positioned at strategic locations upon the spacecraft surface, could be used to detect multiple sources over the same time epoch. 584 Figure E-7 shows a concept sensor system for X-ray pulsar-based navigation. The unit is comprised of a set of five detection sub-units, however, any number of individual sub-units may be utilized depending on the application. Using multiple detection units in a single system alows for simultaneous observation of diferent X-ray sources. Each detection unit may include a coded-aperture mask, a containment structure, a thin collimator, a silicon-strip detector positioned directly beneath the collimator, and supporting electronics for each detector. The five detection units are positioned with one in a zenith position (up), and four positioned around this unit at 45? angles to zenith, although their orientation angles may be optimized depending on the application. The containment boxes shown have dimensions of 10 cm long, 10 cm wide, and 30 cm high, which alows a 100-cm 2 detection area but could be adjusted proportionately. The containment chambers are positioned to reduce overal system size, and the photons paths within each chamber intersect for this system. The intersecting X-ray photons, however, should not collide or interact with one another. This system may be fixed to spacecraft structure or mounted on a gimbaled mechanism to alow for direct pointing to specific sources. Alternatively, each sub-unit could be actuated independently so that they could each be oriented towards a specific source. Aside from the physical X-ray detector, the system would require electronics to proces the ariving photon information. Methods to time the photon arival to high acuracy must be devised for high performing systems. Additionaly, significant data procesing is required for use of the photon arival time within a navigation system. This data procesing would require onboard computers with sufficient procesing potential to produce acurate navigation solutions. 585 Figure E-7. Side, top, and bottom views of conceptual multiple X-ray detector system. Coded-Masks X-ray Silicon-Strip Detectors 1.1.1.1.1 Sid e Vie w 1.1.1.1.2 Top Vie w 1.1.1.1.3 Bot tom Vie w 586 Bibliography [1] The Astronomical Almanac for the year 2001, U. S. Government Printing Ofice, 2000. [2] AVSO, "Types of Variable Stars," [online database], The American Asociation of Variable Star Observers, URL: http:/ww.avso.org/vstar/types.shtml [cited 7 March 2005]. [3] Abdel-Hafez, M. F., Le, Y. J., Wiliamson, W. R., Wolfe, J. D., and Speyer, J. L., "A High-Integrity and Eficient GPS Integer Ambiguity Resolution Method," Journal of the Institute of Navigation, Vol. 50, No. 4, 2003, pp. 295-310. [4] Abidin, H., "On the Construction of the Ambiguity Search Space for On-The- Fly," Journal of the Institute of Navigation, Vol. 40, No. 3, 1993, pp. 321-338. [5] Aldridge, E. C. P. J., Fiorina, C. S., Jackson, M. P., Leshin, L. A., Lyles, L. L., Spudis, P. D., Tyson, N. d., Walker, R. S., and Zuber, M. T., "Report of the President's Commision on Implementation of United States Space Exploration Policy," U. S. Government Printing Ofice, 2004. [6] Alan, D. W., "Statistics of Atomic Frequency Standards," Procedings of the IEE, Vol. 54, No. 2, February 1966, pp. 221-230. [7] Alan, D. W., "Milisecond Pulsar Rivals Best Atomic Clock Stability," 41st Annual Frequency Control Symposium, IEE, Philadelphia PA, 1987, pp. 2-11. [8] Arzoumanian, Z., Nice, D. J., Taylor, J. H., and Thorset, S. E., "Timing behavior of 96 radio pulsars," Astrophysical Journal, Vol. 422, February 1994, pp. 671- 680. [9] Ashby, N., "Relativity in the Global Positioning System," Living Reviews in Relativity, Vol. 6, 28 January 2003, pp. 1-45. [10] Ashby, N., and Alan, D. W., "Coordinate Time On and Near the Earth," Physical Review Leters, Vol. 53, No. 19, November 1984, pg. 1858. [11] Atkinson, K. E., An Introduction to Numerical Analysis, Second ed., John Wiley and Sons, New York, 1989. [12] ATNF, "ATNF Pulsar Catalogue," [online database], Australian Telescope National Facility, URL: http:/ww.atnf.csiro.au/research/pulsar/psrcat/ [cited 22 December 2003]. 587 [13] Bade, W., and Zwicky, F., "Cosmic Rays from Super-novae," Procedings of the National Academy of Science, Vol. 20, No. 5, January 1934, pp. 259-263. [14] Bade, W., and Zwicky, F., "On Super-novae," Procedings of the National Academy of Science, Vol. 20, No. 5, January 1934, pp. 254-259. [15] Backer, D. C., and Helings, R. W., "Pulsar Timing and General Relativity," Annual Review of Astronomy and Astrophysics, Vol. 24, January 1986, pp. 537- 575. [16] Bate, R. R., Mueler, D. D., and White, J. E., Fundamentals of Astrodynamics, Dover Publications Inc., New York, 1971. [17] Batin, R. H., An Introduction to the Mathematics and Methods of Astrodynamics, Revised ed., American Institute of Aeronautics and Astronautics, Washington, DC, 1999. [18] Bauer, W., "Spectrum Applet," [online], 1999, URL: http:/lectureonline.cl.msu.edu/~mp/applist/Spectrum/s.htm [cited March 7 2005]. [19] Becker, W., and Tr?mper, J., "The X-ray luminosity of rotation-powered neutron stars," Astronomy and Astrophysics, Vol. 326, October 1997, pp. 682-691. [20] Becker, W., and Tr?mper, J., "The X-ray emision properties of milisecond pulsars," Astronomy and Astrophysics, Vol. 341, January 1999, pp. 803-817. [21] Beckman, M., and Folta, D., "Mision Design of the First Robotic Lunar Exploration Program Mision: The Lunar Reconnaisance Orbiter," AS/AIA Astrodynamics Specialists Conference, Paper AS 05-300, Lake Tahoe CA, August 7-11 2005. [22] Bel, J. F., "Radio Pulsar Timing," Advances in Space Research, Vol. 21, No. 1/2, January 1998, pp. 137-147. [23] Bergeron, J. Ed., Procedings of 21st General Asembly, Transactions of the International Astronomical Union, Vol. XI B. Reidel, Dordrecht, 1992. [24] Bhatacharya, D., "Milisecond Pulsars," X-ray Binaries, W. H. G. Lewin, J. van Paradijs, and E. P. J. van den Heuvel Eds., Cambridge University Pres, Cambridge UK, 1995, pp. 223-251. [25] Bhatacharya, D., and Srinivasan, G., "The Magnetic Fields of Neutron Stars and Their Evolution," X-ray Binaries, W. H. G. Lewin, J. van Paradijs, and E. P. J. van den Heuvel Eds., Cambridge University Pres, Cambridge UK, 1995, pp. 495-522. 588 [26] Bierman, G. J., Factorization Methods for Discrete Sequential Estimation, Academic, New York, 1977. [27] Bildsten, L., Chakrabarty, D., Chiu, J., Finger, M. H., Koh, D. T., Nelson, R. W., Prince, T. A., Rubin, B. C., Scott, D. M., Stollberg, M., Vaughan, B. A., Wilson, C. A., and Wilson, R. B., "Observations of Acreting Pulsars," Astrophysical Journal Supplement Series, Vol. 113, December 1997, pg. 367. [28] Blandford, R., and Teukolsky, S. A., "Arival-Time Analysis for a Pulsar in a Binary System," Astrophysical Journal, Vol. 205, April 1976, pp. 580-591. [29] Brown, R. G., and Hwang, P. Y. C., Introduction to Random Signals and Applied Kalman Filtering, Third ed., John Wiley and Sons, New York, 1997. [30] Caltech, "Caltech Astronomy: Palomar Observatory," [online], URL: http:/ww.astro.caltech.edu/palomar/ [cited 7 March 2005]. [31] Camilo, F., Manchester, R. N., Gaensler, B. M., Lorimer, D. R., and Sarkisian, J., "PSR J1124-5916: Discovery of a Young Energetic Pulsar in the Supernova Remnant G292.0+1.8," Astrophysical Journal, Vol. 567, March 2002, pp. L71- L75. [32] Camilo, F., Lorimer, D. R., Bhat, N. D. R., Gotthelf, E. V., Halpern, J. P., Wang, Q. D., Lu, F. J., and Mirabal, N., "Discovery of a 136 Milisecond Radio and X- Ray Pulsar in Supernova Remnant G54.1+0.3," Astrophysical Journal, Vol. 574, July 2002, pp. L71-L74. [33] Campana, S., Ravasio, M., Israel, G. L., Mangano, V., and Beloni, T., "XM- Newton Observation of the 5.25 Milisecond Transient Pulsar XTE J1807-294 in Outburst," Astrophysical Journal, Vol. 594, September 2003, pp. L39-L42. [34] Caraveo, P. A., and Mignani, R. P., "A new HST measurement of the Crab Pulsar proper motion," Astronomy and Astrophysics, Vol. 344, April 1999, pp. 367-370. [35] CDS, "SIMBAD Astronomical Database," [online database], Centre de Donn?es astronomiques de Strasbourg, URL: http:/simbad.harvard.edu/cgi- bin/WSimbad.pl [cited 2002-2005]. [36] Chakrabarty, D., and Morgan, E. H., "The two-hour orbit of a binary milisecond X-ray pulsar," Nature, Vol. 394, 23 July 1998, pp. 346-348. [37] Chandrasekhar, S., Stelar Structure and Stelar Atmospheres, University of Chicago Pres, Chicago IL, 1989. [38] Charles, P. A., and Seward, F. D., Exploring the X-ray Universe, Cambridge University Pres, Cambridge UK, 1995. 589 [39] Chen, C.-T., Linear System Theory and Design, Oxford University Pres, New York, 1999. [40] Chester, T. J., and Butman, S. A., "Navigation Using X-ray Pulsars," NASA Technical Reports N81-27129, 1981, pp. 22-25. [41] Chlohesy, W. H., and Wiltshire, R. S., "Terminal Guidance System for Satelite Rendezvous," Journal of Aerospace Sciences, Vol. 27, No. 9, 1960, pp. 653-658, 674. [42] Chobotov, V. A. Ed., Orbital Mechanics, Education Series. American Institute of Aeronautics and Astronautics, Washington, DC, 1991. [43] Corbet, R., Coe, M., Edge, W., Laycock, S., Markwardt, C., and Marshal, F. E., "X-ray Pulsars in the SMC," [online database], URL: http:/lheaww.gsfc.nasa.gov/users/corbet/pulsars/ [cited 30 October 2004]. [44] Cordova, F. A.-D., "Cataclysmic Variable Stars," X-ray Binaries, W. H. G. Lewin, J. van Paradijs, and E. P. J. van den Heuvel Eds., Cambridge University Pres, Cambridge UK, 1995, pp. 331-389. [45] Culhane, J. L., and Sanford, P. W., X-ray Astronomy, Charles Scribner's Sons, New York, 1981. [46] Cunningham, L. E., "On the Computation of the Spherical Harmonic Terms Neded During the Numerical Integration of the Orbital Motion of an Artificial Satelite," Celestial Mechanics, Vol. 2, 1970, pp. 207-216. [47] D'Amico, N., Possenti, A., Manchester, R. N., Sarkisian, J., Lyne, A. G., and Camilo, F., "An Eclipsing ilisecond Pulsar with a Possible Main-Sequence Companion in NGC 6397," Astrophysical Journal, Vol. 561, November 2001, pp. L89-L92. [48] Department of Defense and Department of Transportation, "2001 Federal Radionavigation Systems," United States Government, 2001. [49] Department of Defense: Command Control Comunications and Inteligence, "Global Positioning System Standard Positioning Service Performance Standard," United States Government, 2001. [50] Downs, G. S., "Interplanetary Navigation Using Pulsating Radio Sources," NASA Technical Reports N74-34150, October 1974, pp. 1-12. [51] Downs, G. S., and Reichley, P. E., "Techniques for Measuring Arival Times of Pulsar Signals I: DSN Observations from 1968 to 1980," NASA Jet Propulsion Laboratory, California Institute of Technology, Pasadena CA, NASA Technical Reports NASA-CR-163564, 15 August 1980. 590 [52] Duncan, R. C., and Thompson, C., "Formation of Very Strongly Magnetized Neutron Stars - Implications for Gama-ray Bursts," Astrophysical Journal, Vol. 392, June 1992, pp. L9-L13. [53] Einstein, A., The Meaning of Relativity, Princeton University Pres, Princeton NJ, 1984. [54] Epstein, R., "The binary pulsar - Post-Newtonian timing efects," Astrophysical Journal, Vol. 216, August 1977, pp. 92-100. [55] Escobal, P. R., Methods of Orbit Determination, Krieger Publishing Company, Malabar FL, 1965. [56] Fabbiano, G., "Normal Galaxies and their X-ray Binary Populations," X-ray Binaries, W. H. G. Lewin, J. van Paradijs, and E. P. J. van den Heuvel Eds., Cambridge University Pres, Cambridge UK, 1995, pp. 390-418. [57] Fairhead, L., and Bretagnon, P., "An analytical formula for the time transformation TB-T," Astronomy and Astrophysics, Vol. 229, March 1990, pp. 240-247. [58] Folta, D. C., Gramlin, C. J., Long, A. C., Leung, D. S. P., and Belur, S. V., "Autonomous Navigation Using Celestial Objects," American Astronautical Society (AS) Astrodynamics Specialist Conference, AS Paper 99-439, August 1999, pp. 2161-2177. [59] Fraser, G. W., X-ray Detectors in Astronomy, Cambridge University Pres, Cambridge UK, 1989. [60] Freire, P. C., Camilo, F., Lorimer, D. R., Lyne, A. G., Manchester, R. N., and D'Amico, N., "Timing the milisecond pulsars in 47 Tucanae," Monthly Notices of the Royal Astronomical Society, Vol. 326, September 2001, pp. 901-915. [61] Frommert, H., and Kronberg, C., "The First Known Variable Stars," [online database], URL: http:/ww.seds.org/~spider/spider/Vars/vars.html [cited 7 March 2005]. [62] Frommert, H., and Kronberg, C., "The First Known Variable Stars," [online database], URL: http:/ww.seds.org/~spider/spider/Vars/vars.html [cited 7 March 2005]. [63] Fukushima, T., "Time ephemeris," Astronomy and Astrophysics, Vol. 294, February 1995, pp. 895-906. [64] Galoway, D. K., Chakrabarty, D., Morgan, E. H., and Remilard, R. A., "Discovery of a High-Latitude Acreting Milisecond Pulsar in an Ultracompact Binary," Astrophysical Journal, Vol. 576, September 2002, pp. L137-L140. 591 [65] Gelb, A. Ed., Applied Optimal Estimation. The M.I.T. Pres, Cambridge MA, 1974. [66] Giaconi, R., and Gursky, H. Eds., X-ray Astronomy, Astrophysics and Space Science Library, Vol. 43. D. Reidel Publishing Company, Boston MA, 1974. [67] Giaconi, R., Gursky, H., Paolini, F. R., and Rossi, B. B., "Evidence for X Rays From Sources Outside the Solar System," Physical Review Leters, Vol. 9, No. 11, December 1962, pp. 439-443. [68] Gounley, R., White, R., and Gai, E., "Autonomous Satelite Navigation by Stelar Refraction," Journal of Guidance, Control, and Dynamics, Vol. 7, No. 2, 1984, pp. 129-134. [69] Grifin, M. D., and French, J. R., Space Vehicle Design, American Institute of Aeronautics and Astronautics, Washington, DC, 1991. [70] Grindlay, J. E., Camilo, F., Heinke, C. O., Edmonds, P. D., Cohn, H., and Lugger, P., "Chandra Study of a Complete Sample of Milisecond Pulsars in 47 Tucanae and NGC 6397," Astrophysical Journal, Vol. 581, December 2002, pp. 470-484. [71] Gunckel, T. L., "Orbit Determination Using Kalman's Method," Navigation: Journal of the Institute of Navigation, Vol. 10, No. 3, 1963. [72] Hanson, J. E., "Principles of X-ray Navigation," Doctoral Disertation, Department of Aeronautics and Astronautics, Stanford University, 1996. [73] Hatch, R., and Euler, H.-J., "Comparison of Several AROF Kinematic Techniques," Proceding of Institute of Navigation GPS-94, Salt Lake City UT, September 1994, pp. 363-370. [74] Haugan, M. P., "Post-Newtonian arival-time analysis for a pulsar in a binary system," Astrophysical Journal, Vol. 296, September 1985, pp. 1-12. [75] HEASARC, "HEASARC Observatories," [online database], High Energy Astrophysics Science Archive Research Center NASA/GSFC/SAO, URL: http:/heasarc.gsfc.nasa.gov/docs/observatories.html [cited 1 July 2003]. [76] HEASARC, "HEASARC: WebPIMS - A Portable Mision Count Rate Simulator," [online], URL: http:/heasarc.gsfc.nasa.gov/Tools/w3pims.html [cited 21 January 2003]. [77] HEASARC, "Master Radio Catalog," [online database], NASA/HEASARC, URL: http:/heasarc.gsfc.nasa.gov/W3Browse/al/radio.html [cited 2004]. [78] HEASARC, "Master X-ray Catalog," [online database], NASA/HEASARC, URL: http:/heasarc.gsfc.nasa.gov/W3Browse/master-catalog/xray.html [cited 2004]. 592 [79] Helings, R. W., "Relativistic Efects in Astronomical Timing Measurements," Astronomical Journal, Vol. 91, March 1986, pp. 650-659. [80] Hewish, A., Bel, S. J., Pilkington, J. D., Scot, P. F., and Collins, R. A., "Observation of a Rapidly Pulsating Radio Source," Nature, Vol. 217, 24 February 1968, pp. 709-713. [81] Hobbs, G., Manchester, R., Teoh, A., and Hobbs, M., "The ATNF Pulsar Catalog," IAU Symposium, Vol. 218, 1 January 2004, pg. 139. [82] Hogg, H. S., "Variable Stars," Astrophysics and Twentieth-Century Astronomy to 1950: Part A, The General History of Astronomy, Owen Gingerich Ed., The General History of Astronomy, Vol. 4A, Cambridge, 1984, pp. 73-89. [83] Hoots, F. R., and Roehrich, R. L., "Spacetrack Report No. 3, Model for Propagation of NORAD Element Sets," Department of Defense, Defense Documentation Center, December 1980. [84] Hoots, F. R., Schumacher, P. W. J., and Glover, R. A., "History of Analytical Orbit Modeling in the U.S. Space Surveilance System," Journal of Guidance, Control, and Dynamics, Vol. 27, No. 2, pp. 174-185. [85] Hwang, P. Y. C., "Kinematic GPS: Resolving Integer Ambiguities On The Fly," Procedings IEE PLANS-90, Las Vegas NV, 1990, pp. 579-586. [86] IAU, "IAU Specifications for Nomenclature," [online], URL: http:/vizier.u- strasbg.fr/Dic/iau-spec.htx [cited 1 December 2004]. [87] Irwin, A. W., and Fukushima, T., "A numerical time ephemeris of the Earth," Astronomy and Astrophysics, Vol. 348, August 1999, pp. 642-652. [88] Jet Propulsion Laboratory, "About The Dep Space Network," [online], California Institute of Technology, NASA, 2005, URL: htp:/deepspace.jpl.nasa.gov/dsn/ [cited 14 June 2005]. [89] Jordan, J. F., "Navigation of Spacecraft on Dep Space Misions," Journal of Navigation, Vol. 40, January 1987, pp. 19-29. [90] Karet, P., Marshal, H. L., Aldcroft, T. L., Graesle, D. E., Karovska, M., Murray, S. S., Rots, A. H., Schulz, N. S., and Seward, F. D., "Chandra Observations of the Young Pulsar PSR B0540-69," Astrophysical Journal, Vol. 546, January 2001, pp. 1159-1167. [91] Kalman, R. E., "A New Approach to Linear Filtering and Prediction Problems," Transactions of the American Society of Mechanical Engineering - Journal of Basic Engineering, Vol. 82, No. D, 1960, pp. 35-45. 593 [92] Kane, H. K., "Ancient Hawai'i," [online], 1997, URL: http:/ww.hawaiantrading.com/herb-kane/ah-book/index.html [cited 12 June 2005]. [93] Kaplan, M. H., Modern Spacecraft Dynamics and Control, John Wiley and Sons, New York, 1976. [94] Kaspi, V. M., "Applications of Pulsar Timing," Doctoral Disertation, Department of Physics, Princeton University, 1994. [95] Kaspi, V. M., "High-Precision Timing of Milisecond Pulsars and Precision Astrometry," International Astronomical Union Symposium 166: Astronomical and Astrophysical Objectives of Sub-Miliarcsecond Optical Astrometry, Eds. E. Hog and P. Kenneth Seidelmann, Vol. 166, August 1994, pp. 163-174. [96] Kaspi, V. M., Taylor, J. H., and Ryba, M. F., "High-Precision Timing of Milisecond Pulsars. II: Long-Term Monitoring of PSRs B1855+09 and B1937+21," Astrophysical Journal, Vol. 428, June 1994, pp. 713-728. [97] Kelso, T. S., "NORAD Two-Line Element Sets Historical Archives," [online database], Celestrak, URL: http:/ww.celestrak.com/NORAD/archives/request.asp [cited 22 December 2004]. [98] Khalil, H. K., Nonlinear Systems, Second ed., Prentice Hal, 1996. [99] Kim, Y. H., X-ray Source Tables, Saddleback College, 2002 (unpublished). [100] King, A., "Acretion in Close Binaries," X-ray Binaries, W. H. G. Lewin, J. van Paradijs, and E. P. J. van den Heuvel Eds., Cambridge University Pres, Cambridge UK, 1995, pp. 419-456. [101] Kirsch, M. G. F., Mukerje, K., Breitfelner, M. G., Djavidnia, S., Freyberg, M. J., Kendziorra, E., and Smith, M. J. S., "Studies of orbital parameters and pulse profile of the acreting milisecond pulsar XTE J1807-294," Astronomy and Astrophysics, Vol. 423, August 2004, pp. L9-L12. [102] Kopeikin, S. M., "Milisecond and Binary Pulsars as Nature's Frequency Standards - Part I. A Generalized Statistical Model of Low-Frequency Timing Noise," Monthly Notices of the Royal Astronomical Society, Vol. 288, June 1997, pp. 129-137. [103] Kopeikin, S. M., "Milisecond and Binary Pulsars as Nature's Frequency Standards - Part I. The Efects of Low-Frequency Timing noise on Residuals and Measured Parameters," Monthly Notices of the Royal Astronomical Society, Vol. 305, May 1999, pp. 563-590. 594 [104] Krauss, M. I., Dullighan, A., Chakrabarty, D., van Kerkwijk, M. H., and Markwardt, C. B., "XTE J1814-338," International Astronomical Union Circular, Vol. 8154, June 2003, pg. 3. [105] Kuiper, L., and Hermsen, W., "X-ray and Gama-ray Observations of Milisecond Pulsars," X-ray and Gamma-ray Astrophysics of Galactic Sources, 8 December 2003. [106] Landau, H., and Euler, H.-J., "On-The-Fly Ambiguity Resolution for Precise Diferential Positioning," Procedings Institutes of Navigation GPS-92, Albuquerque NM, September 1992, pp. 607-613. [107] Larson, W. J., and Wertz, J. R. Eds., Space Mision Analysis and Design, 3rd Edition, Space Technology Series. Microcosm Pres and Kluwer Academic Publishers (Jointly), Boston MA, 1999. [108] LBL, "The Electromagnetic Spectrum," [online], URL: http:/ww.lbl.gov/MicroWorlds/ALSTool/EMSpec/EMSpec2.html [cited 7 March 2005]. [109] Lewin, W. H. G., Paradijs, J. V., and Tam, R. E., "X-ray Bursts," X-ray Binaries, W. H. G. Lewin, J. van Paradijs, and E. P. J. van den Heuvel Eds., Cambridge University Pres, Cambridge UK, 1995, pp. 175-232. [110] Liu, Q. Z., van Paradijs, J., and van den Heuvel, E. P. J., "A catalogue of high- mas X-ray binaries," Astronomy and Astrophysics Supplement Series, Vol. 147, November 2000, pp. 25-49. [111] Liu, Q. Z., van Paradijs, J., and van den Heuvel, E. P. J., "A catalogue of low- mas X-ray binaries," Astronomy and Astrophysics, Vol. 368, March 2001, pp. 1021-1054. [112] Lommen, A. N., "Precision Multi-Telescope Timing of Milisecond Pulsars: New Limits on the Gravitational Wave Background and other results from the Pulsar Timing Aray," PhD Disertation, Astrophysics, University of California, Berkeley CA, 2001. [113] Lorimer, D. R., "Binary and Milisecond Pulsars at the New Milennium," Living Reviews in Relativity, Vol. 4, June 2001, pg. 5. [114] Lyne, A. G., and Graham-Smith, F., Pulsar Astronomy, Cambridge University Pres, Cambridge UK, 1998. [115] Lyne, A. G., Jordan, C. A., and Roberts, M. E., "Jodrel Bank Crab Pulsar Timing Results," [online], URL: http:/ww.jb.man.ac.uk/~pulsar/crab.html [cited 13 August 2002]. 595 [116] Majid, W. A., Lamb, R. C., and Macomb, D. J., "X-Ray Pulsars in the Smal agelanic Cloud," Astrophysical Journal, Vol. 609, July 2004, pp. 133-143. [117] Maldonado, A. L., Baylocq, M., and Hannan, G., "Autonomous Spacecraft Navigation - Extended Kalman Filter Estimation of Clasical Orbital Parameters," Guidance and Control Conference, American Institute of Aeronautics and Astronautics, Seatle, WA, August 20-22 1984. [118] Manchester, R. N., and Taylor, J. H., Pulsars, W.H. Freman and Company, San Francisco CA, 1977. [119] Manchester, R. N., Lyne, A. G., Camilo, F., Bel, J. F., Kaspi, V. M., D'Amico, N., McKay, N. P. F., Crawford, F., Stairs, I. H., Possenti, A., Kramer, M., and Sheppard, D. C., "The Parkes multi-beam pulsar survey - I. Observing and data analysis systems, discovery and timing of 100 pulsars," Monthly Notices of the Royal Astronomical Society, Vol. 328, November 2001, pp. 17-35. [120] Markley, F. L., "Approximate Cartesian State Transition Matrix," Journal of Astronautical Sciences, Vol. 34, No. 2, 1986, pp. 161-169. [121] Markwardt, C. B., and Swank, J. H., "XTE J1751-305," International Astronomical Union Circular, Vol. 7867, April 2002, pg. 1. [122] Markwardt, C. B., and Swank, J. H., "XTE J1814-338," International Astronomical Union Circular, Vol. 8144, June 2003, pg. 1. [123] Markwardt, C. B., Juda, M., and Swank, J. H., "XTE J1807-294," International Astronomical Union Circular, Vol. 8095, March 2003, pg. 2. [124] Markwardt, C. B., Smith, E., and Swank, J. H., "XTE J1807-294," International Astronomical Union Circular, Vol. 8080, February 2003, pg. 2. [125] Markwardt, C. B., Swank, J. H., Strohmayer, T. E., in 't Zand, J. J. M., and arshal, F. E., "Discovery of a Second Milisecond Acreting Pulsar: XTE J1751-305," Astrophysical Journal, Vol. 575, August 2002, pp. L21-L24. [126] Martin, C. F., Torence, M. H., and Misner, C. W., "Relativistic Efects on an Earth-Orbiting Satelite in the Barycenter Coordinate System," Journal of Geophysical Research, Vol. 90, No. B11, September 1985, pp. 9403-9410. [127] Matsakis, D. N., Taylor, J. H., and Eubanks, T. M., "A Statistic for Describing Pulsar and Clock Stabilities," Astronomy and Astrophysics, Vol. 326, October 1997, pp. 924-928. [128] Melbourne, W. G., "Navigation Betwen the Planets," Scientific American, Vol. 234, No. 6, 1976, pp. 58-74. 596 [129] Meliani, M. T., "A Catalogue of X-ray sources in the sky region betwen delta = - 73deg. and delta = +27 deg," Publications of the Astronomical Society of Australia, Vol. 16, August 1999, pp. 175-205. [130] Melvin, P. J., "A Kalman Filter For Orbit Determination with Applications to GPS and Stelar Navigation," Advances in Astronautical Sciences, Spaceflight Mechanics Conference, Paper AS 96-145, Procedings of American Astronautical Society (AS), 1996. [131] Meregheti, S., Bandiera, R., Bocchino, F., and Israel, G. L., "BeppoSAX Observations of the Young Pulsar in the Kes 75 Supernova Remnant," Astrophysical Journal, Vol. 574, August 2002, pp. 873-878. [132] Meyer, K. W., Buglia, J. J., and Desai, P. N., "Lifetimes of Lunar Orbits," NASA Technical Paper 3394, March 1994, pp. 1-35, Langley Research Center, Hampton VA. [133] Mikhail, E. M., Observations and Least Squares, IEP-A Dun-Donneley, New York, 1976. [134] Miler, J. M., Wijnands, R., M?ndez, M., Kendziorra, E., Tiengo, A., van der Klis, ., Chakrabarty, D., Gaensler, B. ., and Lewin, W. H. G., "XM-Newton Spectroscopy of the Acretion-driven Milisecond X-Ray Pulsar XTE J1751-305 in Outburst," Astrophysical Journal, Vol. 583, February 2003, pp. L99-L102. [135] Misner, C. W., Thorne, K. S., and Wheeler, J. A., Gravitation, W. H. Freman and Company, San Francisco, 1973. [136] Montenbruck, O., and Gil, E., Satelite Orbits, Springer-Verlag, Berlin, 2000. [137] Moyer, T. D., "Transformation from Proper Time on Earth to Coordinate Time in Solar System Barycentric Space-Time Frame of Reference - Part One," Celestial Mechanics, Vol. 23, January 1981, pp. 33-56. [138] Moyer, T. D., "Transformation from Proper Time on Earth to Coordinate Time in Solar System Barycentric Space-Time Frame of Reference - Part Two," Celestial Mechanics, Vol. 23, January 1981, pp. 57-68. [139] MSFC, "ASM Acreting Pulsars," [online database], NASA/MSFC, URL: http:/gamaray.msfc.nasa.gov/batse/pulsar/asm_pulsars.html [cited 30 October 2004]. [140] Murray, C. A., Vectorial Astrometry, Adam Hilger Ltd, Bristol UK, 1983. [141] Nagase, F., "Acretion-powered X-ray pulsars," Publications of the Astronomical Society of Japan, Vol. 41, January 1989, pp. 1-79. 597 [142] NAIC, "Arecibo Observatory Home," [online], URL: http:/ww.naic.edu/ [cited March 7 2005]. [143] NASA, "The Hubble Project - Technology," [online], URL: http:/hubble.nasa.gov/technology/optics.php [cited March 7 2005]. [144] NASA, "RXTE Guest Observatory Facility," [online], URL: http:/heasarc.gsfc.nasa.gov/docs/xte/xte_1st.html [cited 1 August 2002]. [145] NASA/HEASARC/RXTE, "Types of Sources in the ASM Catalogue," [online], URL: http:/heasarc.gsfc.nasa.gov/docs/xte/learning_center/ASM/source_types.html [cited 15 July 2003]. [146] NASA/PSU/G.Pavlov, "Chandra Photo Album: Vela Pulsar 06 Jun 2000," [online], URL: http:/chandra.harvard.edu/photo/2000/vela/ [cited 7 March 2005]. [147] NASA/SAO/CXC, "Chandra Photo Album Crab Nebula 28 Sep 1999," [online], URL: http:/chandra.harvard.edu/photo/0052/ [cited March 7 2005]. [148] Nelson, R. A., Handbook on Relativistic Time Transfer, Satelite Engineering Research Corporation, 2003 (unpublished). [149] Nelson, R. A., "Relativistic Efects in Satelite Time and Frequency Transfer and Disemination," ITU Handbook on Satelite Time and Frequency Transfer and Disemination, International Telecommunication Union, Geneva, (to be published), pp. 1-30. [150] Newton, I., Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), Josephi Streater, London, 1687. [151] Nicastro, L., Cusumano, G., L?hmer, O., Kramer, M., Kuiper, L., Hermsen, W., Mineo, T., and Becker, W., "BeppoSAX Observation of PSR B1937+21," Astronomy and Astrophysics, Vol. 413, January 2004, pp. 1065-1072. [152] Nice, D. J., and Thorset, S. E., "Pulsar PSR 1744-24A - Timing, eclipses, and the evolution of neutron star binaries," Astrophysical Journal, Vol. 397, September 1992, pp. 249-259. [153] Nordtvedt, K., Jr., and Wil, C. M., "Conservation Laws and Prefered Frames in Relativistic Gravity. Part I. Experimental Evidence to Rule Out Prefered-Frame Theories of Gravity," Astrophysical Journal, Vol. 177, November 1972, pp. 775- 792. [154] NRAO, "NRAO Gren Bank Telescopes," [online], URL: http:/ww.gb.nrao.edu [cited 7 March 2005]. 598 [155] Oppenheimer, J. R., and Volkoff, G. M., "On Masive Neutron Cores," Physical Review, Vol. 55, February 1939, pp. 374-381. [156] Parkinson, B. W., and Spilker, J. J. J. Eds., Global Positioning System: Theory and Applications, Volume I. American Institute of Aeronautics and Astronautics, Washington, DC, 1996. [157] Parkinson, B. W., and Spilker, J. J. J. Eds., Global Positioning System: Theory and Applications, Volume I. American Institute of Aeronautics and Astronautics, Washington, DC, 1996. [158] Possenti, A., Cerutti, R., Colpi, M., and Meregheti, S., "Re-examining the X-ray versus spin-down luminosity correlation of rotation powered pulsars," Astronomy and Astrophysics, Vol. 387, June 2002, pp. 993-1002. [159] Princeton, "Princeton University Pulsar Group Pulsar Catalog," [online database], Princeton University, URL: http:/pulsar.princeton.edu/pulsar/catalog.shtml [cited 4 May 2003]. [160] Prussing, J. E., and Conway, B. A., Orbital Mechanics, Oxford University Pres, Oxford UK, 1993. [161] Rappaport, S., Pulsar SNR Discussion, Masachusets Institute of Technology, October 2004 (personal communication). [162] Rawley, L. A., Taylor, J. H., and Davis, M. M., "Fundamental Astrometry and Milisecond Pulsars," Astrophysical Journal, Vol. 326, March 1988, pp. 947-953. [163] Rawley, L. A., Taylor, J. H., Davis, M. M., and Alan, D. W., "Milisecond pulsar PSR 1937+21 - A highly stable clock," Science, Vol. 238, November 1987, pp. 761-765. [164] Ray, P. S., Wood, K. S., Wolf, M. T., Lovelete, M. N., Sheikh, S., Moon, D. S., Eikenbery, S. S., Roberts, M., Bloom, E. D., Tournear, D., Saz Parkinson, P., and Reily, K., "Absolute Timing of the Crab Pulsar: X-ray, Radio, and Optical Observations," Bulletin of the American Astronomical Society, American Astronomical Society, Vol. 201, December 2002, pg. 1298. [165] Ray, P. S., Wood, K. S., Wolf, M. T., Lovelete, M. N., Sheikh, S., Moon, D. S., Eikenbery, S. S., Roberts, M., Lyne, A., Jordon, C., Bloom, E. D., Tournear, D., Saz Parkinson, P., and Reily, K., "Absolute Timing Calibration of the USA Experiment Using Pulsar Observations," American Astronomical Society (AS) High Energy Astrophysics Division (HEAD), Vol. 7, 1 March 2003. [166] Ray, P. S., Wood, K. S., Fritz, G., Hertz, P., Kowalski, M., Johnson, W. N., Lovelete, M. N., Wolf, M. T., Yentis, D., Bandyopadhyay, R. M., Bloom, E. D., Giebels, B., Godfrey, G., Reily, K., Parkinson, P. S., Shabad, G., Michelson, P., Roberts, M., Leahy, D. A., Cominsky, L., Scargle, J., Beal, J., Chakrabarty, D., 599 and Kim, Y., "The USA X-ray Timing Experiment," X-ray Astronomy: Stelar Endpoints, AGN, and the Difuse X-ray Background, American Institute of Physics (AIP) Procedings, Vol. 599, 1 December 2001, pp. 336-345. [167] Reichley, P., Downs, G., and Morris, G., "Use of Pulsar Signals as Clocks," NASA Jet Propulsion Laboratory Quarterly Technical Review, Vol. 1, No. 2, July 1971, pp. 80-86. [168] Reichley, P. E., Downs, G. S., and Morris, G. A., "Time-Of-Arival Observations of Eleven Pulsars," Astrophysical Journal, Vol. 159, January 1970, pp. L35-L40. [169] Remilard, R. A., Swank, J., and Strohmayer, T., "XTE J0929-314," International Astronomical Union Circular, Vol. 7893, May 2002, pg. 1. [170] Richter, G. W., and Matzner, R. A., "Gravitational deflection of light at 1 1/2 PN order," Astrophysics and Space Science, Vol. 79, September 1981, pp. 119-127. [171] Richter, G. W., and Matzner, R. A., "Second-order contributions to gravitational deflection of light in the parameterized post-Newtonian formalism," Physical Review D, Vol. 26, No. 6, September 1982, pp. 1219-1224. [172] Richter, G. W., and Matzner, R. A., "Second-order contributions to gravitational deflection of light in the parameterized post-Newtonian formalism. I. Photon orbits and deflections in thre dimensions," Physical Review D, Vol. 26, No. 10, November 1982, pp. 2549-2556. [173] Richter, G. W., and Matzner, R. A., "Second-order contributions to relativistic time delay in the parameterized post-Newtonian formalism," Physical Review D, Vol. 28, No. 12, December 1983, pp. 3007-3012. [174] Riter, H., and Kolb, U., "Catalogue of cataclysmic binaries, low-mas X-ray binaries and related objects (Sixth edition)," Astronomy and Astrophysics Supplement Series, Vol. 129, April 1998, pp. 83-85. [175] Roth, G. D., "An Historical Exploration of Modern Astronomy," Compendium of Practical Astronomy, G. D. Roth Ed., Springer Verlag, 1994, pp. 425-435. [176] Rugh, W. J., Linear System Theory, Second ed., Prentice Hal, Upper Saddle River, New Jersey, 1996. [177] Russian Federation Ministry of Defense, "GLONAS," [online], 2002, URL: http:/ww.glonas-center.ru/frame_e.html [cited 7 March 2005]. [178] Samus, N. N., and Durlevich, O. V., "General Catalogue of Variable Stars," VizieR Online Data Catalog, Vol. 2250, November 2004. [179] Samus, N. N., and Durlevich, O. V., "General Catalogue of Variable Stars (GCVS) Variability Types and Distribution Statistics of Designated Variable 600 Stars Acording to their Types of Variability," [online database], URL: http:/ww.sai.msu.su/groups/cluster/gcvs/gcvs/ii/vartype.txt [cited 7 March 2005]. [180] SAO, "6 m telescope short description," [online], URL: http:/ww.sao.ru/Doc- en/Telescopes/bta/descrip.html [cited 7 March 2005]. [181] SAO, "Special Astrophysical Observatory Russian Academy of Sciences Radiotelescope RATAN-600," [online], URL: http:/ww.sao.ru/ratan/ [cited 7 March 2005]. [182] Schumacher, P. W., and Glover, R. A., "Analytic Orbit Model for U.S. Naval Space Surveilance: An Overview," 1995 AS/AIA Astrodynamics Specialist Conference, AS Paper 95-427, American Astronautical Society, Halifax, Nova Scotia, Canada, August 14-17, 1995. [183] Seidelmann, P. K., Explanatory Supplement to the Astronomical Almanac, University Science Books, Sausalito CA, 1992. [184] Shapiro, I. I., "Fourth Test of General Relativity," Physical Review Leters, Vol. 13, No. 26, December 1964, pp. 789-791. [185] Shearer, A., and Golden, A., "Implications of the Optical Observations of Isolated Neutron Stars," Astrophysical Journal, Vol. 547, February 2001, pp. 967-972. [186] Sheikh, S. I., The Use of Pulsars for Interplanetary Navigation, University of Maryland, College Park, MD, 2000 (unpublished). [187] Sheikh, S. I., Crab Comparison Plot Description, University of Maryland, College Park, MD, 2002 (unpublished). [188] Sheikh, S. I., Derivation of Relativistic Corrections and Time Transfer for Spacecraft Clock Proper Time within the Solar System Barycenter Frame, University of Maryland, College Park, MD, 2004 (unpublished). [189] Sheikh, S. I., Absolute and Relative Position Determination Using Variable Celestial Sources, University of Maryland, College Park, MD, 2005 (unpublished). [190] Sheikh, S. I., Navigation Kalman Filter, University of Maryland, College Park, MD, 2005 (unpublished). [191] Sheikh, S. I., and Pines, D. J., "Recursive Estimation of Spacecraft Position Using X-ray Pulsar Time of Arival Measurements," ION 61st Annual Meting, Institute of Navigation, Boston MA, 27-29 June 2005. [192] Sheikh, S. I., Pines, D. J., Wood, K. S., Ray, P. S., Lovelete, M. N., and Wolf, M. T., "The Use of X-ray Pulsars for Spacecraft Navigation," 14th AS/AIA 601 Space Flight Mechanics Conference, Paper AS 04-109, Maui HI, February 8-12 2004. [193] Sheikh, S. I., Pines, D. J., Wood, K. S., Ray, P. S., Lovelete, M. N., and Wolf, M. T., "Spacecraft Navigation Using X-ray Pulsars," Journal of Guidance, Control, and Dynamics, In pres [anticipated 2005 publication]. [194] Shklovskii, I. S., "Possible Causes of the Secular Increase in Pulsar Periods," Soviet Astronomy, Vol. 13, No. 4, February 1970, pp. 562-565. [195] Sidi, M. J., Spacecraft Dynamics and Control, Cambridge University Pres, Cambridge UK, 1997. [196] Singh, K. P., Drake, S. A., and White, N. E., "RS CVn Versus Algol-Type Binaries: A Comparative Study of Their X-Ray Emision," Astronomical Journal, Vol. 111, No. 6, June 1996, pg. 2415. [197] Sobel, D., Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, Penguin Books, New York, 1995. [198] Standish, E. M., "NASA JPL Planetary and Lunar Ephemerides," [online database], NASA, URL: http:/sd.jpl.nasa.gov/eph_info.html [cited 1 December 2004]. [199] Standish, E. M., "Time scales in the JPL and CfA ephemerides," Astronomy and Astrophysics, Vol. 336, August 1998, pp. 381-384. [200] Strohmayer, T. E., Markwardt, C. B., Swank, J. H., and in't Zand, J., "X-Ray Bursts from the Acreting Milisecond Pulsar XTE J1814-338," Astrophysical Journal, Vol. 596, October 2003, pp. L67-L70. [201] Stumpff, P., "On the Computation of Barycentric Radial Velocities with Clasical Perturbation Theories," Astronomy and Astrophysics, Vol. 56, April 1977, pp. 13- 23. [202] Stumpff, P., "The Rigorous Treatment of Stelar Aberation and Doppler Shift, and the Barycentric Motion of the Earth," Astronomy and Astrophysics, Vol. 78, September 1979, pp. 229-238. [203] Taylor, J. H., "Milisecond Pulsars: Nature's Most Stable Clocks," Procedings of the IEE, Vol. 79, No. 7, July 1991, pp. 1054-1062. [204] Taylor, J. H., "Pulsar Timing and Relativistic Gravity," Philosophical Transactions of the Royal Society of London, Vol. 341, January 1992, pp. 117- 134. 602 [205] Taylor, J. H., and Stinebring, D. R., "Recent Progres in the Understanding of Pulsars," Annual Review of Astronomy and Astrophysics, Vol. 24, January 1986, pp. 285-327. [206] Taylor, J. H., and Weisberg, J. M., "Further Experimental Tests of Relativistic Gravity Using the Binary Pulsar PSR 1913+16," Astrophysical Journal, Vol. 345, October 1989, pp. 434-450. [207] Taylor, J. H., Manchester, R., and Nice, D. J., "TEMPO Software Package," [online], URL: http:/pulsar.princeton.edu/tempo/ [cited 10 November 2002]. [208] Taylor, J. H., Manchester, R. N., and Lyne, A. G., "Catalog of 558 Pulsars," Astrophysical Journal Supplement Series, Vol. 88, October 1993, pp. 529-568. [209] Thomas, J. B., "Reformulation of the Relativistic Conversion Betwen Coordinate Time and Atomic Time," Astronomical Journal, Vol. 80, No. 5, May 1975, pp. 405-411. [210] Thompson, C., and Duncan, R. C., "The Soft Gama Repeaters as Very Strongly Magnetized Neutron Stars. I. Quiescent Neutrino, X-Ray, and Alfven Wave Emision," Astrophysical Journal, Vol. 473, December 1996, pp. 322-342. [211] Thompson, D. J., "Pulse period of several wel known pulsars," [online], URL: http:/heasarc.gsfc.nasa.gov/docs/objects/pulsars/pulsars_lc.html [cited 7 March 2005]. [212] Thomson, W. T., Introduction to Space Dynamics, Dover, Mineola NY, 1986. [213] Valado, D. A., Fundamentals of Astrodynamics and Applications, Second ed., Space Technology Library, Kluwer Academic Publishers, Boston MA, 2001. [214] van der Klis, M., "Rapid Aperiodic Variability in X-ray Binaries," X-ray Binaries, W. H. G. Lewin, J. van Paradijs, and E. P. J. van den Heuvel Eds., Cambridge University Pres, Cambridge UK, 1995, pp. 252-307. [215] Verbunt, F., and van den Heuvel, E. P. J., "Formation and Evolution of Neutron Stars and Black Holes in Binaries," X-ray Binaries, W. H. G. Lewin, J. van Paradijs, and E. P. J. van den Heuvel Eds., Cambridge University Pres, Cambridge UK, 1995, pp. 457-494. [216] Voges, W., Aschenbach, B., Boller, T., Br?uninger, H., Briel, U., Burkert, W., Dennerl, K., Englhauser, J., Gruber, R., Haberl, F., Hartner, G., Hasinger, G., Pfefermann, E., Pietsch, W., Predehl, P., Schmit, J., Tr?mper, J., and Zimermann, U., "Rosat Al-Sky Survey Faint Source Catalogue," International Astronomical Union Circular, Vol. 7432, May 2000, pg. 3. [217] Voges, W., Aschenbach, B., Boller, T., Br?uninger, H., Briel, U., Burkert, W., Dennerl, K., Englhauser, J., Gruber, R., Haberl, F., Hartner, G., Hasinger, G., 603 K?rster, M., Pfefermann, E., Pietsch, W., Predehl, P., Rosso, C., Schmit, J. H. M. M., Tr?mper, J., and Zimermann, H. U., "The ROSAT al-sky survey bright source catalogue," Astronomy and Astrophysics, Vol. 349, September 1999, pp. 389-405. [218] Walace, K., "Radio Stars, What They Are and The Prospects for their Use in Navigational Systems," Journal of Navigation, Vol. 41, No. 3, September 1988, pp. 358-374. [219] Weks, C. J., and Bowers, M. J., "Analytical Models of Doppler Data Signatures," Journal of Guidance, Control, and Dynamics, Vol. 18, No. 6, 1995, pp. 1287-1291. [220] Weinberg, S., Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley and Sons, New York, 1972. [221] Wertz, J. R. Ed., Spacecraft Atitude Determination and Control. Kluwer Academic Publishers, Boston MA, 1978. [222] White, N. E., and Zhang, W., "Milisecond X-Ray Pulsars in Low-mas X-Ray Binaries," Astrophysical Journal, Vol. 490, November 1997, pg. L87. [223] White, N. E., Nagase, F., and Parmar, A. N., "The Properties of X-ray Binaries," X-ray Binaries, W. H. G. Lewin, J. van Paradijs, and E. P. J. van den Heuvel Eds., Cambridge University Pres, 1995. [224] Wie, B., Space Vehicle Dynamics and Control, American Institute of Aeronautics and Astronautics, Reston VA, 1998. [225] Wijnands, R., "An XM-Newton Observation during the 2000 Outburst of SAX J1808.4-3658," Astrophysical Journal, Vol. 588, May 2003, pp. 425-429. [226] Wijnands, R., and van der Klis, M., "A milisecond pulsar in an X-ray binary system," Nature, Vol. 394, 23 July 1998, pp. 344-346. [227] Wikipedia, "Astronomical Object," [online], URL: http:/ww.answers.com/topic/astronomical-object/ [cited 15 March 2005]. [228] Wil, C. M., and Nordtvedt, K., Jr., "Conservation Laws and Prefered Frames in Relativistic Gravity. Part I. Prefered-Frame Theories and an Extended PN Formalism," Astrophysical Journal, Vol. 177, November 1972, pp. 757-774. [229] Wood, K. S., "Navigation Studies Utilizing The NRL-801 Experiment and the ARGOS Satelite," Small Satelite Technology and Applications II, Ed. B. J. Horais, International Society of Optical Engineering (SPIE) Procedings, Vol. 1940, 1993, pp. 105-116. 604 [230] Wood, K. S., "USA Observations," [online database], NRL/USA, URL: http:/xweb.nrl.navy.mil/usa/index.html [cited 21 January 2003]. [231] Wood, K. S., Determan, J. R., Ray, P. S., Wolf, M. T., Budzien, S. A., Lovelete, M. N., and Titarchuk, L., "Using the Unconventional Stelar Aspect (USA) Experiment on ARGOS to Determine Atmospheric Parameters by X-ray Ocultation," Optical Spectroscopic Techniques, Remote Sensing, and Instrumentation for Atmospheric and Space Research IV, Eds. A. M. Larar and M. G. Mlynczak, International Society of Optical Engineering (SPIE) Procedings, Vol. 4485, January 2002, pp. 258-265. [232] Wood, K. S., Kowalski, M., Lovelete, M. N., Ray, P. S., Wolf, M. T., Yentis, D. J., Bandyopadhyay, R. ., Fewtrel, G., and Hertz, P. L., "The Unconventional Stelar Aspect (USA) Experiment on ARGOS," American Institute of Aeronautics and Astronautics (AIA) Space Conference and Exposition, AIA Paper 2001- 4664, Albuquerque NM, August 2001. [233] Wood, K. S., Mekins, J. F., Yentis, D. J., Smathers, H. W., McNutt, D. P., Bleach, R. D., Friedman, H., Byram, E. T., Chubb, T. A., and eidav, M., "The HEAO A-1 X-ray source catalog," Astrophysical Journal Supplement Series, Vol. 56, December 1984, pp. 507-649. [234] Wood, K. S., Fritz, G., Hertz, P., Johnson, W. N., Lovelete, M. N., Wolf, M. T., Bloom, E., Godfrey, G., Hanson, J., Michelson, P., Taylor, R., and en, H., "The USA Experiment on the ARGOS Satelite: A Low Cost Instrument for Timing X- Ray Binaries," The Evolution of X-ray Binaries, American Institute of Physics (AIP) Procedings, Vol. 308, January 1994, pp. 561-564. [235] Wood, K. S., Fritz, G. G., Hertz, P. L., Johnson, W. N., Kowalski, M. P., Lovelete, M. N., Wolf, M. T., Yentis, D. J., Bloom, E., Cominsky, L., Fairfield, K., Godfrey, G., Hanson, J., Le, A., Michelson, P. F., Taylor, R., and Wen, H., "USA Experiment on the ARGOS Satelite: A Low-cost Instrument for Timing X- ray Binaries," EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy V, Eds. O. H. Siegmund and J. V. Valerga, International Society of Optical Engineering (SPIE) Procedings, Vol. 2280, September 1994, pp. 19-30. [236] Wright, J. R., "Sequential Orbit Determination with Auto-Correlated Gravity Modeling Erors," Journal of Guidance and Control, Vol. 4, No. 3, May-June 1981, pp. 304-309. [237] Zarchan, P., and Musoff, H., Fundamentals of Kalman Filtering, American Institute of Aeronautics and Astronautics, Washington, DC, 2000.