Navigation: Science and Technology Fucheng Liu Shan Lu Yue Sun Guidance and Control Technology of Spacecraft on Elliptical Orbit Navigation: Science and Technology ThisseriesNavigation:ScienceandTechnology(NST)presentsnewdevelopments and advances in various aspects of navigation - from land navigation, marine navigation, aeronautic navigation to space navigation; and from basic theories, mechanisms, to modern techniques. It publishes monographs, edited volumes, lecture notes and professional books on topics relevant to navigation - quickly, up to date and with a high quality. A special focus of the series is the technologies of the Global Navigation Satellite Systems (GNSSs), as well as the latest progress made in the existing systems (GPS, BDS, Galileo, GLONASS, etc.). To help readers keep abreast of the latest advances in the field, the key topics in NST include but are not limited to: – Satellite Navigation Signal Systems – GNSS Navigation Applications – Position Determination – Navigational Instrument – Atomic Clock Technique and Time-Frequency System – X-ray Pulsar-based Navigation and Timing – Test and Evaluation – User Terminal Technology – Navigation in Space – New Theories and Technologies of Navigation – Policies and Standards More information about this series at http://www.springer.com/series/15704 Fucheng Liu Shan Lu Yue Sun (cid:129) (cid:129) Guidance and Control Technology of Spacecraft on Elliptical Orbit 123 Fucheng Liu Yue Sun ShanghaiAerospace Control Technology ShanghaiAerospace Control Technology Institute Institute Shanghai, Shanghai, China Shanghai, Shanghai, China ShanLu ShanghaiAerospace Control Technology Institute Shanghai, Shanghai, China ISSN 2522-0454 ISSN 2522-0462 (electronic) Navigation: Science andTechnology ISBN978-981-10-7958-0 ISBN978-981-10-7959-7 (eBook) https://doi.org/10.1007/978-981-10-7959-7 JointlypublishedwithNationalDefenseIndustryPress,Beijing,China TheprinteditionisnotforsaleinChinaMainland.CustomersfromChinaMainlandpleaseorderthe printbookfrom:NationalDefenseIndustryPress. LibraryofCongressControlNumber:2018940885 ©SpringerNatureSingaporePteLtd.andNationalDefenseIndustryPress2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublishers,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. Thepublishers,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthis book are believed to be true and accurate at the date of publication. Neither the publishers nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor for any errors or omissions that may have been made. The publishers remains neutral with regard to jurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSingaporePteLtd. Theregisteredcompanyaddressis:152BeachRoad,#21-01/04GatewayEast,Singapore189721, Singapore Preface Since 1957,thefirstman-madesatellitebeinglaunchedintospace, stepsofhuman beings exploring space has never stopped. So far, there are already about 6000 satelliteshavebeenlaunchedglobally,andover900ofthemareinorbit,whichare mainly distributed in nearly circular orbit, such as near-earth orbit, medium orbit, and earth synchronous orbit, according to different mission requirements. While control precision and capability of satellite being enhanced constantly, the ren- dezvous and dock technology being represented by space station is also ever-increasingsophisticatedandhasplayedanimportantroleinspaceexploration mission of human being. Viewing spacecrafts being launched by each country, vast majority of them are operating in circular orbit or nearly circular orbit, which is decided upon com- prehensivefactors,suchasdifficultylevelofspacecraft’sreal-timelocation,attitude and orbit control, and distribution of ground monitoring and control station. However, in recent years, another type of orbit, elliptical orbit has been continu- ously developed and utilized by each country. The distance from spacecrafts operating on such orbit to earth changes continuously within one orbital period. These spacecrafts operate slowly in apogee and operate quickly when passing perigee. Especially when the spacecraft is on the large elliptical orbit, whose perigee altitude is near near-earth orbit and apogee altitude is near earth syn- chronous orbit, it can operate near the apogee for a long time. With this charac- teristic, the spacecraft can maintain the capability of long-time earth observation and communication over special area from apogee and especially utilizes large elliptical orbit of large inclination to realize long-time observation and communi- cation over high latitude areas on the earth, which cannot be realized with space- crafts on circular orbit. One of the typical examples is Molniya series of communication satellite of Russia and SBIRS of America. Strictly speaking, no orbit can realize true circular orbit; however, the nearly circularorbitwithverysmall orbitaleccentricity canbeapproximately regardedas circular orbit, so as to simplify mission requirements, such as spacecraft location andcontrol.Theresearchfocusofthisbookislargeellipticalorbit,especiallyhigh v vi Preface utilityoneswithperigeealtitudenearnear-earthorbitandapogeealtitudenearearth synchronous orbit. To make good use of large elliptical orbit, the design of GNC system of spacecraft will face a series of challenge. First, according to different mission requirements, how to design large elliptical orbit so as to take advantage of spacecraftspecificallyisthepremiseofadoptinglargeellipticalorbit.Second,orbit altitude of large elliptical orbit spacecraft changes quite big and autonomous nav- igation method which traditionally suited for circular orbit is very limited, espe- cially when large elliptical orbit spacecraft operates near the apogee, navigation satellites, such as GPS cannot be used, so new methods should be found for autonomousnavigationoflargeellipticalorbitspacecraft.Meanwhile,autonomous rendezvous and formation flight on large elliptical orbit are the technology devel- opmentdirection offurtherplaying therole of large ellipticalorbit; however,there is an essential distinction in relative orbit dynamics between elliptical orbit and circular orbit, so brand new methods are needed to be taken on the guidance and control of relative motion between spacecrafts. Research over GNC technology of elliptical orbit will propel further development and integrity of world aerospace technology. The book is divided into eight chapters. Chapter 1 mainly introduces charac- teristic,application,anddevelopmentprospectofellipticalorbit,aswellasthekey issues of control system which is worthy of research. Chapters 2 and 3 mainly introducelargeellipticalorbitdesignmethodfordifferentmissionrequirementsand configurationdesignmethodofformationflightunderellipticalorbit.Chapters4–6 mainly introduce autonomous navigation method of single spacecraft on elliptical orbit, autonomous navigation method of regional constellation, and relative navi- gation method. Chapters 7 and 8 mainly introduce control method of formation configuration keeping, rendezvous, and docking of elliptical orbit. The publication of this book should be owed to the support of Shanghai Aerospace Control Technology Institute and Shanghai Key Laboratory of Aerospace Intelligent Control Technology and sponsor of the National Defense Science and Technology Publishing Fund and Program of Shanghai Technology Research Leader (Program No: 17XD1420700). This book is the summary of the author’s years of experience in aerospace engineeringtechnologydevelopment.Itcannotonlybetakenasreferenceteaching material for high-grade undergraduates and postgraduates, but can also provide necessary professional knowledge and engineering reference for researchers and engineering technology personnel engaged in the development of GNC system of spacecraft. Due to limited knowledge, there might be some mistakes and flaws in this book, please do not hesitate to correct me. Shanghai, China Fucheng Liu January 2016 Shan Lu Yue Sun Compilation Committee Director: Fucheng Liu Vice-director: Shan Lu, Yue Sun Committee: Hailei Wu, Longyu Tan, Pengyu Zhan, Wei Xu, Shaoxiong Tian, Yueyang Hou, Youfeng Wang, Yang Peng, Chenglong Jia, Fengwen Wang vii Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Characteristics of Elliptical Orbit. . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Development of Elliptical Orbit Satellite Application . . . . . . . . . . 2 1.3 Key Problems in Control System of Elliptical Orbit Spacecraft . . . 3 1.4 Structure of This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Orbit Design of Spacecraft on Elliptical Orbit . . . . . . . . . . . . . . . . . 7 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Absolute Dynamics Analysis of Elliptical Orbit . . . . . . . . . . . . . . 8 2.2.1 Basic Features of Elliptical Orbit . . . . . . . . . . . . . . . . . . . 8 2.2.2 Elliptical Orbit Perturbation . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Autonomous Orbit Prediction of Elliptical Orbit. . . . . . . . . . . . . . 16 2.3.1 Autonomous Orbit Prediction. . . . . . . . . . . . . . . . . . . . . . 16 2.3.2 OnboardOrbit Prediction Algorithm ofElliptical Orbit.... 17 2.3.3 Analysis and Predigestion of Elliptical Orbit Dynamics Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4 Design of Apogee Rendezvous Orbit. . . . . . . . . . . . . . . . . . . . . . 22 2.4.1 Drift Characteristics Analysis of Elliptical Orbit . . . . . . . . 24 2.4.2 Design of Frozen Elliptical Orbit . . . . . . . . . . . . . . . . . . . 27 2.4.3 Design of Little Inclination Elliptical Orbit . . . . . . . . . . . . 42 2.5 Elliptical Orbit Rendezvous Method for Inspecting GEO Satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3 Formation Configuration Design of Elliptical Orbit . . . . . . . . . . . . . 53 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.2 Formation Configuration Design Based on Algebraic Method . . . . 54 3.2.1 Relative Dynamic Equation . . . . . . . . . . . . . . . . . . . . . . . 54 3.2.2 Relative Periodic Motion . . . . . . . . . . . . . . . . . . . . . . . . . 58 ix x Contents 3.2.3 Characteristics Analysis of Relative Motion Trajectory . . . 61 3.2.4 Fly-Around Configuration Design. . . . . . . . . . . . . . . . . . . 62 3.2.5 Accompanying Flying Configuration Design . . . . . . . . . . . 65 3.3 Formation Configuration Design Based on Geometry . . . . . . . . . . 68 3.3.1 Precise Model of Relative Motion . . . . . . . . . . . . . . . . . . 68 3.3.2 First-Order Approximation Model of Relative Motion . . . . 72 3.3.3 Formation Configuration Design. . . . . . . . . . . . . . . . . . . . 73 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4 Autonomous Navigation Technology of Whole Space . . . . . . . . . . . . 77 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.2 Common Autonomous Navigation Method of Elliptical Orbit . . . . 79 4.2.1 Autonomous Navigation Technology of Elliptical Orbit Based on Astronomical Observation . . . . . . . . . . . . . . . . . 79 4.2.2 Autonomous Navigation Technology of Elliptical Orbit Based on GNSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.3 Merge Autonomous Navigation Based on SINS/GNSS/CNS. . . . . 101 4.3.1 State Equation of Inertial Navigation . . . . . . . . . . . . . . . . 101 4.3.2 Observation Equation of SINS/Star Sensor/GNSS Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.3.3 Merge Scheme of SINS/Star Sensor/GNSS System . . . . . . 109 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5 Autonomous Navigation Technology of Regional Constellation. . . . . 117 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.2 Regional Constellation Autonomous Navigation Based on Inter-satellite Ranging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 5.2.1 Constellation Autonomous Navigation System Scheme of Elliptical Orbit . . . . . . . . . . . . . . . . . . . . . . . . 118 5.2.2 High-Precision Orbit Prediction Technology of Constellation Autonomous Navigation System on Elliptical Orbit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.2.3 Technology of Inter-satellite Link Ranging . . . . . . . . . . . . 126 5.2.4 Whole Net Filter Scheme of Constellation Autonomous Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.3 Rotation Error Estimation of Constellation Configuration Based on Inter-satellite Observation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 5.3.1 Rotation Error Analysis of Region Constellation Autonomous Navigation on Elliptical Orbit. . . . . . . . . . . . 134 5.3.2 RotationErrorMitigationMethodBasedonInter-satellite Observationof ConstellationAutonomousNavigationon Elliptical Orbit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 5.4 High-Precision Orbit Determination Technology Based on Inter-satellite Orientation Determination of Elliptical Orbit. . . . 147