Guochang Xu · Yan Xu GPS Theory, Algorithms and Applications Third Edition (cid:1) GPS Theory, Algorithms and Applications Guochang Xu Yan Xu (cid:129) GPS Theory, Algorithms and Applications Third Edition With 62 Figures 123 GuochangXu Yan Xu Shandong University at Weihai GFZGermanResearchCentreforGeosciences Institute of Space Sciences Geodesy Weihai Potsdam China Germany ISBN978-3-662-50365-2 ISBN978-3-662-50367-6 (eBook) DOI 10.1007/978-3-662-50367-6 LibraryofCongressControlNumber:2016937942 ©Springer-VerlagBerlinHeidelberg2003,2007,2016 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringer-VerlagGmbHBerlinHeidelberg To Liping, Jia, Yuxi, and Pan Preface to the Third Edition After the first edition of this book was published at the end of 2003, Springer requesteda revisionfor the second edition around 2006,andthat was publishedat the end of 2007. The original edition was written based on experience with the software design of KSGsoft (Xu et al. 1998) and KGsoft (Xu 1999), and related researchandpracticeinGermanyandDenmark.Thesecondeditionbenefitedfrom the design of the multi-functional GPS/Galileo software (MFGsoft, Xu 2004). The new model of solar radiation for satellite orbit determination discovered through GPSresearchledtoanattempttosolvetheequationsofsatellitemotionaffectedby second-order disturbances, which resulted in the book Orbits, published at the end of 2008, with a second edition in 2013, combined with intensive research (cf. Xu et al. 2010a,b, 2011; Xu and Xu 2012, 2013a,b). During that time, the author was further involved in GPS activities through his role in the supervision of Ph.D. studies and software development (cf. Wang et al. 2010; He 2015). In 2011, the second edition of GPS was translated into Chinese by the Peking Institute of Satellite Controlling and Telecommunication and was published by Tsinghua University Press Peking, and was sold out around 2015. In 2014, GPS was trans- lated into Persian, and that edition was published by Dhahran University. The preparation of the third edition of GPS was contracted with Springer several years ago,butwasinterruptedbyworkonthebooksOrbits(2008,2013)andSciencesof Geodesy (2010, 2012), as well as other scientific endeavours. In 2014 the author moved from Germany to a position at Shandong University in Weihai to create a new area of study comprising navigation, remotesensing, and celestial mechanics. TherapiddevelopmentoftheGPS,GLONASS,Galileo,andBeiDousystems,and therealisation ofnet-based multi-system real-time civilGNSSapplicationsatGFZ inGermanyandatShandongUniversity,providedtheimpetusforthismostrecent revisionofthebook.Dr.-Ing.YanXu,whohasplayedanimportantrole,wasasked to be the second author. A fully new Chap. 12 has been added, which highlights the newly developed singularity-free theory of analytical satellite orbits. A brief historical review of the singularity problem is presented, and the solution is derived mathematically. The vii viii PrefacetotheThirdEdition study was conducted by the first author of this book with his friends from 2007 to 2015,andthemostelegantformulas—theLagrange-XuandGauss-Xuequationsof motion—werederivedrigorouslyandmathematicallyandaredescribedhereforthe firsttime. Threesingularitycriteriawithclear geometricmeaningaredefined.This theoryopenedupanewareaofstudyinorbitdeterminationusinganalyticaltheory and is believed to be extremely important with respect to GNSS applications for onboard orbit determination. Chapters that have been intensively revised and supplemented are the first, “Introduction”; the fifth, “Physical Influences of GPS Surveying”; the eighth, “CycleSlipDetectionandAmbiguityResolution”;andtheninth,“Parameterisation andAlgorithmsofGPSDataProcessing”.Theothersareminorlyrevised.Theseare reviews of the works of scientists around the world. The supplemented content concerns the following 25 points. 1. Review of GPS modernisation 2. Review of the key developments of GLONASS 3. Review of the development of the Galileo system 4. Review of the development of the Compass (BeiDou) system 5. Review of progress in ionospheric studies 6. Review of tropospheric research 7. Research concerning the GPS clock 8. Review of the use of an external clock 9. Introduction of water vapour measurements 10. Review of activities involving GPS altimetry 11. Review of the study of GPS equivalence algorithms 12. The evaluation of ambiguity search criteria 13. Review of research progress in adaptive filtering 14. Research on GPS data processing by combined and uncombined methods 15. Research on reference satellite changes in the GPS difference algorithm 16. Research on tropospheric models in airborne kinematic positioning 17. Research on reference station changes in the GPS difference algorithm 18. Review offloat ambiguity fixing 19. Outline of the progress in precise point positioning 20. GPS software introduction 21. Review of satellite orbital theory 22. Review of numerical orbit determination 23. Summary of GEO satellite orbit determination 24. Research on independent parameterisation 25. Summary of problems remaining in GPS research With such intensive content supplementation, the authors hope that this new edition of GPS can better serve as a reference for GNSS research and study. The theoreticalcontributionsandnewfindingsintheoriginaleditionofthisbookcanbe summarised as follows: 1. The soft equivalence of differencing and undifferenced GPS algorithms 2. The unified GPS data processing algorithm PrefacetotheThirdEdition ix 3. The general ambiguity search criterion 4. The equivalent ambiguity search criterion 5. The diagonalisation algorithm 6. Yang’s filter—adaptive robust Kalman filtering 7. Theory of numerical orbit determination using GPS 8. The algebraic solution of the variation equation 9. The problem of the ambiguity function criterion The new findings supplemented in the second edition are as follows: 1. The equivalence of combined and uncombined GPS algorithms 2. The independent parameterisation method 3. The equivalence theorem of GPS algorithms 4. The optimal differential GPS baseline network 5. The new model of solar radiation 6. The new model of atmospheric drag New theoretical content in this third edition can be described as follows: 1. The equivalent equations of triple differences 2. The idea of an intelligent Kalman filter 3. Float ambiguity fixing in the case of ionosphere-free combination 4. The singularity-free Lagrange-Xu equations of motion 5. The singularity-free Gauss-Xu equations of motion 6. The criteria of singularity and their geometric meaning The extendedcontentisderived inpartfrom publishedinternational papers and has been subjected to individual review. We thank Academician Yuanxi Yang of the Institute of Surveying and Mapping in Xian, Prof. Ta-Kang Yeh of Taibei University of Taiwan, Prof. Wu Chen of Hong Kong Polytech University, Prof. Yunzhong Shen of TongJi University, and Prof. Zhiping Lv of the Institute of Surveying and Mapping in Zhengzhou for their valuable review of portions of the supplemented content of this book. The first author extends sincere thanks to Prof. Dr. D. Lelgemann of TU Berlin forsupervisionoftheauthor’sPh.D.studyandworkmanyyearsago.Thanksgoto the directors Prof. Dr. Ch. Reigber, Prof. Dr. Markus Rothacher, and Prof. Dr. Harald Schuh of GFZ for their support and faith in the author during his approximately 20 years of research activities at GFZ. Prof. Ming Li of the China Academy of Space Technology (CAST) is thanked for the unwavering support since the author’s involvement at CAST as Thousand Talents expert. Of course, Shandong University at Weihai is thanked for the opportunity to develop a new studyareaandformaninternationalteam,aswellasobtaininginternalandexternal funding support. The second author is thanked for taking over most of the text processing work for this new edition. Thenavigation/remotesensingteammembersofShandongUniversityatWeihai are thanked for their warm support. Special thanks go to Thousand Talents expert Prof. Hermann Kaufmann of Germany, Guest Prof. Pierre Rochus of Belgium, x PrefacetotheThirdEdition GuestProf.LuisaBastosofPortugal,GuestProf.AnnaJenssenofSweden,scientist NinaBoesche,andguestengineerNanJiangofGermany,seniorengineersWenlin Yan and Zhangzheng Sun, engineers Chunhua Jiang and Fangzhao Zhang, post-doctoral researchers Yujun Du and Fang Gao, and Ph.D. candidate Wenfeng Nie. January 2016 Guochang Xu Yan Xu References HeKF(2015)GNSSKinematicPositionandVelocityDeterminationforAirborneGravimetry.PhD Thesis,(ScientificTechnicalReport;15/04).Potsdam:DeutschesGeoForschungsZentrumGFZ. http://doi.org/10.2312/GFZ.b103-15044 Wang Q, Xu G, Chen Z (2010) Interpolation Method of Tropospheric Delay of High Altitude Rover Based on Regional GPS Network. Geomatics and Information Science of Wuhan University,35(12),1405–1408 XuG(1999):KGsoft–KinematicGPSSoftware–SoftwareUserManual,Versionof1999,Kort &Matrikelstyrelsen(NationalSurveyandCadastre–Denmark),ISBN87-7866-158-7,ISSN 0109-1344,35pages,inEnglish Xu G (2004) MFGsoft – Multi-Functional GPS/(Galileo) Software – Software User Manual, (Version of 2004), Scientific Technical Report STR04/17 of GeoForschungsZentrum (GFZ)Potsdam,ISSN1610-0956,70pages,www.gfz-potsdam.de/bib/pub/str0417/0417.pdf XuG,SchwintzerP,ReigberCh(1998)KSGSoft–Kinematic/StaticGPSSoftware–Softwareuser manual (version of 1998). Scientific Technical Report STR98/19 of GeoForschungsZentrum (GFZ)Potsdam XuG,XuJ(2012)OntheSingularity ProblemofOrbitalMechanics,MNRAS, 2013,Vol.429, pp1139-1148 Xu G, Xu J (2013a) On Orbital Disturbance of Solar Radiation, MNRAS, 432 (1): 584-588 doi:10.1093/mnras/stt483 Xu G, Xu J (2013b) Orbits – 2nd Order Singularity-free Solutions, second edition, Springer Heidelberg,ISBN978-3-642-32792-6,426pages,inEnglish Xu G, Xu TH, Chen W, Yeh TK (2010b) Analytic Solution of Satellite Orbit Perturbed by AtmosphericDrag,MNRAS,Vol.410,Issue1,pp654-66287. XuG,XuTH,YehTK,ChenW(2010a)AnalyticSolutionofSatelliteOrbitPerturbedbyLunar andSolarGravitation,MNRAS,Vol.410,Issue1,pp645-653 Xu Y, Yang Y, Zhang Q, Xu G (2011) Solar Oblateness and Mercury’s Perihelion Precession, MNRAS,Vol.415,3335-3343 Preface to the Second Edition After the first edition of this book was published at the end of 2003, I was very happy to put the hard work of book writing behind me and concentrate with my small team on the development of multi-functional GPS/Galileo software (MFGsoft).Theexperiencesfromthepracticeandimplementationofthetheoryand algorithmsintohigh-standardsoftwarecausedmetostronglyfeelthatIwouldlike toreviseandtosupplementtheoriginalbook,tomodifysomeofthecontent,andto reportonthenewdevelopmentsandknowledge.Furthermore,withtheEUGalileo systemnowbeingrealisedandtheRussianGLONASSsystemunderdevelopment, GPS theory and algorithms needed to be re-described so that they would be valid fortheGalileoandGLONASSsystemsaswell.Therefore,Iamgratefultoallofthe readersofthisbook,whoseinterestledSpringertoaskmetocompletethissecond edition. I remember that I was in a hurry during the last check of the layout of the first edition. The description of a numerical solution to the variation equation in Sect. 11.5.1 was added to the book at the last minute, and comprised exactly one page. Traditionally, variation equations in orbit determination (OD), geopotential mapping, and OD Kalman filtering, have been solved by integration, which is complicated and compute-intensive. This marks the first time in the history of OD that the variation equation is not integrated, but is solved by a linear algebraic equation system. However, this was mentioned neither in the preface nor at the beginningofthechapter.Thehighprecisionofthisalgebraicmethodisverifiedby a numerical test. TheproblemsdiscussedinChap.12ofthefirsteditionarelargelysolvedandare now described by the so-called independent parameterisation theory, which points out that in both undifferenced and differencing algorithms, the independent ambi- guity vector is double-differencing. With the use of this parameterisation method, theGPSobservationequationsareregularequations,andcanbesolvedwithoutany a priori information. Many conclusions may be derived from this new knowledge. For example, synchronisation of the GPS clocks may not be realised by the carrier-phaseobservablesbecauseofthelinearcorrelationsbetweentheclockerror xi