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Satellite Orbit and Ephemeris Determination Using Inter Satellite Links

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Satellite Orbit and Ephemeris Determination Using Inter Satellite Links Satellite Orbit and Ephemeris Determination using Inter Satellite Links by Robert Wolf Vollständiger Abdruck der an der Fakultät für Bauingenieur- und Vermessungswesen der Universität der Bundeswehr München zur Erlangung des akademischen Grades eines Doktors der Ingenieurswissenschaften (Dr.-Ing.) eingereichten Dissertation. (© 2000) Inter Satellite Links Page ii R. Wolf Inter Satellite Links Abstract Global navigation satellite systems like GPS, GLONASS or the future systems like Galileo require precise orbit and clock estimates in order to provide high positioning performance. Within the frame of this Ph. D. thesis, the theory of orbit determination and orbit computation is reviewed and a new approach for precise orbit and ephemeris determination using inter- satellite links is developed. To investigate the achievable accuracy, models of the various perturbing forces acting on a satellite have been elaborated and coded in a complex software package, allowing system level performance analysis as well as detailed evaluation of orbit prediction and orbit estimation algorithms. Several satellite constellations have been simulated, involving nearly all classes of orbit altitude and the results are compared. The purpose of orbit determination in a satellite navigation system is the derivation of ephemeris parameters which can be broadcast to the user community (or the other satellites) and allow easy computation of the satellites position at the desired epoch. The broadcast ephemeris model of both today existing satellite navigation systems, GPS and GLONASS are investigated, as well as two new models developed within this thesis, which are derivates of the GLONASS model. Furthermore, the topic of autonomous onboard processing is addressed. A conceptual design for an onboard orbit estimator is proposed and investigated with respect to the computational load. The algorithms have been implemented. The main benefits of ISL onboard processing, especially with respect to the great potential to ephemeris and clock state monitoring are investigated using complex simulations of failure scenarios. By simulating several types of non-integrity cases, it is showed that one single fault detection mechanism is likely to be insufficient. Within the algorithm design of the onboard processor, a reasonable combination of fault detection mechanisms is presented, covering different fault cases. Zusammenfassung Globale Navigationssysteme wie GPS, GLONASS oder zukünftige Systeme wie Galileo erfordern die hochpräzise Bestimmung der Orbital- und Uhrenparameter, um hohe Navigationsgenauigkeit bieten zu können. Im Rahmen dieser Dissertation wurde die Theorie der Orbitprädiktion und der Orbitbestimmung erörtert und ein neuer Ansatz für die präzisen Orbitbestimmung mit Hilfe von Intersatelliten-Messungen entwickelt. Um die erreichbare Genauigkeit und Präzision der Orbitbestimmung zu untersuchen, wurden mathematische Modelle der zahlreiche Orbitstörungen erarbeitet und in einem komplexen Software-Paket implemetiert. Dieses bietet die Möglichkeit für Systemstudien von Satellitennavigations- Systemen beliebiger Orbitklassen, sowie zur detaillierten Untersuchung spezieller Fragestellungen der Orbitprädiktion und -bestimmung. Eine Reihe von Simulationen mit existierenden sowie fiktiven Satelliten-Navigations-Systemen wurden durchgeführt, deren Ergebnisse in dieser Arbeit präsentiert werden. Die präzise Orbitbestimmung in einem SatNav-System ist kein Selbstzweck, sondern dient lediglich der Bestimmung der Ephemeridenparameter, die - vom Satellite gesendet - es dem Nutzer-Empfänger erlauben, mit Hilfe einfacher Berechnungen die Position des Satelliten zu ermitteln. Die Ephemeridenformate beider existierender SatNav-Systeme - GPS und R. Wolf Page iii Inter Satellite Links GLONASS - wurden untersucht und mit zwei weiteren Formaten verglichen, die im Rahmen dieser Arbeit entwickelt wurden. Desweiteren wurde das Thema der bordautonomen Verarbeitung von Messungen behandelt. Ein konzeptuelles Design für einen Onboard-Prozessor wurde vorgeschlagen und die Algorithmen implementiert. Dabei erfolgte eine Abschätzung der benötigten Prozessorleistung. Einer der Hauptvorteile der bordautonomen Verarbeitung von Intersatellitenmessungen, die Möglichkeit zur Überwachung der Integrität der Ephemeriden und Uhrenparameter, wurde in komplexen Simulationen untersucht. Durch die Simulation verschiedener Fehlerfälle wurde gezeigt, das kein Detektionsmechanismus allein, wohl aber eine sinnvolle Kombination solcher Mechanismen, zur bordautonomen Integritätsüberwachung geeignet sind. Die Ergebissen werden hier präsentiert. Page iv R. Wolf Inter Satellite Links Table of Contents 1 INTRODUCTION............................................................................................................................ 1 2 ISL OBSERVATION MODEL....................................................................................................... 4 2.1 DERIVATION OF THE RANGE EQUATION .................................................................................. 4 2.2 DERIVATION OF THE RANGE RATE EQUATION ........................................................................ 5 3 STATE ESTIMATION.................................................................................................................... 7 3.1 LINEARIZATION OF DYNAMIC AND OBSERVATION MODEL .................................................... 7 3.2 STATE VECTOR........................................................................................................................... 8 3.3 STATE TRANSITION AND TRANSITION MATRIX ..................................................................... 10 3.4 LEAST SQUARES BATCH ESTIMATION .................................................................................... 13 3.4.1 WEIGHTED LEAST SQUARES ............................................................................................... 14 3.4.2 INTRODUCING APRIORI STATISTIC INFORMATION............................................................... 15 3.5 KALMAN FILTERING ................................................................................................................ 15 3.5.1 REAL TIME ESTIMATION ..................................................................................................... 15 3.5.2 FILTERING TO EPOCH........................................................................................................... 16 3.5.3 FILTER STRUCTURES ........................................................................................................... 17 4 ORBIT COMPUTATION.............................................................................................................19 4.1 ANALYTICAL SOLUTION .......................................................................................................... 19 4.1.1 KEPLER ORBITS ................................................................................................................... 20 4.1.2 ACCOUNTING FOR SECULAR PERTURBATIONS.................................................................... 22 4.2 NUMERICAL INTEGRATION OF THE EQUATIONS OF MOTION............................................... 23 4.2.1 EARTH’S GRAVITY .............................................................................................................. 26 4.2.1.1 Computation of Legendre Polynomials and Functions................................................. 27 4.2.1.2 Normalisation................................................................................................................ 28 4.2.1.3 Computation of Gravity ................................................................................................ 29 4.2.2 THIRD BODY ATTRACTION.................................................................................................. 32 4.2.3 SOLAR PRESSURE ................................................................................................................ 32 4.2.4 AIR DRAG ............................................................................................................................ 33 4.2.5 SOLID EARTH TIDES ............................................................................................................ 35 4.2.6 OCEAN TIDES....................................................................................................................... 36 4.2.7 EARTH ALBEDO ................................................................................................................... 37 4.2.8 VEHICLE THRUST ................................................................................................................ 37 4.3 FORCE MODEL ERRORS........................................................................................................... 39 4.3.1 EARTH'S GRAVITY ............................................................................................................... 39 4.3.2 THIRD BODY ATTRACTION (DIRECT TIDAL EFFECTS) ........................................................ 47 4.3.3 SOLAR RADIATION PRESSURE ............................................................................................. 50 4.3.4 AIR DRAG ............................................................................................................................ 52 4.3.5 OTHER PERTURBATIONS...................................................................................................... 55 4.3.6 NUMERICAL ERRORS ..........................................................................................................
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