Satellite Orbit and Ephemeris Determination using Inter Satellite Links
Satellite Orbit and Ephemeris Determination using Inter Satellite Links Satellite Orbit and Ephemeris Determination using Inter Satellite Links
Inter Satellite LinksGLONASS - wurden untersucht und mit zwei weiteren Formaten verglichen, die im Rahmendieser Arbeit entwickelt wurden.Desweiteren wurde das Thema der bordautonomen Verarbeitung von Messungen behandelt.Ein konzeptuelles Design für einen Onboard-Prozessor wurde vorgeschlagen und dieAlgorithmen implementiert. Dabei erfolgte eine Abschätzung der benötigtenProzessorleistung. Einer der Hauptvorteile der bordautonomen Verarbeitung vonIntersatellitenmessungen, die Möglichkeit zur Überwachung der Integrität der Ephemeridenund Uhrenparameter, wurde in komplexen Simulationen untersucht. Durch die Simulationverschiedener Fehlerfälle wurde gezeigt, das kein Detektionsmechanismus allein, wohl abereine sinnvolle Kombination solcher Mechanismen, zur bordautonomenIntegritätsüberwachung geeignet sind. Die Ergebissen werden hier präsentiert.Page ivR. Wolf
Inter Satellite LinksTable of Contents1 INTRODUCTION............................................................................................................................ 12 ISL OBSERVATION MODEL....................................................................................................... 42.1 DERIVATION OF THE RANGE EQUATION .................................................................................. 42.2 DERIVATION OF THE RANGE RATE EQUATION........................................................................ 53 STATE ESTIMATION.................................................................................................................... 73.1 LINEARIZATION OF DYNAMIC AND OBSERVATION MODEL.................................................... 73.2 STATE VECTOR........................................................................................................................... 83.3 STATE TRANSITION AND TRANSITION MATRIX ..................................................................... 103.4 LEAST SQUARES BATCH ESTIMATION .................................................................................... 133.4.1 WEIGHTED LEAST SQUARES ............................................................................................... 143.4.2 INTRODUCING APRIORI STATISTIC INFORMATION............................................................... 153.5 KALMAN FILTERING ................................................................................................................ 153.5.1 REAL TIME ESTIMATION ..................................................................................................... 153.5.2 FILTERING TO EPOCH........................................................................................................... 163.5.3 FILTER STRUCTURES ........................................................................................................... 174 ORBIT COMPUTATION.............................................................................................................194.1 ANALYTICAL SOLUTION .......................................................................................................... 194.1.1 KEPLER ORBITS ................................................................................................................... 204.1.2 ACCOUNTING FOR SECULAR PERTURBATIONS.................................................................... 224.2 NUMERICAL INTEGRATION OF THE EQUATIONS OF MOTION............................................... 234.2.1 EARTH’S GRAVITY .............................................................................................................. 264.2.1.1 Computation of Legendre Polynomials and Functions................................................. 274.2.1.2 Normalisation................................................................................................................ 284.2.1.3 Computation of Gravity ................................................................................................ 294.2.2 THIRD BODY ATTRACTION.................................................................................................. 324.2.3 SOLAR PRESSURE ................................................................................................................ 324.2.4 AIR DRAG ............................................................................................................................ 334.2.5 SOLID EARTH TIDES ............................................................................................................ 354.2.6 OCEAN TIDES....................................................................................................................... 364.2.7 EARTH ALBEDO ................................................................................................................... 374.2.8 VEHICLE THRUST ................................................................................................................ 374.3 FORCE MODEL ERRORS........................................................................................................... 394.3.1 EARTH'S GRAVITY............................................................................................................... 394.3.2 THIRD BODY ATTRACTION (DIRECT TIDAL EFFECTS) ........................................................ 474.3.3 SOLAR RADIATION PRESSURE............................................................................................. 504.3.4 AIR DRAG ............................................................................................................................ 524.3.5 OTHER PERTURBATIONS...................................................................................................... 554.3.6 NUMERICAL ERRORS ........................................................................................................... 58R. Wolf Page i
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<strong>Inter</strong> <strong>Satellite</strong> <strong>Links</strong>Table of Contents1 INTRODUCTION............................................................................................................................ 12 ISL OBSERVATION MODEL....................................................................................................... 42.1 DERIVATION OF THE RANGE EQUATION .................................................................................. 42.2 DERIVATION OF THE RANGE RATE EQUATION........................................................................ 53 STATE ESTIMATION.................................................................................................................... 73.1 LINEARIZATION OF DYNAMIC AND OBSERVATION MODEL.................................................... 73.2 STATE VECTOR........................................................................................................................... 83.3 STATE TRANSITION AND TRANSITION MATRIX ..................................................................... 103.4 LEAST SQUARES BATCH ESTIMATION .................................................................................... 133.4.1 WEIGHTED LEAST SQUARES ............................................................................................... 143.4.2 INTRODUCING APRIORI STATISTIC INFORMATION............................................................... 153.5 KALMAN FILTERING ................................................................................................................ 153.5.1 REAL TIME ESTIMATION ..................................................................................................... 153.5.2 FILTERING TO EPOCH........................................................................................................... 163.5.3 FILTER STRUCTURES ........................................................................................................... 174 ORBIT COMPUTATION.............................................................................................................194.1 ANALYTICAL SOLUTION .......................................................................................................... 194.1.1 KEPLER ORBITS ................................................................................................................... 204.1.2 ACCOUNTING FOR SECULAR PERTURBATIONS.................................................................... 224.2 NUMERICAL INTEGRATION OF THE EQUATIONS OF MOTION............................................... 234.2.1 EARTH’S GRAVITY .............................................................................................................. 264.2.1.1 Computation of Legendre Polynomials <strong>and</strong> Functions................................................. 274.2.1.2 Normalisation................................................................................................................ 284.2.1.3 Computation of Gravity ................................................................................................ 294.2.2 THIRD BODY ATTRACTION.................................................................................................. 324.2.3 SOLAR PRESSURE ................................................................................................................ 324.2.4 AIR DRAG ............................................................................................................................ 334.2.5 SOLID EARTH TIDES ............................................................................................................ 354.2.6 OCEAN TIDES....................................................................................................................... 364.2.7 EARTH ALBEDO ................................................................................................................... 374.2.8 VEHICLE THRUST ................................................................................................................ 374.3 FORCE MODEL ERRORS........................................................................................................... 394.3.1 EARTH'S GRAVITY............................................................................................................... 394.3.2 THIRD BODY ATTRACTION (DIRECT TIDAL EFFECTS) ........................................................ 474.3.3 SOLAR RADIATION PRESSURE............................................................................................. 504.3.4 AIR DRAG ............................................................................................................................ 524.3.5 OTHER PERTURBATIONS...................................................................................................... 554.3.6 NUMERICAL ERRORS ........................................................................................................... 58R. Wolf Page i
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