Geoscience Laser Altimeter System (GLAS) Algorithm Theoretical Basis Document Version 2.2 PRECISION ORBIT DETERMINATION (POD) Prepared by: H. J. Rim B. E. Schutz Center for Space Research The University of Texas at Austin October 2002 TABLE OF CONTENTS 1.0 INTRODUCTION..................................................................................................................... 1 1.1 BACKGROUND ....................................................................................................................... 1 1.2 THE POD PROBLEM............................................................................................................... 2 1.3 GPS-BASED POD.................................................................................................................... 2 1.3.1 Historical Perspective ..................................................................................................... 3 1.3.2 GPS-based POD Strategies............................................................................................. 4 1.4 OUTLINE ................................................................................................................................. 6 2.0 OBJECTIVE.............................................................................................................................. 7 3.0 ALGORITHM DESCRIPTION: ORBIT ............................................................................... 8 3.1 ICESAT/GLAS ORBIT DYNAMICS OVERVIEW.................................................................... 8 3.2 EQUATIONS OF MOTION, TIME AND COORDINATE SYSTEMS .......................................... 8 3.2.1 Time System.....................................................................................................................9 3.2.2 Coordinate System......................................................................................................... 10 3.3 GRAVITATIONAL FORCES................................................................................................... 11 3.3.1 Geopotential .................................................................................................................. 11 3.3.2 Solid Earth Tides........................................................................................................... 13 3.3.3 Ocean Tides................................................................................................................... 14 3.3.4 Rotational Deformation................................................................................................. 15 3.3.5 N-Body Perturbation ..................................................................................................... 17 3.3.6 General Relativity.......................................................................................................... 18 3.4 NONGRAVITATIONAL FORCES........................................................................................... 19 3.4.1 Atmospheric Drag ......................................................................................................... 20 2 3.4.2 Solar Radiation Pressure .............................................................................................. 22 3.4.3 Earth Radiation Pressure.............................................................................................. 23 3.4.4 Thermal Radiation Perturbation ................................................................................... 25 3.4.5 GPS Solar Radiation Pressure Models ......................................................................... 26 3.4.6 ICESat/GLAS "Box-Wing" Model ................................................................................. 28 3.5 EMPIRICAL FORCES............................................................................................................. 29 3.5.1 Empirical Tangential Perturbation ............................................................................... 29 3.5.2 Once-per Revolution RTN Perturbation........................................................................ 30 4.0 ALGORITHM DESCRIPTION: MEASUREMENTS ........................................................ 32 4.1 ICESAT/GLAS MEASUREMENTS OVERVIEW ................................................................... 32 4.2 GPS MEASUREMENT MODEL ............................................................................................. 32 4.2.1 Code Pseudorange Measurement.................................................................................. 32 4.2.2 Phase Pseudorange Measurement ................................................................................ 33 4.2.3 Double-Differenced High-Low Phase Pseudorange Measurement .............................. 37 4.2.4 Corrections.................................................................................................................... 41 4.2.4.1 Propagation Delay ................................................................................................. 41 4.2.4.2 Relativistic Effect .................................................................................................. 43 4.2.4.3 Phase Center Offset ............................................................................................... 44 4.2.4.4 Ground Station Related Effects ............................................................................. 44 4.2.5 Measurement Model Partial Derivatives ...................................................................... 46 4.3 SLR MEASUREMENT MODEL ............................................................................................. 49 4.3.1 Range Model and Corrections ...................................................................................... 49 3 4.3.2 Measurement Model Partial Derivatives ...................................................................... 50 5.0 ALGORITHM DESCRIPTION: ESTIMATION ................................................................ 51 5.1 LEAST SQUARES ESTIMATION ........................................................................................... 51 5.2 PROBLEM FORMULATION FOR MULTI-SATELLITE ORBIT DETERMINATION ............... 56 5.3 OUTPUT ................................................................................................................................68 6.0 IMPLEMENTATION CONSIDERATIONS ....................................................................... 69 6.1 POD SOFTWARE SYSTEM ................................................................................................... 69 6.1.1 Ancillary Inputs ............................................................................................................. 70 6.2 POD PRODUCTS ................................................................................................................... 70 6.3 ICESAT/GLAS ORBIT AND ATTITUDE .............................................................................. 71 6.4 POD ACCURACY ASSESSMENT.......................................................................................... 72 6.5 POD PROCESSING STRATEGY ............................................................................................ 74 6.5.1 Assumptions and Issues................................................................................................. 74 6.5.2 GPS Data Preprocessing............................................................................................... 74 6.5.3 GPS Orbit Determination.............................................................................................. 76 6.5.4 Estimation Strategy ....................................................................................................... 77 6.6 POD PLANS .......................................................................................................................... 77 6.6.1 Pre-Launch POD Activities........................................................................................... 77 6.6.1.1 Standards ............................................................................................................... 78 6.6.1.2 Gravity Model Improvements ............................................................................... 81 6.6.1.3 Non-Gravitational Model Improvements .............................................................. 81 6.6.1.4 Measurement Model Developments...................................................................... 83 4 6.6.1.5 Preparation for Operational POD .......................................................................... 84 6.6.1.6 Software Comparison ............................................................................................ 84 6.6.1.7 POD Accuracy Assessment................................................................................... 85 6.6.2 Post-Launch POD Activities.......................................................................................... 85 6.6.2.1 Verification/Validation Period .............................................................................. 85 6.6.2.2 POD Product Validation........................................................................................ 87 6.6.2.3 POD Reprocessing ................................................................................................ 87 6.7 COMPUTATIONAL: CPU, MEMORY AND DISK STORAGE ................................................ 88 7.0 BIBLIOGRAPHY ................................................................................................................... 91 1.0 INTRODUCTION 1.1 Background