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The GLAS Algorithm Theoretical Basis Document for Precision Orbit Determination (POD) NASA/TM–2013-208641 / Vol 11 ICESat (GLAS) Science Processing Software Document Series The GLAS Algorithm Theoretical Basis Document for Precision Orbit Determination (POD) Hyung Jin Rim, S. P. Yoon, and Bob E. Schutz National Aeronautics and Space Administration Goddard Space Flight Center Greenbelt, Maryland 20771 March 2013 NASA STI Program ... in Profile Since its founding, NASA has been dedicated to the • CONFERENCE PUBLICATION. Collected advancement of aeronautics and space science. The papers from scientific and technical conferences, NASA scientific and technical information (STI) pro- symposia, seminars, or other meetings sponsored or gram plays a key part in helping NASA maintain this co-sponsored by NASA. important role. • SPECIAL PUBLICATION. 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Yoon Center for Space Research, The University of Texas at Austin Bob E. Schutz Center for Space Research, The University of Texas at Austin National Aeronautics and Space Administration Goddard Space Flight Center Greenbelt, Maryland 20771 March 2013 Notice for Copyrighted Information This manuscript has been authored by employees of Center for Space Research, The University of Texas at Austin with the National Aeronautics and Space Administration. The United States Government has a non-exclusive, irrevocable, worldwide license to prepare derivative works, publish, or reproduce this manuscript, and allow others to do so, for United States Government purposes. Any publisher accepting this manuscript for publication acknowledges that the United States Government retains such a license in any published form of this manuscript. All other rights are retained by the copyright owner. Trade names and trademarks are used in this report for identification only. Their usage does not constitute an official endorsement, either expressed or implied, by the National Aeronautics and Space Administration. Level of Review: This material has been technically reviewed by technical management Available from: NASA Center for AeroSpace Information National Technical Information Service 7115 Standard Drive 5285 Port Royal Road Hanover, MD 21076-1320 Springfield, VA 22161 Price Code: A17 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 3.4.2 Solar Radiation Pressure ............................................................................................... 22 i 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
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