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INFORMATION TO USERS This manuscript has been reproduced from the m icrofilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. A Bell & Howell Information Com pany 300 North Zeeb Road. Ann Arbor. Ml 48106-1346 USA 313/761-4700 800/521-0600 INVESTIGATION OF STOCHASTIC MODELS TO IMPROVE THE GLOBAL POSITIONING SYSTEM SATELLITE ORBITS DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By C. David Chadwell, B.S.C.E., B.S.S., M.S. ***** The Ohio State University 1995 Dissertation Committee Approved by Clyde C. Goad Christopher Jekeli Adviser Richard H. Rapp Department of Geodetic Science and Surveying UMI Number: 9526006 UMI Microform 9526006 Copyright 1995, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 DEDICATION To Susan ACKNOWLEDGMENTS This research work has been the possible through the help of many people. First, I would like to thank my adviser, Professor Clyde C. Goad for his guidance, availability, enthusiasm and flexibility. I thank the reading committee: Professor Christopher Jekeli and Professor Richard R. Rapp for their valuable comments that improved this work. I would like to express my sincere gratitude to Professor Ivan I. Mueller for his comments and for the use of his well-organized library. Also, thanks to Dr. Erricos C. Pavlis and Mr. David Rowlands of the Space Geodesy branch, Goddard Spaceflight Center, who answered my many questions about the GEODYNII software. During my stay at Ohio State, I met many people with whom discussions of things, geodetic and other, have made my time there quite enjoyable. Most recently, I want to thank Ms. Dorota Grejner-Brzezinska, Mr. Ming Yang, Mr. Jeong Hee Kim, Dr. Yan Ming Wang, and Mr. Jarir Saleh, and from earlier times Mr. Kevin Stacy and Mr. Rob Tudhope. Thanks also to Dr. Lonnie G. Thompson for two years of GRA support at the Byrd Polar Research Center and hiring an undergraduate surveyor many years ago. A special thanks to my wife Susan for her typing, and more importantly, her constant enthusiasm during the many years of my graduate studies. Thanks to NASA/GSFC for the support to work on an interesting project involving their GEODYNII orbit determination software on Grant NAG 5-2041 Many thanks to the Department of Geodetic Science and Surveying for support as a Graduate Teaching Associate and a Graduate Research Associate. I’d also like to thank the Ohio Supercomputer Center for providing computer support for this study. iv TABLE OF CONTENTS DEDICATION .......................................................................................................... ii ACKNOWLEDGMENTS......................................................................................... iii LIST OF TABLES ................................................................................................... viii LIST OF FIGURES ................................................................................................... x CHAPTER PAGE I INTRODUCTION ............................................................................................. 1 II ORBITAL DYNAMICS AND SITE DISPLACEMENT........................... 7 2.1 Reference F ram e s ...................................................................................... 11 2.1.1 Celestial Reference Fram e .............................................................. 12 2.1.2 Terrestrial Reference Fram e .......................................................... 12 2.1.3 Transformations ............................................................................... 13 2.1.4 Relativistic Effects ........................................................................ 15 2.2 Earth’s Geopotential .................................................................................. 18 2.2.1 Admission o f C2i ,S 2l Coefficients ................................................ 21 2.2.2 Pole T ide ......................................................................................... 22 2.3 Third Body Acceleration and the Indirect Oblation E ffect ................ 23 2.3.1 Indirect Oblation Perturbation ....................................................... 24 2.4 Solar Radiation Pressure ........................................................................... 25 2.4.1 ROCK4 and ROCK42 M o d e ls ................................................... 27 2.4.2 Y-Bias Acceleration ........................................................................ 31 2.4.3 Earth Radiation (Albedo) .............................................................. 33 2.4.4 GPS Eclipse Effects on Acceleration M odeling ........................ 33 2.4.5 New GPS Attitude M odel .............................................................. 36 2.4.6 Resonant Acceleration M odel ....................................................... 37 2.5 Ocean Tide M odel .................................................................................... 38 2.6 Solid Earth Tide M odel .......................................................................... 40 2.6.1 Treatment of Permanent T id e ...................................................... 42 v 2.7 Station Displacement Due to Pole T id e ................................................ 43 2.8 Station Displacement Due to Solid Earth ................................................. 45 2.9 Ocean Loading .......................................................................................... 47 III OBSERVATION MODELING .................................................................... 49 3 .1 The GPS Observables............................................................................... 50 3.2 Selective Availability (SA) and Anti-Spoofing (A S ) ........................... 52 3.3 Satellite and Receiver C locks ................................................................. 53 3.4 Propagation M edium ............................................................................... 55 3 .4.1 Ionospheric Refraction ................................................................. 56 3.4.2 Troposphere .................................................................................. 60 3.4.3 Relativistic Propagation ................................................................. 65 3.5 M ultipath.................................................................................................... 66 3 .6 Antenna Offset and Orientation .............................................................. 66 IV. ESTIM A TO R S.................................................................................................... 67 4.1 Filtering and Sm oothing ........................................................................... 70 4.2 Square Root Information Filter and Smoother (SRIF/SRIS) 75 4.3 Epoch State SRIF/SRIS........................................................................... 82 4.4 Time-Varying Stochastic Parameter M odels ......................................... 96 4.5 The Dynamic Stochastic Parameter Transition M atrix ........................ 98 4.6 Observable Decorrelation and Normalization ......................................... 100 V ORBIT DETERMINATION USING A BATCH LEAST-SQUARES ESTIMATOR AND DETERMINISTIC M ODELS .................................. 102 5.1 Experiments A, B, and C, Parameter Selection .................................. 103 5 .2 The International GPS Geodynamics Service (IGS) Tracking Data and O rb its ................................................................................................... 109 5.3 Experiments A, B, and C, Deterministic Dynamic Model Fits to the IGS O rb its .................................................................................................... 114 5 .4 Ground Station Tracking Data Preprocessing ...................................... 116 5.5 Experiment A, B, and C, Batch Least-Squares GPS Orbit Determination Using IGS Tracking Stations ......................................... 124 VI ORBIT DETERMINATION USING A SQUARE ROOT INFORMATION FILTER/SMOOTHER AND STOCHASTIC MODELS 127 6.1 Empirical Autocorrelation Functions ....................................................... 128 6.2 Stochastic