INFORMATION TO USERS This manuscript has been reproduced horn the microfilm 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 bleedthrough, 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 Company 300 North Zeeb Road. Ann Arbor. Ml 48106-1346 USA 313-'761-4700 800/521-0600 ANALYSIS OF GPS DATA PROCESSING TECHNIQUES: IN SEARCH OF OPTIMIZED STRATEGY OF ORBIT AND EARTH ROTATION PARAMETER RECOVERY DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the Graduate School of The Ohio State University By Dorota A. Grejner-Brzezinska, M.S., M.S. ***** The Ohio State University 1995 Dissertation Committee: Approved by John D. Bossier Clyde C. Goad Ivan L Mueller Adviser Department of Geodetic Science and Surveying UMI N um ber: 9612187 OMI Microform 9612187 Copyright 1996, 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 To my daughter Bogna ...who always keeps my spirit up... ACKNOWLEDGMENTS First and foremost, I wish to express my deepest appreciation and thanks to my husband Robert and my daughter Bogna for their patience, constant support and unshakable faith in me during the difficult and long but certainly fruitful years of my graduate studies. To my daughter, Bogna, I thank you for understanding my frequent absences. Very special thanks go to my mother, my sister and my mother-in-law in Poland, for their encouragement, support and belief in me. I wish to express my deep gratitude to my adviser, Dr. Clyde C. Goad, for his professional guidance and assistance, and the valuable help throughout my graduate studies at the Department of Geodetic Science and Surveying, and during the course of my doctoral research. His support, understanding and encouragement are greatly appreciated. I am also very thankful and truly indebted to Dr. Ivan I. Mueller, for his valuable guidance, expert advice and constant encouragement. I want to thank him for his support and understanding, for many stimulating discussions, and also for permission to use his invaluable and unique personal library. My gratitude and appreciation go to Dr. John D. Bossier, for the stimulating and constructive discussions and valuable suggestions which greatly enhanced the quality of this dissertation. In addition, I wish to acknowledge the invaluable contribution of all the faculty of the Department of Geodetic Science and Surveying to my education. Special thanks are also due to my fellow students, past and present: Dr. David Chadwell (now at Scripps Institution of Oceanography, La Jolla), Dr. Ming Yang (now at National Cheng Kung University in Tainan, Taiwan) and Jarir Saleh (now at the University of the West Indies, Trinidad), for their help, valuable comments and stimulating discussions during all the years we spent together in Cockins Hall. My deep appreciation goes to Mrs. Irene Tesfai, “expert grammarian and dialectician,” for her help and advice during the typing of this manuscript. VITA March 10,1963 ....................................... Bom, Poland 1986 ........................................................ M.S., Agricultural and Technical University of Olsztyn, Poland 1986-1990 ............................................... Agricultural and Technical University of Olsztyn, Poland 1995 ................ ........................................ M.S., The Ohio State University, Columbus, Ohio 1990-present ............................................Graduate Teaching Associate & Graduate Research Associate, The Ohio State University, Columbus, Ohio PUBLICATIONS Goad, C. C., Grejner-Brzezinska, D. A , Yang, M., Determination of High-Precision GPS Orbits Using Triple Differencing Technique, submitted to Bulletin Geodesique/manuscripta geodaetica/Journal o f Geodesy, June 1995. Grejner, G., Grejner-Brzezinska, D. A , New Methods in Land Information Data Gathering, Proceedings of International Conference of Young Scholars, Olsztyn, Poland, September 1990. Grejner, D. A , Successors of the Transit System. GPS - Future of the Space Methods for Positioning, Przeglad Geodezyjny 61(1), pp. 3-9, 1989. Grejner, D. A, Precise Relative Positioning with GPS Phases - Accuracy Analysis, Acta Academiae AC Technicae Olstenesis 19, pp. 19-29,1989. FIELDS OF STUDY Major Field: Geodetic Science and Surveying • Studies in Geodetic Astronomy, Satellite Geodesy, Geodynamics: Prof. Ivan I. Mueller • Studies in Physical Geodesy, Geometric Geodesy: Prof. Richard H. Rapp • Studies in Global Positioning System, Advanced Satellite Geodesy, Geometric Geodesy: Prof. Clyde C. Goad • Studies in Adjustment Computations: Prof Burkhard Schaflrin TABLE OF CONTENTS DEDICATION.................................................................................................... ii ACKNOWLEDGMENTS.................................................................................... iii VITA.................................................................................................................. v LIST OF FIGURES.............................................................................................. xi LIST OF TABLES.............................................................................................. xv CHAPTER PAGE I. INTRODUCTION................................................................................... 1 n . GLOBAL POSITIONING SYSTEM. GENERAL OVERVIEW AND DATA MODELING................................................................................ 8 2.1. GPS System and Signal Description .................................................... 8 2.2. GPS Data Modeling .......................................................................... 15 2.2.1. Types of Observables: Pseudoranges, Carrier Phases and Their Combinations ....................................................... 15 2.2.2. Correlation Between Differenced Observations .................... 21 2.3. GPS Observation Error Sources and Corrections ................................ 23 2.3.1. Ionospheric Refraction ......................................................... 28 2.3.2. Tropospheric Refraction ...................................................... 32 m . REFERENCE FRAMES AND TIME SYSTEMS..................................... 39 3.1. Conventional Celestial Reference System ............................................ 40 3.2. Conventional Terrestrial Reference System ......................................... 41 3.3. Transformation Between Terrestrial and Celestial Reference Systems.. 44 3.4. Relativistic Effects on Reference Frames and Time ............................. 47 3.5. Time Systems.................................................................................... 50 3.5.1. Sidereal and Solar Time Systems .......................................... 51 3.5.2. Atomic Time Scale............................................................. 53 3.5.3. Dynamical Time Scale .......................................................... 53 vii IV. MODELING OF THE MOTION OF THE EARTH ORBITING SPACECRAFT; TERRESTRIAL SITE DYNAMICS.............................. 56 4.1. Equations of Motion and Variational Equations of the Earth Orbiting Satellite ............................................................................... 56 4.2. Numerical Integration of Equations of Motion and Variational Equations .......................................................................................... 59 4.2.1. Adams Type Predictor/Corrector Formulae .......................... 60 4.3. Total Perturbation Model .................................................................. 61 4.3.1. Noncentral Gravitational Potential of The Earth ................... 62 4.3.2. Third-Body Attraction and the Indirect Oblation Effect 66 4.3.3. Direct Solar Radiation Pressure ............................................ 67 4.3.3.1. Solar Radiation Pressure Model for GPS Satellites: ROCK4 and ROCK42 ........................................ 68 4.3.3.2. Acceleration due to the 7-bias ............................ 70 4.3.3.3. Effect of the Eclipse on the Modeling of the Motion of GPS satellites ..................................... 71 4.3.3.4. Spacecraft Attitude Model .................................. 77 4.3.4. Earth Radiation (Albedo) ...................................................