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Xerox University Microfilms 300 North Zoeb Road Ann Arbor, Michigan 48100 - - - .K <1 I**—. 74-17,815 WALSH, Thomas Michael, 1930- ATTITUDE DETERMINATION OF A SPINNING SPACECRAFT THROUGH APPLICATION OF DETECTED AND IDENTIFIED STAR TRANSITS TO THE ESTIMATION OF SPACECRAFT 1 MODEL PARAMETERS. I The Ohio State University, Ph.D., 1974 Engineering, electrical j University Microfilms, A XJERQXCompany, Ann Arbor, Michigan j THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED. ATTITUDE DETERMINATION OF A SPINNING SPACECRAFT THROUGH APPLICATION OF DETECTED AND IDENTIFIED STAR TRANSITS TO THE ESTIMATION OF SPACECRAFT MODEL PARAMETERS DISSERTATION Presented la Partial Fulfillment of the Requirements for the Degraa Doctor of Philosophy In the Graduate School of The Ohio S tate U niversity By Thomas Michael Walsh, B.S.E.E., M.S.E. The Ohio S tate U niversity 1974 Reading Comlttes: Approved By Professor F. C. Weiner Professor C. E. Warren Professor R. B. McGhee Professor F. C. Weiner Adviser Depsrtnsnt of Electrical Engineering ACKNOWLEDGEMENTS As is the case in most investigations of this type, the work reported here is the result of the effort of many people. The author would like to thank all of those who contributed. The author is grate­ ful for the guidance and advice provided by his advisor, Professor F. C. Welmer, throughout the graduate study program and all phases of this dissertation. The author is also grateful to Professors C. E. Warren and R. B. McGhee for serving as memberB of the Reading Committee and for their help and suggestions in the preparation of this dissertation. Acknowledgement must also be given to P rofessor E. C. Foudriat of Marquette University for motivating this author and for his encourage­ ment throughout the course of this work. The research was performed at the Langley Research Center of NASA, who provided the time, facilities, and support for the research program. The help of the staff of the Flight Instrumentation and Analysis and Computation Divisions is appreciated. Among them, the author would most like to thank Mr. Dwayne E. Hinton, whose assistance in all phases of th is e ffo rt was of g reat value. Special thanka must be given to Ms. Julia Gats for her aaeiatance in the preparation of the manuscript and to Ma. Dolllne Clayton for the final typing. Finally, without the understanding and tolerance of my wife and family, completion of this graduate program would not have been possible. ii J VITA July 15, 1930.... Born - Canonsburg, Pennsylvania 1953 ......................... B.S.E.E., Ohio University, Athens, Ohio 1953-1955... ........ Research Engineer, E le c tric a l Power Laboratory Engineers Research and Development Laboratories Ft. Belvoir, Virginia 1955-1957 ............... Research Engineer, Aerospace Division, Westlng- 1958-1959 house Electric Corporation, Baltimore, Maryland 1957-1958 ............... Research Engineer, Martin - Marietta Corporation Orlando, Florida 1959-196 2 ............. Research Engineer, Goodyear Aerospace Corporation Akron, Ohio 1962 ....................... M.S.E., Akron University, Akron, Ohio 1962-1974 . ........... Aerospace Technologist, Langley Research Center N ational Aeronautics and Space A dm inistration Hampton, Virginia 1963-1965....... Lecturer in Electrical Engineering, University of Virginia, Charlottesville, Virginia 1969-1974....... Lecturer In Electrical Engineering, George Washington University, Washington, D.C. 1971-1974 ............. Faculty Meofcer, U niversity of Kansas, Lawrence Kansas 1974 ....................... Lecturer in Electrical Engineering, Old Dominion University, Norfolk, Virginia. i l l PUBLICATIONS "Analysis of a S tar F ie ld Mapping Technique for Use in Determining the Attitude of a Spin Stabilized Spacecraft." NASA TN D-4637, July 1968. "The Project Scanner Star Mapper." NASA TN D-4742, August 1968. "Development and Application of a Star Mapping Technique to the Attitude Determination of the Spin Stabilized Project Scanner Spacecraft." Proceedings, Spacecraft Attitude Determination Symposium (Aerospace Corporation), El Segundo, California, September 30 - October 2, 1969. "Attitude Determination of the Spin Stabilized Project Scanner Space­ craft." NASA TN D-4740, August 1968. "An Investigation of Vehicle Dependent Aspects of Terminal Area ATC Operations." Proceedings, 1972 AIAA Joint Automatic Control Conference, Palo Alto, California, August 16-18, 1972. "New Design and Operating Techniques for Improved Terminal Area Compatibility." Accepted for Publication in Proceedings, Society of Automative Engineers National Transportation Meeting, Dallas, Texas, April 30-May 2, 1974. iv FIELDS OF STUDY Major Field: Electrical Engineering Studies In Control Theory. Professor F. C. Uelmer Studies in Communication Theory. Professor C. E. Warren Studies in Electromagnetic Field Theory. Professor R. G. Kouyoumjian Studies In Classical Mechanics. Professor W. H. Shaffer Studies In Mathematics. Professor H. D. Colson v TABLE OF CONTENTS Page ACKNOWLEDGEMENTS l i VITA, i l l LIST OF TABLES lx LIST OF ILLUSTRATIONS x CHAPTER 1. INTRODUCTION 1 Properties Best Suited for Stellar Attitude Determination Review of C e le s tia l Sensing Techniques Problem Description Organization of the Dissertation 2. SYSTEM EQUATIONS OF ATTITUDE AND MOTION.................................. 14 Space Attitude Geometry Basic Reference Frames Dynamical Model and Equations of Motion Appropriateness of the Assumed Dynamical Model for an Asymmetrical Body Effects of a Residual Control Torque on the Assumed Dynamical Model 3. DEVELOPMENT OF A PARAMETER ESTIMATION PROCEDURE................... 33 4. SINGULARITIES IN THE ESTIMATOR COVARIANCE MATRIX, ESTIMATOR MODEL AND INITIAL ESTIMATES OF THE UNDETERMINED PARAMETERS....................................................................... '4 9 Observability Near Singularities for Small Cone Angles Initial Estimates 5. DEVELOPMENT OF A MODEL FOR GENERATING SIMULATED STAR | TRANSIT TIMES ............................................................................. 65 Vi CHAPTER Page 6. SIMULATION STUDIES 77 Monte Carlo Study: Expected Accuracy of Attitude Determination Procedure Baals fo r Selection of Ensemble Sample Size Attitude Determination Procedure Error Analysis Relationship of Transit Time Errors to Least Squares Functional Residuals and a Method for Assessing the Adequacy of an Estim ate 7. FLIGHT RESULTS. ......................................................................................... 116 Spacecraft and Launch Data Star Mapper Signal and Data Processing Procedures Sumry of Signal Characteristics and Identified Stars Parameter Estimation and Pointing Direction Computation Results Relationship of Data Anomalies and Dynamical Model Inaccuracies Periodicities In the Estimation Residuals Mon-Zero Angular A cceleration and Non-Zero Control Torques Summary of Flight Results 8. RESULTS t CONCLUSIONS AMD RECOMMENDATIONS........................................... 160 Results Conclusions and Recommendations APPENDIX A. DYNAMICAL EQUATIONS OF MOTION FOR AM ARBITRARY SPACECRAFT . 168 Case 1. - Zero Body Torques - Symmetrical Body Case 2. - Zero Body Torques and Small Asymmetry Case 3. - Symmstrlcal Body and a Small Constant Torque B. STAR MAPPER TIME DETECTION CONCEPT 188 Principle of Operation System Description Data Proceeslng Sensitivity and Noise Consideration Desired Characteristics Telescope and Detector Characteristics Signal and Noise Characteristics Coding and Signal D etection Performance Estimates of a Specific System System Probability of Response Glossary of Sypbols for Appendix B vii APPENDIX Page C. STAR MAPPER DESCRIPTION