Purdue University Purdue e-Pubs Open Access Theses Theses and Dissertations 4-2016 Dynamic sensor tasking and IMM EKF estimation for tracking impulsively maneuvering satellites Arthur A. Lace Purdue University Follow this and additional works at: https://docs.lib.purdue.edu/open_access_theses Part of the Aerospace Engineering Commons Recommended Citation Lace, Arthur A., "Dynamic sensor tasking and IMM EKF estimation for tracking impulsively maneuvering satellites" (2016). Open Access Theses. 784. https://docs.lib.purdue.edu/open_access_theses/784 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. Graduate School Form 30 Updated PURDUE UNIVERSITY GRADUATE SCHOOL Thesis/Dissertation Acceptance This is to certify that the thesis/dissertation prepared By Arthur A Lace Entitled Dynamic Sensor Tasking and IMM EKF Estimation for Tracking Impulsively Maneuvering Satellites For the degree of Master of Science in Aeronautics and Astronautics Is approved by the final examining committee: Inseok Hwang Chair Carolin E. Frueh Dengfeng Sun To the best of my knowledge and as understood by the student in the Thesis/Dissertation Agreement, Publication Delay, and Certification Disclaimer (Graduate School Form 32), this thesis/dissertation adheres to the provisions of Purdue University’s “Policy of Integrity in Research” and the use of copyright material. Approved by Major Professor(s): Inseok Hwang Approved by: Weinong Wayne Chen 4/18/2016 Head of the Departmental Graduate Program Date DYNAMIC SENSOR TASKING AND IMM EKF ESTIMATION FOR TRACKING IMPULSIVELY MANEUVERING SATELLITES A Thesis Submitted to the Faculty of Purdue University by Arthur A. Lace In Partial Fulfillment of the Requirements for the Degree of Master of Science in Aeronautics and Astronautics May 2016 Purdue University West Lafayette, Indiana ii ACKNOWLEDGMENTS Sangjin Lee provided a great deal of assistance during the writing of this thesis. His research into IMM EKF satellite tracking was the initial inspiration for this work. Meetings and discussion with him are part of what enabled this paper to be written. The time he was willing to spare while working on his own doctoral thesis was greatly appreciated. Inseok Hwang's guidance as a thesis advisor was invaluable in understanding satel- lite tracking and tasking as a guidance, navigation, and control problem, enabling the creation of this thesis. His criticisms were also essential in refining this thesis into its present form. Robert Lace and Mina Adsit provided essential support during the process of writ- ing this paper. Without their assistance maintaining a positive mentality throughout this process would have been nearly impossible. Robert's assistance with editing was also critical in making sure a much reduced number of errors made it into the final paper. iii TABLE OF CONTENTS Page LIST OF TABLES :::::::::::::::::::::::::::::::: v LIST OF FIGURES ::::::::::::::::::::::::::::::: vi SYMBOLS :::::::::::::::::::::::::::::::::::: xii ABBREVIATIONS :::::::::::::::::::::::::::::::: xiii ABSTRACT ::::::::::::::::::::::::::::::::::: xiv 1 INTRODUCTION :::::::::::::::::::::::::::::: 1 1.1 Motivation :::::::::::::::::::::::::::::::: 1 1.2 Maneuvering Satellite Tracking :::::::::::::::::::: 1 1.3 Interacting Multiple Model Extended Kalman Filter ::::::::: 3 1.4 Information Gain Sensor Allocation :::::::::::::::::: 4 1.5 Sensor Systems ::::::::::::::::::::::::::::: 5 1.6 Proposed Tasking Method Improvement ::::::::::::::: 6 2 METHODOLOGY :::::::::::::::::::::::::::::: 7 2.1 Sensor Modeling ::::::::::::::::::::::::::::: 7 2.2 Reference Frames :::::::::::::::::::::::::::: 9 2.3 Fisher Information Gain :::::::::::::::::::::::: 10 2.4 Tasking Methodology :::::::::::::::::::::::::: 11 2.5 Maneuver Probability :::::::::::::::::::::::::: 14 2.6 Estimated State Mixing :::::::::::::::::::::::: 18 2.7 Interacting Multiple Model Extended Kalman Filter ::::::::: 19 2.8 Estimated State Fusion ::::::::::::::::::::::::: 20 3 NUMERICAL SIMULATION :::::::::::::::::::::::: 23 3.1 Simulation Overview :::::::::::::::::::::::::: 23 3.2 Orbital Mechanics Modeling :::::::::::::::::::::: 25 3.3 Maneuver Modeling ::::::::::::::::::::::::::: 28 3.4 State Probability :::::::::::::::::::::::::::: 30 3.5 Extended Kalman Filter Details :::::::::::::::::::: 32 3.6 Simulation Results ::::::::::::::::::::::::::: 34 3.6.1 Single EKF Tasking :::::::::::::::::::::: 35 3.6.2 Fisher and Covariance Tasking ::::::::::::::::: 40 3.6.3 Fisher, Probability and Covariance Tasking :::::::::: 46 3.6.4 Method Comparisons :::::::::::::::::::::: 52 iv Page 3.7 Discussion :::::::::::::::::::::::::::::::: 56 4 SUMMARY :::::::::::::::::::::::::::::::::: 65 REFERENCES :::::::::::::::::::::::::::::::::: 67 A Sensor Specific Tasking Comparison ::::::::::::::::::::: 69 A.1 First LEO Satellite Maneuver ::::::::::::::::::::: 70 A.2 Second LEO Satellite Maneuver :::::::::::::::::::: 75 A.3 Tasking Discussion ::::::::::::::::::::::::::: 80 B ADDITIONAL SIMULATION CONFIGURATION :::::::::::: 81 B.1 Alternate Simulation Configuration :::::::::::::::::: 81 B.1.1 Single EKF Tasking :::::::::::::::::::::: 82 B.1.2 Fisher and Covariance Tasking ::::::::::::::::: 85 B.1.3 Fisher and Covariance Tasking with altered GEO maneuvering mode ::::::::::::::::::::::::::::::: 87 B.1.4 Fisher, Probability and Covariance Tasking :::::::::: 90 B.1.5 Fisher, Probability and Covariance Tasking with altered GEO maneuvering mode ::::::::::::::::::::::: 92 B.1.6 Method Comparisons :::::::::::::::::::::: 94 v LIST OF TABLES Table Page 3.1 Tasking coefficients ::::::::::::::::::::::::::::: 24 3.2 Satellite simulation parameters :::::::::::::::::::::: 26 3.3 IMM EKF parameters ::::::::::::::::::::::::::: 32 3.4 Satellite maneuver times :::::::::::::::::::::::::: 34 3.5 Method error comparison from 700500s to 730000s ::::::::::: 54 3.6 Method error comparison from 703500s to 704500s ::::::::::: 57 3.7 Method error comparison from 707800s to 708800s ::::::::::: 58 B.1 Alternative tasking coefficients ::::::::::::::::::::::: 82 B.2 Alternate Simulation method error comparison from 700500s to 730000s with variable Q2 :::::::::::::::::::::::::::::: 95 vi LIST OF FIGURES Figure Page 1.1 Sensor and satellite configuration where earth orbiting or ground-based sensors (black) observe certain limited regions (gray) and attempt to track target satellites (red) :::::::::::::::::::::::::::: 2 2.1 Tracking and tasking method block diagram ::::::::::::::: 7 2.2 Geostationary mode transition boundaries in LHLV ::::::::::: 16 2.3 LEO mode transition boundary in LHLV around apsis point :::::: 17 3.1 Station keeping maneuver of GEO Satellite 2 over the course of 9 days in LHLV reference frame ::::::::::::::::::::::::::: 30 3.2 Orbital transfer maneuver of LEO Satellite 11 in the ECF frame during the time period between 700000s − 730000s ::::::::::::::: 31 3.3 RMS position error for all satellites averaged over 100 simulations using only Fisher information based tasking ::::::::::::::::::: 35 3.4 RMS position error for all satellites averaged over 100 simulations using Fisher information and covariance based sensor tasking with a single EKF estimator :::::::::::::::::::::::::::::::::: 36 3.5 RMS velocity error for all satellites' except Satellite 11 averaged over 100 simulations using Fisher information and covariance based sensor tasking with a single EKF estimator :::::::::::::::::::::::: 37 3.6 Number of sensor observations of a given satellite averaged over 100 simu- lations using Fisher information and covariance based sensor tasking with a single EKF estimator ::::::::::::::::::::::::::: 38 3.7 Satellite 11 RMS position error averaged over 100 simulations using Fisher information and covariance based sensor tasking with a single EKF esti- mator :::::::::::::::::::::::::::::::::::: 38 3.8 Satellite 11 RMS velocity error averaged over 100 simulations using Fisher information and covariance based sensor tasking with a single EKF esti- mator :::::::::::::::::::::::::::::::::::: 39 3.9 Satellite 11 RMS velocity error averaged over 100 simulations using Fisher information and covariance based sensor tasking with a single EKF esti- mator during first LEO maneuver ::::::::::::::::::::: 39 vii Figure Page 3.10 RMS position error for all satellites except Satellite 11 averaged over 100 simulations using Fisher information and covariance based sensor tasking 41 3.11 RMS velocity error for all satellites except Satellite 11 averaged over 100 simulations using Fisher information and covariance based sensor tasking 42 3.12 Number of sensor observations of a given satellite averaged over 100 sim- ulations using Fisher information and covariance based sensor tasking : 42 3.13 Satellite 11 RMS position error averaged over 100 simulations using Fisher information and covariance based sensor tasking ::::::::::::: 43 3.14 Satellite 11 RMS velocity error averaged over 100 simulations using Fisher information and covariance based sensor tasking ::::::::::::: 43 3.15 Satellite 11 RMS position error averaged over 100 simulations using Fisher information and covariance based sensor tasking around the first LEO maneuver :::::::::::::::::::::::::::::::::: 44 3.16 Satellite 11 RMS velocity error averaged over 100 simulations using Fisher information and covariance based sensor tasking around the first LEO maneuver :::::::::::::::::::::::::::::::::: 44 3.17 Average trace of the covariance matrix for Satellite 11 over 100 simulations using Fisher information