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Development of Magnetometer-Based Orbit And DEVELOPMENT OF MAGNETOMETER-BASED ORBIT AND ATTITUDE DETERMINATION FOR NANOSATELLITES THOMAS WRIGHT A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE GRADUATE PROGRAM IN EARTH AND SPACE SCIENCE YORK UNIVERSITY, TORONTO, ONTARIO AUGUST, 2014 © THOMAS WRIGHT, 2014 Abstract Attitude and orbit determination are critical parts of nanosatellite mission operations. The ability to perform attitude and orbit determination autonomously could lead to a wider array of mission possibilities for nanosatellites. This research examines the feasibility of using low-cost magnetometer measurements as a method of autonomous, simultaneous orbit and attitude determination for the novel application of redundancy on nanosatellites. Individual Extended Kalman Filters (EKFs) are developed for both attitude determination and orbit determination. Simulations are run to compare the developed systems with previous work on attitude and orbit determination. The EKFs are combined to provide both attitude and orbit determination simultaneously. Simulations are run and show that this approach for autonomous attitude and orbit determination on nanosatellites provides 8.5 and 12.5 km of attitude and orbit knowledge, respectively. The results of the simulations are then validated using Hardware-In-The-Loop (HITL) testing. Additionally, a Helmholtz cage is evaluated for future use in the HITL test setup. ii Acknowledgements I would like to acknowledge my supervisors Professor Sunil Bisnath and Professor Regina Lee for their guidance and support. I will carry the skills they helped me to develop through the rest of my career. I would also like to thank the grad students in both the GNSS and YuSEND Labs for their assistance and encouragement throughout my studies. And thank you to my wife, Janet, the myriad things she has done to help me through my Master’s education have been invaluable. iii Table of Contents Abstract ........................................................................................................................................... ii Acknowledgements ........................................................................................................................ iii Table of Contents ........................................................................................................................... iv List of Tables ................................................................................................................................ vii List of Figures .............................................................................................................................. viii List of Symbols ............................................................................................................................... x List of Acronyms .......................................................................................................................... xii 1 Introduction ............................................................................................................................. 1 1.1 Overview of Nanosatellites .............................................................................................. 3 1.2 Overview of Attitude Determination on Nanosatellites ................................................... 3 1.3 Overview of Orbit Determination .................................................................................... 8 1.4 Overview of the Extended Kalman Filter ...................................................................... 12 1.5 Recent Related Research ................................................................................................ 15 1.6 Research Contributions .................................................................................................. 17 2 Earth’s Magnetic Field .......................................................................................................... 19 2.1 Previous Missions Interacting with the Earth’s Magnetic Field .................................... 20 2.1.1 Missions to Measure the Earth’s Magnetic Field ..................................................... 20 2.1.2 Missions that Utilize the Earth’s Magnetic Field ..................................................... 21 2.1.3 Magnetometers Utilized on Satellites ....................................................................... 23 2.1.4 Effects of Magnetorquers on Satellites ..................................................................... 29 2.2 Models of the Earth’s Magnetic Field ............................................................................ 30 2.2.1 International Geomagnetic Reference Field (IGRF) ................................................. 32 3 Attitude Determination ......................................................................................................... 37 3.1 Attitude Representation using Quaternions and Angular Rates ..................................... 37 3.2 Disturbance Torques Included in the Simulations ......................................................... 39 3.2.1 Gravity Gradient Disturbance Torques ..................................................................... 40 3.3 Implemented Extended Kalman Filter for Attitude Determination ............................... 40 3.3.1 Dynamic Update of the Attitude State Vector .......................................................... 41 3.3.2 Measurement Update of the Attitude State Vector ................................................... 42 3.4 Simulation Studies Used in Evaluating the Attitude Determination EKF ..................... 43 3.4.1 Initialization of the State Vector for the Attitude Determination Simulations ......... 44 iv 3.4.2 Simulation Results for the Attitude Determination EKF .......................................... 45 3.5 Summary of the Attitude Determination Extended Kalman Filter ................................ 48 4 Orbit Determination .............................................................................................................. 49 4.1 Representations of Orbits Used in the Orbit Determination EKF .................................. 49 4.1.1 Position and Velocity Representation of Orbits........................................................ 49 4.1.2 Orbital Element Representation of Orbits – SGP4 Representation .......................... 52 4.2 Implemented Orbit Determination EKF ......................................................................... 54 4.2.1 Measurement Update of the Orbit Determination State Vector ................................ 55 4.3 Simulation Studies Used in Evaluating the Orbit Determination EKF .......................... 57 4.3.1 Initialization of the State Vector for Orbit Determination Simulations .................... 57 4.3.2 Simulation Results for the Orbit Determination EKF............................................... 58 4.4 Summary of the Orbit Determination Extended Kalman Filter ..................................... 61 5 Combined Attitude and Orbit Determination ....................................................................... 63 5.1 Interface Between the Attitude and Orbit Determination EKFs .................................... 63 5.2 Simulation Test Cases Used in Evaluating the Combined EKF .................................... 65 5.3 Results of Combining Attitude and Orbit EKFs ............................................................ 67 5.4 Evaluation of Simultaneous Orbit and Attitude Estimation ........................................... 73 5.5 Summary of the Combined Attitude and Orbit Determination EKF ............................. 74 6 Hardware-In-The-Loop Simulation ...................................................................................... 77 6.1 HITL Test Procedure ...................................................................................................... 77 6.2 HITL Test Apparatus ..................................................................................................... 78 6.2.1 Air Bearing Table Used in HITL Tests..................................................................... 79 6.2.2 Satellite Analog Used in HITL Tests ........................................................................ 79 6.3 Helmholtz Cage Testing ................................................................................................. 85 6.3.1 Calibration of the Helmholtz Cage ........................................................................... 86 6.4 HITL Test Results .......................................................................................................... 89 6.5 Summary of the HITL Simulations ................................................................................ 94 7 Conclusions and Future Work .............................................................................................. 97 7.1 Conclusions .................................................................................................................... 97 7.2 Future Considerations .................................................................................................. 100 References ................................................................................................................................... 103 Appendix A CubeSat™ Orbit Survey .................................................................................... 109 Appendix B Partial Derivatives of the Magnetic field .........................................................
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