Air Force Institute of Technology AFIT Scholar Theses and Dissertations Student Graduate Works 3-24-2016 Satellite Ephemeris Correction via Remote Site Observation for Star Tracker Navigation Performance Improvement Jorge E. Diaz Follow this and additional works at: https://scholar.afit.edu/etd Part of the Other Engineering Commons Recommended Citation Diaz, Jorge E., "Satellite Ephemeris Correction via Remote Site Observation for Star Tracker Navigation Performance Improvement" (2016). Theses and Dissertations. 296. https://scholar.afit.edu/etd/296 This Thesis is brought to you for free and open access by the Student Graduate Works at AFIT Scholar. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. SATELLITE EPHEMERIS CORRECTION VIA REMOTE SITE OBSERVATION FOR STAR TRACKER NAVIGATION PERFORMANCE IMPROVEMENT THESIS Capt Jorge E. D´ıaz AFIT-ENG-MS-16-M-013 DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. The views expressed in this document are those of the author and do not reflect the official policy or position of the United States Air Force, the United States Department of Defense or the United States Government. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. AFIT-ENG-MS-16-M-013 SATELLITE EPHEMERIS CORRECTION VIA REMOTE SITE OBSERVATION FOR STAR TRACKER NAVIGATION PERFORMANCE IMPROVEMENT THESIS Presented to the Faculty Department of Electrical and Computer Engineering Graduate School of Engineering and Management Air Force Institute of Technology Air University Air Education and Training Command in Partial Fulfillment of the Requirements for the Degree of Master of Science in Electrical Engineering Capt Jorge E. D´ıaz, B.S.E.E. March 2016 DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. AFIT-ENG-MS-16-M-013 SATELLITE EPHEMERIS CORRECTION VIA REMOTE SITE OBSERVATION FOR STAR TRACKER NAVIGATION PERFORMANCE IMPROVEMENT THESIS Capt Jorge E. D´ıaz, B.S.E.E. Committee Membership: Maj Scott J. Pierce, PhD Chair John F. Raquet, PhD Member Richard G. Cobb, PhD Member AFIT-ENG-MS-16-M-013 Abstract In order for celestial navigation observing satellites to provide accurate positioning estimates, precise ephemerides of the observed satellites are necessary. This work analyzed a method to correct for satellite ephemeris to be used in celestial navigation applications. This correction is the measured angle differences between the expected location of the satellite, which is given by propagating publicly available Two-Line Elements (TLE), and their observed angles from a precisely known reference site. Therefore, the angle difference can be attributed completely to satellite ephemeris error assuming instrument error was accounted for. The intent is to calculate this correction from the reference site and relate it to remote sites that have visibility of the same satellite, but where its own location is known with some uncertainty. The effects of increased baseline distances from the reference site, in addition to time delays when the correction was calculated are studied. Satellite observations were simulated and propagated using TLEs. This simulated data was manipulated to calculate the angle difference and transform that angle to the viewpoint of the remote sites. This corrected observed angle was integrated using an extended Kalman Filter (EKF) with an inertial measurement unit (IMU) and a barometric altimeter. The performance of the position solution in the navigation filter was calculated as the error from simulated truth. The satellite ephemeris error measured at a reference location becomes less ob- servable by a remote user according to the line-of-sight transformation due to the reference-satellite-remote geometry. A mathematical formula for calculating the ap- plicability of projecting the remote site observation to other locations is developed and compared to simulated ephemeris errors. This formula allows a user to de- iv fine geographic regions of validity through ephemeris error tolerance. Estimating the ephemeris error with regular updates from a reference site resulted in a reduc- tion of inertial measurement unit (IMU) drift and reducing the distance root mean squared (DRMS) error by a maximum of 98% under certain conditions. v AFIT-ENG-MS-16-M-013 To my wife, daughter and son. vi Acknowledgements I would like to thank my advisor, Maj Pierce, for his guidance, support and mentoring throughout this process. I also want to express my gratitude to Dr. Raquet and Dr. Cobb, my thesis committee members, for sharing their advice and expertise that helped keep me on track and fine tune this work. Special thanks to the great ANT center staff for providing the equipment, technical assistance, and admin support needed during this research. I would also like to extend my thanks to my friends and mentors from my previous unit at Patrick AFB, since it was there where they encouraged and motivated me to pursue my graduate degree here at AFIT. Finally, I wish to thank my family, especially my wife for her support and constant encouragement during these last 18 months. Without their support, none of the work presented in this thesis would have been possible. Capt Jorge E. D´ıaz vii Table of Contents Page Abstract........................................... ....................iv Acknowledgements .................................... vii List ofAbbreviations ................................... ..................x ListofFigures........................................ xii ListofTables......................................... xiii I. Introduction...................................... ..................1 1.1 Objective ......................................... .............2 1.2 Assumptions and Applicability . ........2 1.3 Thesis Overview..................................... ............3 II. Background ...................................... ..................5 2.1 Angles Only Navigation . .........5 2.2 CoordinateSystems ................................. ............7 2.3 Observations...................................... ..............8 2.4 Differential Site Ephemeris Correction . .........11 2.5 Navigation Estimation . .........14 2.5.1 StateModel ...................................... .......15 2.5.2 Kalman Filter . .....16 2.6 Summary .......................................... ...........17 III. Computer Modeling ................................. ...............18 3.1 Introduction...................................... .............18 3.2 Systems Took Kit (STK) Simulation . ......18 3.3 STK Baseline Distance Variant . ........21 3.4 STKTimeVariant ..................................... ........22 3.5 EKFModel......................................... ...........23 3.5.1 IMUModel........................................ ......23 3.5.2 Barometric Altimeter Model . ....31 3.5.3 StarTracker Model ................................ .......31 3.5.4 Complete System Dynamics Model ....................... ..33 3.5.5 Measurement Model ................................ ......34 3.6 SPIDER ........................................... ...........39 3.7 Summary .......................................... ...........39 viii Page IV. Results .......................................... .................40 4.1 Introduction...................................... .............40 4.2 Distance Variant Results .............................. ..........40 4.3 TimeVariantResults .................................. .........43 4.4 EKFResults........................................ ...........45 4.4.1 FreeINS ......................................... .......47 4.4.2 AnglesOnly ........................................ ....48 4.4.3 Angles and Ephemeris Updates ......................... ...48 4.4.4 EKFBiasState ..................................... .....51 4.5 PositionError ...................................... ...........54 4.6 Summary .......................................... ...........56 V. Conclusion ......................................... ...............58 5.1 Introduction...................................... .............58 5.2 Summary ofDocument................................ ..........58 5.3 Summary of Contributions............................. ..........59 5.4 FutureWork....................................... ............60 Appendix A. Star Tracker Angle Measurement Linearization . ...........62 Bibliography .......................................... .................75 ix List of Abbreviations LOP line of position RA right ascension DEC declination COTS Commercial off-the-shelf AFRL Air Force Research Laboratory CCD charged-coupled device LEO low-Earth orbit SSN Space Surveillance Network RSO resident space object JSpOC Joint Space Operations Center TLE Two-Line Element sets FOV field of view SGP4 Simplified General Perturbations-4 STK System Tool Kit GPS Global Positioning System COM Component Object Model GNSS Global Navigation Satellite System IMU inertial measurement unit x EKF extended Kalman filter DoD Department of Defense INS Inertial Navigation System FOGM first-order Gauss Markov ECEF Earth-Centered, Earth-Fixed NED North-East-Down DCM direction cosine matrix AWGN additive white Gaussian noise ANT Autonomy & Navigation Technology ICD interface control document SPIDER Sensor Processing for Inertial Dynamics