Optical Co-orbital Measurements in Low Earth Orbit by Kevin Bernard A thesis submitted to the Faculty of Graduate and Postdoctoral Affairs in partial fulfillment of the requirements for the degree of Master of Applied Science in Aerospace Engineering Carleton University Ottawa, Ontario © 2019 Kevin Bernard For all the support my family has provided over the years, this work is dedicated to them. ii Abstract The increasing access to the space domain has led to the growth of the on-orbit object population, as well as the evolution of space surveillance capabilities. With the increased public attention paid to spacecraft proximity and rendezvous operations, is an opportunity to examine what and how current space surveillance capabilities can contribute to this field. This thesis examines the feasibility and challenges associated with re-purposing an existing on-orbit space surveillance capability, the NEOSSat microsatellite, to per- form proximity operations. The ability of NEOSSat to collect a sufficient number of accurate optical observations to determine the relative orbit of a target spacecraft is explored. A variety of observation events are explored with a collection of space- craft to generate relative orbits using inertial orbit determination techniques. These practical results, to the author's knowledge, are the first in the field of relative or- bit determination using inertial techniques between two co-orbital Low Earth Orbit satellites. iii Acknowledgements I would like to sincerely thank my supervisors, Dr. Steve Ulrich and Dr. Lauchie Scott. Thank you Steve for providing guidance, and for taking a chance on someone who walked in to your office in the Spring of 2016. Thank you Lauchie for supporting this work with access to NEOSSat, and especially for convincing me that I should. I would also like to express my gratitude to Stefan Thorsteinson for the insights he provided on NEOSSat image processing, as well as taking the time to produce the required NEOSSat schedules to observe satellites in close proximity. Finally, I would like to thank USSTRATCOM and the ILRS for providing high- precision ephemerides on a variety of target spacecraft, for without those, this work would not have been possible. iv Table of Contents Abstract iii Acknowledgements iv List of Tables x List of Figures xi List of Accronyms xv Chapter 1 Introduction 1 1.1 Motivation ................................. 1 1.2 Problem Statement ............................ 2 1.3 Previous Work .............................. 3 1.3.1 Inertial-based Techniques ..................... 3 1.3.2 LVLH-based Techniques ..................... 4 1.4 Thesis Objectives ............................. 6 1.5 Contributions ............................... 7 1.6 Organization ............................... 7 Chapter 2 Fundamental Concepts 9 2.1 Introduction ................................ 9 2.2 Satellite Orbits .............................. 9 2.2.1 Orbit Classes ........................... 12 2.2.2 Reference Frames ......................... 13 2.3 Space Surveillance ............................ 14 2.3.1 Ground-Based Observers ..................... 14 2.3.2 Space-Based Observers ...................... 15 2.3.3 NEOSSat ............................. 16 v 2.4 Relative Motion Dynamics ........................ 21 2.5 Observability ............................... 25 2.6 Relative Orbit Determination ...................... 28 2.6.1 Relative Orbit Observability ................... 29 2.6.2 Relative Orbit Observability Solutions . 31 Chapter 3 Proposed Methodologies 36 3.1 Introduction ................................ 36 3.2 Orbit Determination ........................... 36 3.2.1 Dynamics ............................. 38 3.2.2 Initial Orbit Determination ................... 39 3.2.3 Least Squares ........................... 40 3.2.4 Linearization ........................... 42 3.2.5 Differential Correction ...................... 43 3.2.6 Covariance Matrices ....................... 45 3.2.7 Sequential Processing ....................... 45 3.3 Method 1 ................................. 47 3.4 Method 2 ................................. 48 3.5 Metric Assessment ............................ 48 Chapter 4 Experiment Setup 51 4.1 Introduction ................................ 51 4.2 Close Approaches ............................. 51 4.3 Observed Spacecraft ........................... 53 4.3.1 SARAL .............................. 53 4.3.2 Sapphire .............................. 54 4.3.3 BriteAustria ............................ 54 4.3.4 UniBRITE-1 ........................... 55 4.3.5 AAUSAT3 ............................. 55 4.3.6 QuikScat .............................. 56 4.4 Observation Events ............................ 57 vi 4.4.1 Observation Schedule ....................... 59 4.5 Data Processing .............................. 59 4.5.1 NEOSSat Tasking ......................... 60 4.5.2 Image Processing ......................... 61 4.5.3 Reference Ephemerides ...................... 63 4.5.4 ODTK Orbit Determination ................... 65 4.5.5 Generated Orbits vs. Reference Ephemerides . 67 4.5.6 LVLH Transformation & Exploitation . 67 4.6 Error Characterization .......................... 67 4.6.1 Data Source Errors ........................ 68 4.6.2 Observation Errors ........................ 68 4.6.3 Data Processing Errors ...................... 69 Chapter 5 Experiment Results 70 5.1 Introduction ................................ 70 5.2 Metric Assessment ............................ 70 5.3 BriteAustria (1) .............................. 75 5.3.1 Method 1 ............................. 75 5.3.2 Method 2 ............................. 76 5.3.3 LVLH ............................... 78 5.4 UniBRITE-1 ................................ 81 5.4.1 Method 1 ............................. 81 5.4.2 Method 2 ............................. 82 5.4.3 LVLH ............................... 83 5.5 AAUSAT3 (1) ............................... 87 5.5.1 Method 1 ............................. 87 5.5.2 Method 2 ............................. 89 5.5.3 LVLH ............................... 90 5.6 SARAL .................................. 93 5.6.1 Method 1 ............................. 93 vii 5.6.2 Method 2 ............................. 94 5.6.3 LVLH ............................... 96 5.7 AAUSAT3 (2) ............................... 99 5.7.1 Method 1 ............................. 99 5.7.2 Method 2 ............................. 99 5.7.3 LVLH ............................... 100 5.8 BriteAustria (2) .............................. 101 5.8.1 Method 1 ............................. 101 5.8.2 Method 2 ............................. 102 5.8.3 LVLH ............................... 102 5.9 QuikScat .................................. 103 5.9.1 Method 1 ............................. 103 5.9.2 Method 2 ............................. 104 5.9.3 LVLH ............................... 105 5.10 Sapphire .................................. 108 5.10.1 Method 1 ............................. 108 5.10.2 Method 2 ............................. 110 5.10.3 LVLH ............................... 111 5.11 Discussion ................................. 111 Chapter 6 Conclusion 113 6.1 Introduction ................................ 113 6.2 Objectives Review ............................ 113 6.3 Summary of Findings . 114 6.4 Recommendations for Future Work . 117 6.5 A Final Note ............................... 118 Bibliography 119 Appendix A Data Formats 122 A.1 ILRS Standard Product 3 Format Ephemeris . 122 viii A.2 STK Ephemerides ............................. 123 Appendix B ODTK Settings 124 ix List of Tables 2.1 GPS Campaign Metric Results (values in arcseconds) . 21 4.1 PSLV C20 Spacecraft Orbit Parameters . 52 4.2 QuikScat Orbit Parameters .................... 57 4.3 Observation Events ........................ 59 5.1 Metric Assessment Results (values in arcseconds) . 72 5.2 UniBRITE-1 Observations .................... 81 5.3 AAUSAT3 Observations ...................... 87 5.4 Saral Observations ......................... 93 5.5 BriteAustria Observations . 101 5.6 QuikScat Observations . 103 5.7 Sapphire Observations . 108 5.8 Results Summary . 112 B.1 ODTK Settings . 124 x List of Figures 2.1 Orbit Types ............................ 10 2.2 Keplerian Elements ........................ 11 2.3 Orbit Classes ........................... 13 2.4 Artist's Rendition of NEOSSat . 17 2.5 NEOSSat TRM Image ...................... 18 2.6 NEOSSat SSM Image ....................... 18 2.7 NEOSSat Science and Star Tracker CCD FOVs observing a GEO satellite ........................... 20 2.8 LVLH ............................... 21 2.9 Target (red) and Chaser (blue) orbit planes intersecting . 29 2.10 Shape Parameter [1] (modified) . 30 2.11 LOS altered by manoeuvres [1] (modified) . 32 2.12 Constrained Cylindrical Coordinates [2] (modified) . 34 3.1 Right Ascension and Declination . 37 3.2 Initial Gooding Iteration ..................... 40 3.3 Final Gooding Iteration ..................... 40 3.4 Method 1 Data flow ........................ 47 3.5 Method 2 Data flow ........................ 48 4.1 Sapphire and NEOSSat aboard the PSLV dual launch adapter 52 4.2 SARAL .............................. 53 4.3 Artist's Rendition of Sapphire . 54 4.4 BriteAustria and UniBRITE ................... 55 4.5 AAUSAT3 ............................. 56 4.6 Artist's rendition of QuikScat. 56 4.7 Close Approaches with NEOSSat . 58 4.8 Data Flow for observation campaign . 59 xi 4.9 SARAL's Relative Angular Velocity relative to NEOSSat dur- ing an observation interval in arcsec/sec . 61 4.10 Predicted NEOSSat Orbit while observing