Analyses for a Modernized GNSS Radio Occultation Receiver by Erin R. Griggs B.S., Colorado School of Mines, 2007 M.S., Colorado School of Mines, 2008 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Aerospace Engineering Sciences 2015 This thesis entitled: Analyses for a Modernized GNSS Radio Occultation Receiver written by Erin R. Griggs has been approved for the Department of Aerospace Engineering Sciences Prof. Dennis Akos Prof. Judah Levine Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. iii Griggs, Erin R. (Ph.D., Aerospace Engineering Sciences) Analyses for a Modernized GNSS Radio Occultation Receiver Thesis directed by Prof. Dennis Akos Global Navigation Satellite System (GNSS) radio occultation (RO) is a remote sensing tech- nique that exploits existing navigation signals to make global, real-time observations of the Earth's atmosphere. A specialized RO receiver makes measurements of signals originating from a trans- mitter onboard a GNSS spacecraft near the Earth's horizon. The radio wave is altered during passage through the Earth's atmosphere. The changes in the received signals are translated to the refractivity characteristics of the intervening medium, which enable the calculation of atmospheric pressure, temperature, and humidity. Current satellite missions employing GNSS RO have provided invaluable and timely informa- tion for weather and climate applications. Existing constellations of occultation satellites, however, are aging and producing fewer quality measurements. Replacement fleets of RO satellites are im- perative to sustain and improve the global coverage and operational impact achieved by the current generation of RO satellites. This dissertation describes studies that facilitate the development of next generation RO receivers and satellite constellations. Multiple research efforts were conducted that aim to improve the quantity and quality of measurements made by a future satellite-based RO collection system. These studies range in magnitude and impact, and begin with a receiver development study using ground-based occultation data. Future RO constellations and collection opportunities were simulated and autonomous occultation prediction and scheduling capabilities were implemented. Finally, a comprehensive study was conducted to characterize the stability of the GNSS atomic frequency standards. Oscillator stability for a subset of satellites in the GNSS was found to be of insufficient quality at timescales relevant to RO collections and would degrade the atmospheric profiling capabilities of an RO system utilizing these signals. Recommendations for a high-rate clock iv correction network are proposed, which provides significant improvement to the fractional errors in the derived refractivity, pressure, and temperature values caused by the oscillator instabilities. Dedication This thesis is dedicated to my Fizeks Grandpa, for without his early inspiration, tutelage, and encouragement in my educational endeavors, I would not have found my passion for outer space. vi Acknowledgements There are a number of people without whom this thesis might not have been finished, and to whom I am greatly indebted. I would like to express my deepest appreciation for my committee chair, Professor Dennis Akos. He has continually pushed and stretched me beyond my limitations, but has always been in my corner to back me up. I would also like to thank Dr. E. Robert Kursinksi and Dr. Judah Levine for their invaluable input and continued guidance in the areas of radio occultation and oscillator stability. Thank you to my committee members, Professor Penina Axelrad and Professor George Born, for their support and expertise in all things GNSS and orbit determination. My thanks to Chris McCormick and Broad Reach Engineering for their considerable support and invested interest in bettering humanity with scientific endeavors. I am greatly indebted to both the ARCS Foundation and the Colorado Space Business Roundtable for their generous support and great networking opportunities. Thank you Staffan Back´en,Elliot Barlow, and Jordan Riggs for your great company and assistance for the mountain-based collection campaigns. My thanks to William Diener, Stephan Esterhuizen, and Larry Young for your input, assistance, and allowing me to use your facilities at JPL for needed data collections. Many thanks to my family, especially Dan and Mary Griggs and Bonnie LaFleur, for proof reading my papers and patiently letting me practice my presentations for them. And finally, thank you to my hockey family for keeping me sane. Contents Chapter 1 INTRODUCTION 5 1.1 History of Radio Occultation . 7 1.1.1 Interplanetary Occultations . 7 1.1.2 Earth Occultation Missions . 8 1.2 Motivation . 11 1.2.1 Future of Radio Occultation . 11 1.2.2 Signal Sources . 13 1.3 Thesis Synopsis . 15 2 THE GNSS RADIO OCCULTATION PROCESS 18 2.1 Generic Occultation Event . 19 2.2 Calculation of Excess Delay . 19 2.3 Bending Angle Calculation . 21 2.4 Transformation to Atmospheric Quantities . 23 3 GROUND-BASED OCCULTATION 26 3.1 Background . 26 3.2 Experiment . 28 3.2.1 Data Collected . 28 3.2.2 Hardware . 29 viii 3.3 Occultation Signal Processing . 32 3.3.1 Signal Acquisition . 32 3.3.2 Closed-loop Tracking . 33 3.3.3 Open-loop Tracking . 35 3.4 Results . 37 3.4.1 Occultation of PRN 1 . 38 3.4.2 Occultation of PRN 17 . 41 3.5 Significance . 42 4 RADIO OCCULTATION CONSTELLATION STUDIES 46 4.1 Constellation Simulations . 46 4.1.1 Simulation Description . 47 4.1.2 Number of Occultation Satellites . 48 4.1.3 Occultation Analysis Period . 49 4.1.4 High Density RO Network . 53 4.2 Simulation Outcomes . 60 5 ORBIT DETERMINATION AND SCHEDULING 61 5.1 Real-time Orbit Determination . 61 5.2 Occultation Scheduler . 63 5.2.1 Geometric Interpretation . 64 5.2.2 Scheduler Simulation . 65 5.2.3 Occultation Metrics . 67 5.3 Scheduler Summary . 74 6 GNSS SATELLITE CLOCK CHARACTERIZATION 75 6.1 Carrier Phase Development . 76 6.2 Statistic of Measuring Time Stability . 79 ix 6.2.1 Allan Deviation . 79 6.2.2 Pre-filtered Allan Deviation . 80 6.3 Receiver Clock Error Compensation . 83 6.3.1 Differencing Method . 83 6.3.2 Active Hydrogen Masers . 85 6.4 Thermal Noise Compensation . 88 6.4.1 Heuristic Approach . 88 6.4.2 Analytic Approach . 90 6.5 Sub-second Analysis . 92 7 SATELLITE CLOCK EXPERIMENTS 94 7.1 Background . 94 7.2 Data Collections . 95 7.2.1 University of Colorado . 96 7.2.2 Timing Facilities . 99 7.3 Data Validation . 103 7.3.1 Comparison to Reference Stations . 103 7.3.2 Sample Size Compensation . 105 7.4 Allan Deviation Results . 105 7.4.1 GPS and GLONASS . 106 7.4.2 Galileo and BeiDou . 113 7.5 Implications . 115 7.5.1 Carrier Phase Error . 116 7.5.2 Network Corrections . 117 7.5.3 One-second Errors . 118 7.6 Stability Conclusions . 122 8 SUMMARY AND CONCLUSIONS 125 x Bibliography 130 Appendix A OCCULTATION SCHEDULER SIMULATION RESULTS 137 B GNSS ALLAN DEVIATION ANALYSIS 139 C SUB-SECOND GPS CLOCK ANALYSIS 142 C.1 Derivation . 142 C.1.1 Carrier Tracking Error . 142 C.1.2 Power Law Domain Conversions . 143 C.1.3 Modified Allan Deviation . 144 C.2 Theoretical vs. Measured Results . 145 Tables Table 1.1 Radio Occultation Missions . 6 3.1 Data Characteristics of Occultation Events . 29 3.2 Signal Spectrum Search Space . 37 4.1 Projected GNSS Constellations as of 2017 . 48 4.2 Projected GNSS Constellations as of 2020 . 49 5.1 Total Occultation Time for One Orbit . 72 5.2 Occultation Priority List . 72 5.3 Individual Occultation Duration Statistics . 73 6.1 Carrier Phase Definitions . 76 6.2 Power Law Noise . ..