Evaluation of a Single Frequency Satellite Navigation Software Receiver THESIS Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Seyedfarhad Mirkazemi, M.S. Graduate Program in Electrical and Computer Science The Ohio State University 2019 Master's Examination Committee: Dr. Lee Carson Potter, Advisor Dr. Emre Ertin Copyrighted by Seyedfarhad Mirkazemi 2019 Abstract Principles of satellite navigation will be reviewed. An existing open source single- frequency C/A code Global Positioning System (GPS) software receiver is investigated in terms of observable generation. Maximum-likelihood detection and estimation of the received signal is formulated. Experimental results using Universal Software Radio Peripheral (USRP) platform is compared to a benchmark double difference static solution provided by Online Positioning User Service (OPUS) based on observations from a Topcon Net-G3 geodetic-grade receiver. The final horizontal RMSE is 6.865 meter with standard deviation of 4.144 meter for a recorded signal at 5 Msps. ii To My Invisible Partner iii Acknowledgments I would like to express my appreciation to Professor Lee Potter for his logistic support and for teaching me principles of signal processing. I cannot forget Professor Christopher Jekeli generous guidance, helping me understand complicated math problems. None of the steps towards my second graduate degree would have been possible without financial support of Professor Dorota Brzezinska. My sincere thanks go to Dr. Kyle Snow who open-mindedly trusted me and gave me access to the Topcon hardware facilities during and after my internship solely for the purpose of my research. iv Vita 2004 ...........................................................Dr. Hesabi High School 2009 ...........................................................B.S. Geodetic Engineering, National Geographic Organization of Iran 2017 ...........................................................M.S. Geodetic Engineering, The Ohio State University 2017 to present .........................................PHD Geodetic Engineering, The Ohio State University 2015 to present .........................................Graduate Teaching Associate, Department of Civil and Geodetic Engineering, The Ohio State University Fields of Study Major Field: Electrical and Computer Engineering v Table of Contents Abstract .............................................................................................................................. ii Acknowledgments ............................................................................................................. iv Vita ..................................................................................................................................... v List of Tables .................................................................................................................. viii List of Figures ................................................................................................................... ix Chapter 1: GNSS Positioning Principles ..................................................................... 11 1.1 Introduction ...................................................................................................... 11 1.2 GNSS Reference Frames .................................................................................. 14 1.2.1 GNSS Spatial Reference System ............................................................. 14 1.2.2 GNSS Time Reference System................................................................. 27 1.3 GNSS Errors ..................................................................................................... 30 1.3.1 Satellite Dependent Errors ....................................................................... 30 vi 1.3.2 Channel Dependent Error ........................................................................ 37 1.3.3 Receiver Dependent Error ........................................................................ 45 1.4 GNSS Access and Modulation Schemes ......................................................... 51 Chapter 2: GNSS Measurement .................................................................................... 60 2.1 Signal Acquisition ............................................................................................. 60 2.2 Signal Tracking ................................................................................................. 70 2.3 Navigation Message Decoding ......................................................................... 83 2.4 Navigation Solution .......................................................................................... 89 2.5 Conclusion ......................................................................................................... 94 Bibliography .................................................................................................................... 97 Appendix A. Hardware Specifications and Setups ...................................................... 99 Appendix B. Acquisition and Tracking Results & Algorithms ............................... 104 vii List of Tables Table 1.Terrestrial Reference Systems for GNSS ................................................... 19 Table 2.GNSS Orbit Specifications ......................................................................... 24 Table 3. Modulation Scheme for GNSS at center frequency of 1575.42 MHz ........ 59 Table 4 Statistics of the final solution for 36 seconds period and final solution computed at rate of 100 ms .................................................................................... 94 Table 5 Channels statistics over period of 36 seconds ........................................... 106 viii List of Figures Figure 1. Ellipsoidal Geometry ............................................................................... 16 Figure 2. Keplerian Orbit........................................................................................ 21 Figure 3. Schematic Spread BPSK and BOC Modulated Signal ............................ 59 Figure 4.Time representation of a millisecond of recorded signal ........................... 63 Figure 5. Frequency representation of a millisecond of recorded signal ................. 64 Figure 6.Acquisition Search Space Channel #1 ...................................................... 69 Figure 7. Schematic Diagram of GNSS Signal Acquisition Based on GLRT ......... 70 Figure 8. Block Diagram of Early Minus Late Power DLL .................................... 75 Figure 9. First 6 Seconds of Output of Early Minus Late Power DLL Discriminator for Channel #1........................................................................................................ 76 Figure 10. Open Loop Initial Doppler Estimation/Reacquisition ........................... 78 Figure 11. Block Diagram of Costas PLL ............................................................... 81 Figure 12. First Second of Output of Costas PLL Discriminator for Channel #1 . 83 Figure 13. Structure of GPS NAV Data ................................................................. 85 ix Figure 14. First 15 Second of Demodulated Data Bits for Channel #1 ................. 86 Figure 15. Detected Sub-frames Using The Preamble for Channel #1 .................. 87 Figure 16. Final Solution Error with Respect to Topcon Net-G3 Hardware Receiver ................................................................................................................................ 95 Figure 17. Location of the Antenna on the Rooftop ............................................... 96 Figure 18 Acquisition Plots .................................................................................... 105 Figure 19 Evolution of DLL Discriminators .......................................................... 107 Figure 20 Evolution of early, late and prompt correlators .................................... 108 Figure 21 Evolution of PLL discriminators ........................................................... 109 x Chapter 1: GNSS Positioning Principles 1.1 Introduction Long before technology took over, mathematics of positioning and timing have been developed and practiced within the oldest and most unknown science of the earth, geodesy by means of celestial observations. The basic idea is straightforward, referencing to an external celestial object described in a pre-defined barycenteric celestial reference system (BCRS) followed by a set of transformations to a secondary Earth-Centered Earth-Fixed (ECEF) reference frame to solve for observer position and to determine non-uniform periodic variations of the second coordinate system with respect to the first to scale time. By the advent of engineering, however, technological tools for imitating geodetic astronomy were invented and horizons for location based applications and services were expanded. Global Positioning System (GPS) as the first substantiation of the family of Global Navigation Satellite Systems (GNSS) is a realization of such a perspective to address the high demands of universal 11 solution for positioning applications. Russia was the second contributor to launch its constellation called (GLONASS) to space. European Union and China have joined the satellite navigation community and by the time of writing this report European (Galileo) has 15 global satellites in orbit and China’s (BeiDou) has 18 satellites in orbit for global positioning.