Characterization of the clock and ephemeris error distributions of the global satellite navigation (GNSS)
Keywords: Engineering.
Aeronautics and Astronautics.

With the rapid development and the broadened usage of GNSS technology, it becomes increasingly important to ensure the safety of the positioning, navigation, and timing provided by GNSS. Concepts such as Advanced Receiver Autonomous Integrity Monitoring (ARAIM) are designed to provide integrity guarantees for this purpose. These concepts rely on the characterization of the errors. Reliable upper bounds can be placed on the potential errors in the positioning and timing estimates. As more navigation signals are incorporated, it becomes more likely that one or more signals may contain a significant error. Further, different error characteristics are expected to be encountered with new constellations and new signals. Multiple frequencies allow the near elimination of ionospheric errors, leaving satellite clock and ephemeris error as one of the largest potential error sources. Therefore more emphasis is put on characterizing the clock and ephemeris errors. To shed light on the satellite clock and ephemeris error behavior, we focus on characterizing the behavior of nominal satellite clock and ephemeris errors using Gaussian bounding parameters ias$ and $\sigma$. The errors are normalized by the user range accuracy ($\sigma_{URA}$). The ias$ and $ \sigma$ parameters correspond to the Gaussian mean and standard deviation, respectively. In particular, we investigate the inherent variability of the Gaussian error bounding parameters and the stability of the parameters with respect to different partitions such as time, different space vehicle numbers, different user range accuracy, etc. To do so, we provide two algorithms to quantify the inherent variability of the bounding parameters. We also provide an algorithm to capture this variability using a single set of statistics corresponding to the Gaussian mean and standard deviation. We call these $BIAS$ and $\Sigma$. In the first part of the thesis, we briefly introduce the GNSS integrity concept and the necessary background regarding the bounding method. We also provide the motivation for this work and the outline of the thesis. In the second part of the thesis, we provide the data processing method used in the thesis and provide a preliminary examination of how the error-bounding parameters evolve through time. We find that the error bounding parameters are relatively stable over time and that near-fault data points affect the stability. In the third part of the thesis, we provide two algorithms to quantify the inherent variability in the bounding parameters for the error data. We find that the error bounding parameters have low variability based on the simulation results. In the fourth part of the thesis, we provide a single set of statistics $BIAS$ and $\Sigma$ to capture the quantified variability. We also provide detailed algorithms and the corresponding optimization techniques. The experimental results show that the $BIAS$ and ias$ values are small and that the $\Sigma$ and $\sigma$ values are mostly below $\sigma_{URA}$. We also show that the near-fault data points affect the stability. Finally, we explore how lowering the $\sigma_{URA}$ affects the bounding parameter stability. The experimental results show that the bounding parameters become more stable after lowering the $\sigma_{URA}$. These results provide insights into the stability of GNSS clock and ephemeris errors and can be used to aid the development of ARAIM