Modeling and Performance Analysis of GPS Vector Tracking Algorithms

Abstract

This dissertation provides a detailed analysis of GPS vector tracking algorithms and the advantages they have over traditional receiver architectures. Standard GPS receivers use a decentralized architecture that separates the tasks of signal tracking and position/velocity estimation. Vector tracking algorithms combine the two tasks into a single algorithm. The signals from the various satellites are processed collectively through a Kalman filter. The advantages of vector tracking over traditional, scalar tracking methods are thoroughly investigated. A method for making a valid comparison between vector and scalar tracking loops is developed. This technique avoids the ambiguities encountered when attempting to make a valid comparison between tracking loops (which are characterized by noise bandwidths and loop order) and the Kalman filters (which are characterized by process and measurement noise covariance matrices) that are used by vector tracking algorithms. The improvement in performance offered by vector tracking is calculated in multiple different scenarios. Rule of thumb analysis techniques for scalar Frequency Lock Loops (FLL) are extended to the vector tracking case. The analysis tools provide a simple method for analyzing the performance of vector tracking loops. The analysis tools are verified using Monte Carlo simulations. Monte Carlo simulations are also used to study the effects of carrier to noise power density (C/No) ratio estimation and the advantage offered by vector tracking over scalar tracking. The improvement from vector tracking ranges from 2.4 to 6.2 dB in various scenarios. The difference in the performance of the three vector tracking architectures is analyzed. The effects of using a federated architecture with and without information sharing between the receiver’s channels are studied. A combination of covariance analysis and Monte Carlo simulation is used to analyze the performance of the three algorithms. The federated algorithm without information sharing performs poorer than the other two architectures. However, at low C/N0 ratios the difference in the performance of the three algorithms becomes virtually zero. The analysis of different vector tracking architectures is then extended to an analysis of different Deeply Integrated (DI) architectures. The effects of using a federated filtering architecture on DI’s performance are investigated. Covariance analysis and Monte Carlo simulation are also used to study the performance of the different DI algorithms. The results from the DI analysis mirror the results from the analysis of different vector tracking algorithms. The different DI architectures exhibit the same performance at low C/N0 ratios. The vector tracking algorithms are also implemented in MATLAB. The algorithms are tested using data collected from an environment with dense foliage (having widely fluctuating signal levels) and from an urban canyon type environment. The performance of the vector tracking algorithms is compared to that of a NovAtel ProPak-V3 receiver in the same scenarios. The vector tracking algorithms provide near continuous coverage through both environments while the NovAtel receiver exhibits periods of prolonged outages.