Approximate Nonlinear Filtering with Applications to Navigation

Abstract : This dissertation addresses nonlinear techniques in filtering, estimation, and detection that arise in satellite-based navigation. The author first introduces particle filtering for an exponential family of densities. He proves that under certain conditions the approximated conditional density converges to the true conditional density. For the case in which the conditional density does not lie in an exponential family but stays close to it, he shows that under certain assumptions the error of the estimate given by this approximate nonlinear filtering, projection particle filtering, is bounded. He gives similar results for a family of mixture densities. The author then uses projection particle filtering for an exponential family of densities to estimate the position of a mobile platform that has a combination of inertial navigation system (INS) and global positioning system (GPS). He shows via numerical experiments that projection particle filtering exceeds regular particle filtering methods in navigation performance. Using carrier phase measurements enables the differential GPS to reach centimeter-level accuracy. The phase lock loop of a GPS receiver cannot measure the full cycle part of the carrier phase. This unmeasured part is called integer ambiguity, and it should be resolved through other means. Here, the author presents a new integer ambiguity resolution method. Reliability of a positioning system is of great importance for navigation purposes. Failures or changes due to malfunctions in sensors and actuators should be detected and repaired to keep the integrity of the system intact. Since in most practical applications, sensors and actuators have nonlinear dynamics, this nonlinearity should be reflected in the corresponding change detection methods. In this dissertation, the author presents a change detection method for nonlinear stochastic systems based on projection particle filtering.

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