Generalized Polynomial Chaos and Markov Chain Monte Carlo Methods for Nonlinear Filtering
In science and engineering research, filtering or estimation of system’s states is widely used and developed, so the structure of a new nonlinear filter is proposed. This thesis focuses on the procedures of propagation and update step of the new filter. The algorithms used in the filter, including generalized Polynomial Chaos Algorithms, Markov Chain Monte Carlo algorithms, and Gaussian Mixture Model algorithms, are introduced. Then, the propagation and update step of the proposed filter are applied in solving two nonlinear problems: Van der Pol Oscillator and Two Body System. The simulation shows that the results of the propagation and update step are reasonable and their designs are valuable for further tests. The propagation step has the same accuracy level compared with a Quasi Monte Carlo simulation while using a much smaller number of points. The update step can build a useful Gaussian Mixture Model as the posterior distribution.