Particle Filter And Its Application In Satellite Navigation And Positioning

This dissertation mainly focuses on particle filter which is based on Bayesian theory and its application in satellite navigation and positioning. The main works and contributions are summarized as follows:1. Bayesian theory and Bayesian theorem have been introduced. Base on these, the filtering, prediction and smoothing functions are given. The commonly used point estimations which base on Bayesian theory are followed.2. Three nonlinear filter algorithms, extended Kalman filter, Unscented Kalman filter and parti-cle filter, have been discussed. Numerical example with these filters shows that in nonlinear case, particle filter is more appropriate than the others.3. Particle filter has been introduced in detail. Four particle filter resampling algorithms, simple random resampling, stratified resampling, systematic resampling and residual resampling, have been analyzed. The comparison has been made among these four algorithms on resampling and filter qualities and computational complexity. Numerical examples contrasting with these four methods are given. The results show that the systematic resampling is the recommended algo-rithm.4. A dual algorithm, dual particle filter, for nonlinear state and parameters estimation is pre-sented. Two separate particle filters run con-currently: one for signal estimation which is called particle state filter, and another for model estimation which is called particle weight filter. The signal filter uses the current estimate of the system parameters for signal particle filtering, and the new estimate of signal with observations are used for parameters estimation. Methods are compared by a simulation example of nonlinear noisy time series.5. Colored Noises Model has been introduced. Aimed to solve colored observation noises, polynomial-quotient has been used, which translates colored observation noises into infinite series, and the variances of colored observation noises have been calculated. Particle filter is followed to estimate the parameters. A contrast between this method and the approach of ob-servation expand filter is given. The result shows that the approach can control the influences of the colored observation noises effectively.6. A new approach, which is called robust particle filter, has been put forward based on the ro-bust estimation. With the equivalent weight, this method can resist outliers. A numerical exam- ple contrast between this method and the traditional way is given. The result shows that the ap-proach can control the influence by observation outliers effectively.7. Applies particle filter in target tracking, GPS navigation.