Studies And Applications On Improved Particle Filter Algorithm

The traditional nonlinear filtering method can not meet the requirements of some applications because the models are more complex, and also those applications need higher filter precision. Particle filter, as a recent research focus of nonlinear filtering method, can deal with the nonlinear/non-Gaussian filtering problem effectively without assumption on the state distribution. So it is more applicable for practical filtering problem. However, there are still some problems need to be solved even though the particle filtering theory has been rapid development, so improvement on the particle filtering method have significant theoretical and practical value. This thesis utilized the new statistical learning theory to study the particle filtering algorithm and its applications. The research focused on following aspects.Firstly, based on the unified recursive Bayesian estimation theory, three typical nonlinear filtering methods—Extend Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Particle Filter (PF) were studied. The thesis analyzed and compared the basic theory, application conditions, advantages and disadvantages of these three methods. Especially for particle filtering method, the basic principle, algorithm, particle degeneration and impoverishment, convergence theory were studied in depth as the basis of further study.Secondly, the thesis improved the particle filtering method from the perspective of the probability density estimation to overcome the particle degeneration and impoverishment. Started with the mathematical description of ill-posed probability density estimation problem, the basic idea of a density estimation method based on Support Vector Machine (SVM) was proposed, which built the posterior density models and resampled the new particles. Then the efficiency of this estimation algorithm was improved by using linear optimization theory. And the multi-dimensional extension problem was discussed also. Furthermore, for the more severe degeneracy problem in weak measurement noise applications, an improved likelihood particle filter algorithm based on SVM resampling was proposed. This algorithm used likelihood function as proposed distribution, took account of the most recent observation information, and increased the diversity of sampled particles. So that the degeneration problem was solved effectively and the states estimation precision was improved. Simulation results demonstrated the feasibility and superiority of the proposed algorithms.Thirdly, the thesis studied how to solve the problem of particle degeneration and impoverishment from the perspective of function regression estimation. The proposed algorithm used particles and their weights to build regression model during iteration, and adjusted weights of particles by this model to overcome the degeneration and increase the diversity of particles. In order to avoid solving quadratic optimization problem, the Mean Filed Support Vector Regression (MF-SVR) particle filter and Least Squares Support Vector Regression (LSSVR) particle filter were proposed, where the mean filed theory and equality constraint method were implemented respectively. Simulation results illustrated the superiority of the two algorithms to existing methods. In addition, the application on large scale data set algorithm of LSSVR was discussed.Then, the thesis studied the method of improving the real-time performance of particle filter. The Proximal Support Vector Machines (PSVM), used in classification problems, was extended into this regression problem. By solving the optimization problem directly, the algorithms for linear, nonlinear, and large scale data sets applications were derived, and compared with LSSVR. According to that, an improved real-time particle filter algorithm was proposed, which was based on data fusion with Proximal Support Vector Regression (PSVR), to estimate the filtering result of particles within the estimation window. The new algorithm reduced the calculation complexity, and was more practical for real-time applications. The simulation results of bearings-only tracking problem demonstrated the feasibility and superiority of the proposed algorithm.Finally, the thesis studied the particle filter that based on multiple models and its application on maneuvering target tracking. According to the principle of recursive Bayesian estimation theory, the basic algorithm of interacting multiple model particle filter was derived and also the practical algorithm based on Gaussian approximation method was provided. Based on the analysis of the basic motion model of maneuvering target, and using the particle filter as model matched filter, the thesis solved the problem that the nonlinear observation equation was difficult to apply directly. The proposed method used Doppler measurement method to estimate the turning angular rate, reduced the number of models, and improved the efficiency of the filter algorithm. The simulation results of a multi-turn maneuvering target tracking problem demonstrated the feasibility and superiority of the proposed algorithm, and also extended the applications of particle filter in target tracking.