Research On Some Problems In Bayesian Filtering In Nonlinear Non-Gaussian Environment

Target tracking filter is proposed in the50’s of last century, and after half a century of researching and development, it has become indispensable in modern society of high-end technology. It is playing a broad role in the military and civilian and plentiful results have been acquired in these fields. 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. In this dissertation, some problems on non-linear target tracking filter in complex conditions are studied. The main contributions are as follows:(1) Despite many theoretical advances have been reported in the last decade, the study of the convergence properties of Particle Filters (PF) is still an open problem. In this dissertation, the almost sure convergence of the Auxiliary Particle Filter (APF) is discussed in a outfrank way. First, a Modified Auxiliary Particle Filter (MAPF) is constructed. Different from the APF, the MAPF will determine whether it is necessary to rerun the Importance Sampling (IS) step according to a conditional criterion after performing the IS step at each time. Then the almost sure convergence of MAPF will be concerned. Later, when the recursive time is finite and the interesting function with extended state as independent variable is4th power integrable with respect to the posterior probability distribution of the extended state, the sufficient condition for APF estimation converges almost surely to the optimal estimation is discussed. A simulation experiment is designed to illustrate the almost sure convergence of APF(2) A novel Particle Filter, in which the Unscented Transformation (UT) on the noise space is adopted to construct the Proposal Distribution, is proposed in the frame of the Particle Filter (PF), named Extended Noise Space Gauss Sum Unscented Particle Filter (ENSGSUPF). Each particle in traditional UT based PF such as Unscented Particle Filter (UPF) and Unscented Transformation based Auxiliary Particle Filter (UTAPF), denotes a sample of the state sequence. However, in ENSGSUPF, each particle denotes a sample of the extended process noise sequence, which is combined by the initial state and the process noise sequence. ENSGSUPF has three advantages over the UPF and the UTAPF. Firstly, ENSGSUPF doesn’t need to make the assumption that the state transition probability distribution is available. Hence, ENSGSUPF has wider application scope than UPF and UTAPF. Secondly, ENSGSUPF has lower computational cost. Thirdly, each particle in UPF or UTAPF is assumed to have a state covariance, which is inherited from its parent particle, but it is still uncertain whether this assumption is reasonable or not. This assumption can be avoided in ENSGSUPF. ENSGSUPF achieves better performance when compared with Sampling Importance Resampling (SIR), Gaussian Sum Particle Filter (GSPF), UPF and UTAPF in two simulation experiments.(3) In order to solve the problem of Non-Gaussian Nonlinear filtering with unknown continuous system parameter, Gauss Sum Simplex Unscented Transformation and Model Error based Interacting Multiple Model (GSSME-IMM) is proposed. GSSUKF is used here for each model to handle Non-Gaussian nonlinear estimation problem. The results of Monte-Carlo simulations show that the new algorithm can avoid performance deterioration effectively than IMM, SIR, and UKF, and it achieves global superiority in comparison with IMM when the true mode is constant.(4) To solve multiple maneuvering targets tracking problem under the complex environment, Model Error based Interacting Multiple Model Probability Hypothesis Density Filter (MEIMM-PHDF) algorithm is proposed. The algorithm combines the stronger adaptability of IMM with the higher estimation accuracy and less computation load of PF-PHDF to different target maneuvering model, realizes accurate tracking for multiple maneuvering targets under the clutter environment, and greatly improves the accuracy of multiple maneuvering targets tracking.