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Research on Some Problems in Bayesian Filtering in Nonlinear Non-Gaussian Environment

Author: HeKeKe
Tutor: TangZhenMin
School: Nanjing University of Technology and Engineering
Course: Pattern Recognition and Intelligent Systems
Keywords: Auxiliary Particle Filter Almost Sure Convergence Unscented Transformation Simplex Unscented Kalman Filter Interacting Multiple Model Model Error ProbabilityHypothesis Density Filter
CLC: TN713
Type: PhD thesis
Year: 2012
Downloads: 58
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Abstract

After several decades of research and development, target tracking filter, which was proposed in the1950s, becomes a very important technology in modern society. It is playing important part in the applications of military and civilian and achieves plentiful results in these fields. The traditional nonlinear filtering methods can not meet the requirements of some applications with the increase of complex and filter precision. In this dissertation, some problems on non-linear target tracking filter under complex conditions are studied. The main contributions are as follows:(1) A Modified Auxiliary Particle Filter (MAPF) is proposed to solve the almost sure convergence of the Auxiliary Particle Filter (APF).Then we analyze the almost sure convergence of MAPF and apply it to the APF. Moreover, when the recursive time is finite and the independent variables of interesting function is extended state vector, we prove that the sufficient condition for APF estimation converges almost surely to the optimal estimation as is4th power integrable with respect to the posterior probability distribution of the extended state. A simulation experiment is designed to illustrate the almost sure convergence of APF.(2) Based on Improved Unscented Particle Filter, we proposed Extended Noise Space Gauss Sum Unscented Particle Filter (ENSGSUPF). Compared to Unscented Particle Filter (UPF) and Unscented Transformation based Auxiliary Partcile Filter (UTAPF), ENSGSUPF、 IUPF and ISUPF do not need make the assumption that the state transition probability distribution is available. Moreover, ENSGSUPF has lower computational cost. And 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 the 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 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, which combines the stronger adaptability of IMM with the higher estimation accuracy and less computation load of PF-PHDF to different target maneuvering model, achieves accurate tracking for multiple maneuvering targets under the clutter environment. The experimental results show that the proposed method greatly improves the accuracy of multiple maneuvering targets tracking.

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