Research On Gaussian Sum Filter Of Nonlinear Markov Switching Systems

In Markov switching systems, there exist complex system characters, such as mode uncertainty, information uncertainty and nonlinearity, and the fact that such characters are coupled with each other will make the state estimation of the system become more complicated. In this paper, under the application background of the near space hypersonic target tracking and ground maneuvering target tracking, in view of the mode uncertainty and nonlinearity coupled problem in Markov switching systems, and the filtering problem of the mode transition probability related with the state, surrounding the multiple model estimation method and the nonlinear filtering algorithm, the estimation methods of continuous-state and discrete-mode of the system are studied. The main contributions are as follows:1. For the state estimation problem of non-linear Markov switching systems, under the optimal Bayesian estimation theory, a fast and highly accurate Gaussian sum filtering algorithm is designed based on Gaussian sum approximation. The procedure of this filter design includes the mixing and filtering steps. In the mixing step, the Minor Gaussian-set design using moment matching is utilized to control the number of Gaussian components. The filtering step includes analytical computation and Gaussian weighted integrals, thus the divided difference filter(DDF) based on the second-order Stirling's interpolation is chosen as the sub-filter. Finally, to verify the effectiveness of the proposed algorithm, simulations are performed in a typical single-model nonlinear system and the near space hypersonic target tracking system, respectively. Simulation results show that the proposed algorithm can make a compromise between estimation accuracy and computational cost.2. For the case that the model transition probability is time-varying and uncertain in Markov switching systems, namely the state estimation problem of the time-varying and non-homogeneous Markov switching systems, this paper considers the case that the model transition probability is related with the system state. Firstly, on the basis of the Gaussian sum filtering framework established in the third chapter, this paper derives the Gaussian sum filtering method for the nonlinear and non-homogeneous Markov switching systems. Secondly, for the application of the maneuvering target tracking, this paper establishes an effective and reasonable model for the model transition probability. Finally, a typical road maneuvering target tracking scenario is established. Simulation comparison with the case that model transition probability keeps constant is carried on, and the results show that the tracking accuracy of the target is improved.