Bayesian Filtering for Non-linear Markov Jump Systems with Non-homogeneous Transition Probabilities
非线性非齐次Markov跳变系统的贝叶斯滤波

A method of Bayesian state estimation is presented for non-linear non-homogeneous Markov jump systems where the transition probabilities (TPs) are time-variant and uncertain. The proposed method firstly utilizes constrained Gaussian probability density function to describe the real characters of TPs, and then the recursion of information state is obtained by using the reference probability method by which the actual probability measure is mapped into an ideal one. Meanwhile, the maximum a posterior (MAP) estimate of transition probability matrix is given in the Bayesian framework. To implement the MAP estimation and solve the problem of multiple integral of non-linear function, particle approximation is employed further. Finally, an example is simulated to illustrate the effectiveness of our method.