The identification of stochastic time-varying parameters for nonlinear system

In this paper, a method for a sort of nonlinear system identification with stochastic time-varying parameter is investigated. This kind of nonlinear systems is referring to the system where probability density functions (PDFs) of the parameters are known. This parameter identification and states estimation method is realized based on expectation maximization (EM) algorithm and particle filter. Firstly, parameter particles are generated randomly according to the PDF of parameter. Secondly, the particle filter is employed to estimate system states corresponding to each group of the parameters, and the weight of each group parameters is calculated according to the Bayesian theory. Then the new iteration of parameter is obtained by adopting the expectation maximization algorithm. Lastly, the real parameters are obtained along with system operation. Numerical illustrations are presented to exhibit the effectiveness of the method proposed herein, and the performance of the method is examined.