Identification of switched linear systems based on expectation-maximization and Bayesian algorithms

Abstract

This study aims to determine how to deal with the identification from input and output data of switched linear systems (SLSs) with Box and Jenkins models. The identification difficulties of this system are that there exist unknown switched signal, unknown middle variables, and colored noise terms in the identification process. To address these issues, the proposed identification method proceeds in two stages, including the estimation of the switched signal of SLSs and the identification of the parameters of all subsystems. First, the Gaussian mixture model is established to represent the distribution of the input and output data of SLSs. Then, the posterior probability is calculated by the expectation-maximization (EM) algorithm and the naive Bayes classifier, and the switched signal is estimated according to the maximum probability criterion. Next, the auxiliary model based multi-innovation generalized extended least square (AM-MI-GELS) algorithm is used to estimate the parameters of all subsystems. Finally, the effectiveness of the proposed method is verified through the simulation example.