Expectation–maximization algorithm for bilinear systems by using the Rauch–Tung–Striebel smoother

Abstract

Bilinear system is a special class of nonlinear system. This paper is concerned with the identification problem of the bilinear systems in the state–space form. By treating the unknown states as the latent variables, the expectation–maximization algorithm is designed for identifying the bilinear systems. More specifically, the expectation step involves solving a state estimation problem by using the Rauch–Tung–Striebel (RTS) smoother, which can improve the estimation accuracy compared with the Kalman filtering. The maximization step is solved by numerical optimization. Under the principle of the expectation–maximization, an RTS smoother based expectation–maximization algorithm is proposed for the joint estimation for unknown system parameters and states. The simulation examples demonstrate the validity of our proposed solution.