Online state and inputs identification for stochastic systems using recursive expectation-maximization algorithm

Abstract In this paper, an online joint state estimation and unknown inputs (UIs) identification approach for industrial processes represented by the state-space model is proposed. The UIs identification is achieved by applying the recursive expectation-maximization (REM) technique. In E-step, a recursively calculated Q-function is derived based on the maximum likelihood framework, and the Kalman filter (KF) is adopted to estimate the states. In M-step, analytical solutions for UIs are obtained via locally maximizing the recursive Q-function. A numerical example of a quadrupled water tank process and practice application to system modeling of a distillation tower are employed to illustrate the proposed REM-KF algorithm's effectiveness. It is also demonstrated that the REM-KF algorithm is more accurate than existing online solutions.