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

• Published in: Chemometrics and intelligent laboratory systems Vol. 217; p. 104403
• Main Authors: Liu, Zhuangyu, Zhao, Shunyi, Luan, Xiaoli, Liu, Fei
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.10.2021
• Subjects: Kalman filter (KF); Recursive expectation-maximization (REM) algorithm; State estimation; Unknown inputs (UIs) identification; Unknown inputs (UIs) identification; Recursive expectation-maximization (REM) algorithm; State estimation; Kalman filter (KF)
• ISSN: 0169-7439; 1873-3239
• DOI: 10.1016/j.chemolab.2021.104403

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. •An online joint estimation and identification approach is formulated for the state-space model coupling with unknown inputs.•A recursive Q-function based on sufficient statistics for state-space model integrating with unknown inputs is derived.•The proposed recursive EM algorithm is verified to meet real-time modeling requirements of the distillation tower.