Joint state and process inputs estimation for state-space models with Student’s t-distribution

This paper proposes a joint state and unknown inputs (UIs) discrete-time estimation method for industrial processes, represented by a state-space model. To cope with the outliers in process data, the measurement noise is characterized by the Student’s t-distribution. The identification of UIs is accomplished through the recursive expectation–maximization (REM) approach. Specifically, in the E-step, a recursively calculated Q-function is formulated by the maximum likelihood criterion, and the states and the variance scale factor are estimated iteratively. In the M-step, UIs are updated analytically together with the degree of freedom is updated approximately. The effectiveness of the proposed algorithm is validated using a quadruple water tank process and a continuous stirred tank reactor. It shows that the proposed method significantly enhances the robustness and estimation accuracy of state and UIs in industrial processes, effectively handling outliers and reducing computational demands for real-time applications.