Multi-Sensor Recursive EM Algorithm for Robust Identification of ARX Models

A robust multi-sensor recursive Expectation-Maximization (RMSREM) algorithm is proposed in this paper for autoregressive eXogenous (ARX) models, addressing the challenges of heavy-tailed noise, as well as the difficulty in simultaneously processing multi-sensor information. First, for the potential outliers in industrial processes, the Student’s t-distribution is introduced to model the statistical characteristics of measurement noise, whose heavy-tailed property enhances the algorithm’s robustness. Second, a recursive framework is integrated into the Expectation-Maximization (EM) algorithm to satisfy the real-time requirement of dynamic system identification. Through a recursive scheme of the Q-function and sufficient statistics, model parameters are updated in real-time, allowing them to adapt to time-varying system characteristics. Finally, by exploiting the redundancy and complementarity of multi-sensor data, a multi-sensor information fusion mechanism is designed that adaptively calculates the weight of each sensor based on the noise variances. This mechanism effectively fuses multi-source observation information and mitigates the impact of single-sensor failure or inaccuracy on identification performance. Numerical examples and simulations of the continuous stirred-tank reactor (CSTR) demonstrate the validity of the proposed RMSREM algorithm.