Laplace Distribution Based Online Identification of Linear Systems With Robust Recursive Expectation–Maximization Algorithm

• Published in: IEEE transactions on industrial informatics Vol. 19; no. 8; pp. 9028 - 9036
• Main Authors: Chen, Xin, Zhao, Shunyi, Liu, Fei, Tao, Chongben
• Format: Journal Article
• Language: English
• Published: Piscataway The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 01.08.2023
• Subjects: Algorithms; Autoregressive models; Linear systems; Maximization; Optimization; Parameters; Recursive functions; Regression coefficients; Robustness
• ISSN: 1551-3203; 1941-0050
• DOI: 10.1109/TII.2022.3225026

The robust online identification problem of linear systems is considered in this article using a faster robust recursive expectation–maximization (RREM) framework. To improve the convergence rate, the outliers, which would deteriorate the identified models, are accommodated with a Laplace distribution instead of Student's [Formula Omitted]-distribution. Then, the recursive transformation of the maximum likelihood function is realized with a recursive [Formula Omitted]-function. The extensively recognized autoregressive exogenous (ARX) models are used for the description of general linear systems. As a result, the unknown parameters, including the regression coefficient vector of the ARX models, the variance of the noise without outliers, and the scale parameter of the Laplace distribution, are determined in a recursive manner. The performance of the proposed approach is tested with a simulated continuous fermentation reactor system example and a coupled-tank experiment.