Laplace Distribution Based Online Identification of Linear Systems With Robust Recursive Expectation–Maximization Algorithm
Xin Chen, Shunyi Zhao, Fei Liu, Chongben Tao
Abstract
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t$</tex-math></inline-formula> -distribution. Then, the recursive transformation of the maximum likelihood function is realized with a recursive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> -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.