Robust online identification for hybrid multirate systems based on recursive EM algorithm

This paper focuses on robust identification for both linear time-invariant and time-variant multirate systems with time delays subject to outliers. The time delays are time varying and modeled by a Markov chain. Furthermore, the collected output data, which is corrupted by outliers, is described through a Laplace distribution. Parameters for the time-invariant model are estimated utilizing the batch expectation maximization (BEM) algorithm, whereas the recursive EM (REM) algorithm is employed for parameter estimation of the time-variant model. Upon receiving new data, the BEM first incorporates it in the historical batch data set and then iteratively recalculates parameter estimation using the updated data set. In contrast, the REM algorithm uses the parameter values obtained from the preceding step to recursively refine its estimates according to the new data sample. The efficacy of the proposed methods is demonstrated through a numerical example and a simulated continuous fermentation reactor process.