Online identification for output-error models with random time delays based on auxiliary model and recursive expectation maximization algorithm - Li, Ronghuan; Ma, Junxia; Ma, Yujie; Xiong, Weili (Digital signal processing, 2025)
This article considers the identification of output-error (OE) models with random time delays under the framework of a recursive expectation maximization (REM) algorithm. Polynomial transformation of OE models will cause the problem of colored noise. To avoid the interference of colored noise, an intermediate variable is directly defined to construct a pseudo-linear regression model, but its information vector contains unknown noise-free outputs. Therefore, under the help of the auxiliary model, an auxiliary variable with the same structure is constructed to replace the unknown intermediate term. At the same time, the expectation maximization (EM) algorithm is used to estimate unknown parameters by treating the time delay as a hidden variable. However, the classic EM algorithm can only process a fixed batch of offline data and cannot update model parameters in real time. Therefore, an online REM algorithm is proposed based on the sliding data window to achieve real-time updates of parameters. When a sliding data window moves forward, the algorithm can consider the newest data and discard the oldest data, improving data utilization. Further, this article analyzes the unbiasedness of the proposed REM algorithm under a batch of data. Finally, a numerical example and a simulated continuous stirred tank reactor are employed to illustrate the effectiveness of the REM algorithm. •By defining the intermediate variable, the problem caused by the polynomial transformation of OE models is avoided.•When new data is collected, a fixed-length sliding data window moves forward to realize the online identification.•The sliding data window makes up for the shortcomings of iterative algorithms under limited measurement data.•The unbiased estimator of the proposed algorithm under a batch of data is proved.