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SummaryA stochastic average gradient (SAG) algorithm is proposed for multirate (MR) finite impulse response (FIR) models with varying time delays in this article. The time delays at each sampling instant are computed through the self‐organizing maps technique, and then the parameters are estimated by using the SAG algorithm. Considering that the SAG algorithm updates the parameters using all the directions up to and including the current sampling instant, but only compute one gradient at each sampling instant, thus it has less computational efforts and quicker convergence rates. Furthermore, some modified SAG algorithms are also developed. Two simulation examples show that these algorithms identify MR FIR models with varying time delays correctly.

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This paper develops a biased compensation recursive least squares based threshold (BCRLS-TH) algorithm for a time-delay rational model. The time-delay rational model is first transformed into an augmented model by using the redundant rule, and then a RLS algorithm is proposed to estimate the parameters of the augmented model. Since the output of the augmented model is correlated with the noise, a biased compensation method is derived to eliminate the bias of the parameter estimates. Furthermore, based on the structures of the augmented model parameter vector and the rational model parameter vector, the unknown time-delay can be computed by using a threshold given in prior. A simulated example is used to illustrate the efficiency of the proposed algorithm.

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