Robust Recursive Least M-Estimate Adaptive Filter for the Identification of Low-Rank Acoustic Systems

To identify acoustic systems (which are low-rank in nature) in non-Gaussian and Gaussian noise, a robust recursive least M-estimate adaptive filtering algorithm is developed in this paper by applying the nearest Kronecker product to decompose the acoustic impulse response. Two M-estimators, i.e., the Cauchy and Welsch estimators, are employed to define the cost function of the adaptive filter, leading to a class of numerically stable adaptive filtering algorithms, which are robust to non-Gaussian noise. The effectiveness of the developed algorithm is validated in acoustic environments with both Gaussian and non-Gaussian noise.