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

Abstract

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.

Identification of Linear and Bilinear Systems: A Unified Study

“…Here, we set L 1 = L 2 = 32 for the decomposition. In both cases, we evaluate the normalized misalignment from (55) and the evolution of the singular values σ l (l = 1, 2, . .…”

“…In this context, the basic concept is to reformulate a high-dimension system identification problem as a combination of lowdimension solutions, thereby gaining in terms of both performance and complexity. Due to its features, this approach can be used in different practical applications-e.g., [48][49][50][51][52][53][54][55], among which we can mention acoustic feedback cancellation, adaptive beamforming, speech dereverberation, multichannel linear prediction, and nonlinear system identification.…”