A Regularized Block Diagonal RLS Algorithm for Acoustic Echo Cancellation

The autocovariance least squares (ALS) method is a computationally efficient approach for estimating noise covariances in Kalman filters without requiring specific noise models. However, conventional ALS and its variants rely on the classic least mean squares (LMS) criterion, making them highly sensitive to measurement outliers and prone to severe performance degradation. To overcome this limitation, this paper proposes a novel outlier-robust ALS algorithm, termed ALS-IRLS, based on the iteratively reweighted least squares (IRLS) framework. Specifically, the proposed approach introduces a two-tier robustification strategy. First, an innovation-level adaptive thresholding mechanism is employed to filter out heavily contaminated data. Second, the outlier-contaminated autocovariance is formulated using an $ε$-contamination model, where the standard LMS criterion is replaced by the Huber cost function. The IRLS method is then utilized to iteratively adjust data weights based on estimation deviations, effectively mitigating the influence of residual outliers. Comparative simulations demonstrate that ALS-IRLS reduces the root-mean-square error (RMSE) of noise covariance estimates by over two orders of magnitude compared to standard ALS. Furthermore, it significantly enhances downstream state estimation accuracy, outperforming existing outlier-robust Kalman filters and achieving performance nearly equivalent to the ideal Oracle lower bound in the presence of noisy and anomalous data.

Real-time multichannel speech extraction (MSE) under diffuse noise conditions is an important task with a wide range of applications, such as speech recognition and hearing aids. In this paper, we propose online algorithms for independent low-rank matrix analysis (ILRMA) and rank-constrained spatial covariance matrix estimation (RCSCME). Previously, we proposed a real-time extension of the RCSCME-based method: an MSE method based on ILRMA and RCSCME using the blockwise batch algorithm. However, it assumes that the spatial characteristics are stationary within a single batch, and thus, in dynamic situations where the target speaker moves, its performance may degrade. To address this problem, we derive the online algorithms for ILRMA and RCSCME in the following three steps. First, we formulate framewise cost functions for ILRMA and RCSCME on the basis of maximum weighted likelihood estimation. Second, we derive the update rules for the framewise cost functions on the basis of auxiliary-function techniques. These naive update rules are computationally costly for real-time execution on a practical machine. Thus, we finally derive the online algorithms by approximating some intermediate parameters with their estimates. Furthermore, we propose stabilization and further acceleration techniques for these online algorithms. In experiments, we simulate situations where a target speaker is stationary or moves and show that the proposed method achieves superior speech extraction performance compared with conventional methods. In addition, using real-world recorded signals, we demonstrate the effectiveness of the proposed method in practical scenarios.

Reliable adaptive beamforming is critical for large microphone arrays operating in highly dynamic acoustic environments. In scenarios characterized by fast-moving talkers and interferers, the available sample support for estimating the spatial correlation matrix is often snapshot-deficient. This deficiency degrades the White Noise Gain (WNG), leading to severe target signal cancellation. To ensure stable and robust beamforming, we previously proposed an adaptive diagonal loading method that leverages the Kantorovich inequality to guarantee the WNG remains strictly within specified bounds. However, accurately determining the smallest necessary loading level requires calculating the extreme eigenvalues of the spatial correlation matrix, a computationally expensive $\mathcal{O}(M^3)$ operation for large arrays. In this paper, we introduce a highly efficient $\mathcal{O}(kM^2)$ estimation technique using Lanczos iterations to build a small Krylov subspace. By projecting the correlation matrix onto a tridiagonal matrix of dimension $k \ll M$, we extract Ritz values that rapidly converge to the exact extreme eigenvalues. Our evaluations demonstrate that this Lanczos-accelerated approach achieves performance identical to exact Eigenvalue Decomposition (EVD), ensuring optimal interference suppression and strict WNG adherence at a fraction of the computational cost.