Robust Multichannel Linear Prediction for Online Speech Dereverberation Using Weighted Householder Least Squares Lattice Adaptive Filter

Speech dereverberation has been an important component of effective far-field voice interfaces in many applications. Algorithms based on multichannel linear prediction (MCLP) have been shown to be especially effective for blind speech dereverberation and numerous variants have been introduced in the literature. Most of these approaches can be derived from a common framework, where the MCLP problem for speech dereverberation is formulated as a weighted least squares problem that can be solved analytically. Since conventional batch MCLP-based dereverberation algorithms are not suitable for low-latency applications, a number of online variants based on the recursive least squares (RLS) algorithm have been proposed. However, RLS-based approaches often suffer from numerical instability and their use in online systems can further be limited due to high computational complexity with a large number of channels or filter taps. In this paper, we aim to address the issues of numerical robustness and computational complexity. More specifically, we derive alternative online weighted least squares algorithms through Householder RLS and Householder least squares lattice (HLSL), which are numerically stable and retain the fast convergence capability of the RLS algorithm. Furthermore, we derive an angle-normalized variant of the HLSL algorithm and show that it is robust to speech cancellation for a wide range of forgetting factors and filter taps. Finally, we support our findings through experimental results and demonstrate numerical and algorithmic robustness, long-term stability, linear complexity in filter taps, low memory footprint, and effectiveness in speech recognition applications.