Multichannel active noise control using numerically robust recursive least-squares algorithms

Abstract

Recursive least-squares (RLS) algorithms and fast-transversal-filters (FTF) algorithms were recently introduced for multichannel active noise control (ANC) systems. It was reported that these algorithms can greatly improve the convergence speed of ANC systems using adaptive FIR filters, compared to steepest descent algorithms or their variants. However, numerical instability of the algorithms was an issue that needed to be resolved. In this presentation, extensions of stable realizations of recursive least-squares algorithms such as the inverse QR-RLS and the QR decomposition least-squares-lattice (QRD-LSL) algorithms are first introduced for multichannel ANC. A first set of simulations will verify that these algorithms have indeed a better numerical stability than the previously published recursive least-squares ANC algorithms. The case of underdetermined ANC systems (i.e., systems with more actuators than error sensors) is then considered, to show that in these cases it may be required to use constrained algorithms in order to have numerical stability. Constrained least-squares algorithms for multichannel ANC systems are therefore introduced for two types of contraints: minimization of the actuator signals power and minimization of the adaptive filter coefficients squares. A second set of simulations will verify the stabilized behavior of the constrained algorithms.