Numerically stable fast convergence least-squares algorithms for multichannel active sound cancellation systems and sound deconvolution systems

Abstract

In recent years, recursive least-squares (RLS) algorithms and fast-transversal-filters (FTF) algorithms have been introduced for multichannel active sound cancellation (ASC) systems and multichannel sound deconvolution (MSD) systems. It was reported that these algorithms can greatly improve the convergence speed of the ASC/MSD systems using adaptive FIR filters. However, numerical instability of the algorithms is an issue that needs to be resolved. In this paper, extensions of numerically stable realisations of RLS algorithms such as the inverse QR-RLS, the QR decomposition least-squares-lattice (QRD-LSL) and the symmetry preserving RLS algorithms are introduced for the specific problem of multichannel ASC/MSD. Multichannel versions of some of these algorithms have previously been published for prediction or identification systems, but not for control systems. The case of underdetermined ASC/MSD systems (i.e. systems with more actuators than error sensors) is also considered, to show that in these cases it may be required to use constrained algorithms in order to have numerical stability. Constrained algorithms for multichannel ASC/MSD systems are therefore introduced for two types of constraints: minimisation of the actuator signals power and minimization of the adaptive filters square coefficients. Simulation results are shown to verify the numerical stability of the algorithms introduced in the paper.