Exponentially Convergent IIR Filter-based RLS Algorithm Equipped with Commutation Error for Active Noise Control

Abstract

In this study, an infinite-impulse-response (IIR) filter-based recursive-least-squares (RLS) algorithm equipped with commutation error (CE) is developed for active noise control (ANC). This algorithm is referred to as FxdRLS/CE algorithm and a deterministic approach is established to explore convergence properties of the algorithm. The FxdRLS/CE algorithm with forgetting factor between zero and one is theoretically shown to be exponentially convergent, provided that a persistent excitation condition is satisfied. This guaranteed property of convergence is benefited from the use of CE with RLS for ANC. Despite numerical instability that may occur in computer simulation at sufficient small forgetting-factor value, the proper forgetting-factor value FxdRLS/CE algorithm can achieve a better ANC performance for band-limited white noise in terms of convergence rate and level of noise reduction as compared with that using an FxdRLS algorithm without CE and that using the algorithms in our previous studies. Experimental results also show an effective ANC performance of the proposed algorithm for multiple-frequency noise under our hardware limitation of computation capability. Altogether, these results support the effectiveness of the FxdRLS/CE algorithm for enhanced ANC performance.