Convergence analysis of the filtered-U algorithm for active noise control

Stochastic gradient methods such as the filtered-X LMS (Widrow and Stearns, 1985) algorithm and its variants are the most widely used algorithms for adaptive active noise control. While these algorithms typically employ finite impulse response (FIR) filters, the filtered-U LMS algorithm developed by Eriksson and Allie (1989) uses an infinite impulse response (IIR) filter structure to achieve better performance and also to address the problem of acoustic feedback. In this paper, the ODE method is used to study the asymptotic behavior of the filtered-U LMS algorithm, considering general stationary disturbances. A strictly positive real (SPR) condition is shown to be sufficient for convergence. The analysis suggests conditions under which the algorithm can be simplified. (C) 1999 Elsevier Science B.V. All rights reserved.