A new adaptive algorithm for reducing non-linear effects from saturation in active noise control systems

Adaptive algorithms applied to active noise and vibration control are frequently designed for maximum performance in linear environments. In many cases, non-linear effects can severely, impair the adaptive algorithm performance. One of the most common non-linear effects is saturation, which can occur at the electronic circuits that drive the acoustic or mechanical transducers. An effective solution to mitigate such non-linear distortions is to embed an automatic control of the non-linear effects within the adaptive algorithm. Algorithms that use this approach are called minimum effort adaptive filters. This work presents a new minimum effort Algorithm (MOV-FXLMS), based on the minimum output variance least mean square estimator, for situations in which the influence of the secondary path cannot be neglected and its output is constrained by a saturation non-linearity. Analytical expressions are obtained for the behaviour of the mean weight vector and for the mean square error for Gaussian inputs and slow learning. Monte Carlo simulations show excellent agreement with the predictions of the theoretical model.. The optimum penalty factor (a design parameter of the MOV-FXLMS algorithm) is determined as a function of the system's degree of non-linearity. The new algorithm provides an unbiased solution to the associated nonlinear mean square estimation problem for small estimation error's of the secondary path and degree of non-linearity. Robustness of the algorithm's performance to such errors is addressed. The new algorithm is compared with the conventional FXLMS algorithm for performance. Copyright (c) 2004 John Wiley & Sons, Ltd.