The Filtered-x Least Mean Fourth Algorithm for Active Noise Control and Its Convergence Analysis

In this paper, we propose the filtered-x least mean fourth (LMF) algorithm where the error raised to the power of four is minimized and analyze its convergence behavior for a multiple sinusoidal acoustic noise and Gaussian measurement noise. Application of the filtered-x LMF adaptive filter to active noise control(ANC) requires estimating of the transfer characteristic of the acoustic path between the output and error signal of the adaptive controller. The results of the convergence analysis of the filtered-x LMF algorithm indicates that the effects of the parameter estimation inaccuracy on the convergence behavior of the algorithm are characterized by two distinct components : Phase estimation error and estimated gain. In particular, the convergence is shown to be strongly affected by the accuracy of the phase response estimate. Also, we newly show that convergence behavior can differ depending on the relative sizes of the Gaussian measurement noise and convergence constant.