A family of threshold based robust adaptive algorithms for active impulsive noise control

The common active noise control (ANC) algorithm, namely the filtered-x least mean square (FxLMS) algorithm, becomes unstable for the non-Gaussian impulsive noise. This is because the typical FxLMS algorithm is based on the minimization of variance of the error signal (the second order moment in L2L2 space), which does not exist for the non-Gaussian impulsive noise. In this study, a family of threshold based algorithms is proposed by minimizing several robust objective error functions as well as thresholding the reference signal to further refine the robustness of the ANC system for impulsive noise. The proposed algorithms are also expected to generalize the existing adaptive algorithms for impulsive noise control. These robust error functions are typically represented by (1) robust space vectors: LpLp and Log space; and (2) re-descending M-estimators: Huber, Fair and Hampel threshold functions. The threshold parameters in the reference signal and those M-estimators can be determined by using online and/or offline statistical estimation approaches. Numerical simulations are carried out to verify the performance of proposed algorithms by using synthesized impulsive noise following symmetric α  -stable (SαS)(SαS) distribution. Results show the improved robustness and convergence performance of the proposed algorithms for ANC of impulsive noises as compared to the conventional algorithms.