Enhanced filtered-x least mean M-estimate algorithm for active impulsive noise control

Applying the typical active noise control (ANC) algorithm, namely the filtered-x least mean square (FxLMS) algorithm, to the non-Gaussian impulsive noise will experience difficulty. This is because the FxLMS algorithm is based upon the minimization of variance of the error signal, which is normally with the assumption of Gaussian distribution. To deal with this issue, the filtered-x least mean M-estimate (FxLMM) algorithm has been proposed based on the robust statistics theory to minimize the objective M-estimator error function. The Hampel's three-part M-estimator has been applied to provide thresholds for detecting and rejecting the outliers/impulses in the error signal. To further enhance the robustness of the conventional FxLMM algorithm, in this study a modified FxLMM (MFxLMM) algorithm is proposed, where the reference signal is fed through another Hampel's three-part M-estimator by setting thresholds for the impulsive samples. Numerous computer simulations are performed to validate the performance of the proposed algorithm. The generic impulsive noise is synthesized by using the contaminated Gaussian (CG) noise model, where certain number of impulses with different amplitudes and widths can be added in the background white Gaussian noise to represent different impulsive characteristics. In addition, extensive laboratory tests are carried out to further demonstrate the enhanced efficacy of the algorithm in a real-time environment. Results indicate that the proposed MFxLMM algorithm with online-threshold estimation is a very promising alternative for ANC of impulsive noise, and it shows similar convergence performance as the prevalent FxLMS algorithm for noise not corrupted by impulses.