A robust active noise control algorithm using an adjustable arctangent function

Abstract The filtered-x least mean square (FxLMS) algorithm is a classic algorithm in the field of active noise control (ANC). However, its stability is compromised in the presence of impulsive noise, resulting in a poor noise reduction outcome. To address this issue, a normalized step size adjustable filtered-x arctangent least mean square (NAFxatanLMS) algorithm is proposed in this paper, which operates without the need of prior knowledge for threshold estimation. The algorithm employs an adjustable arctangent function as the cost function to perform a nonlinear transformation of the error signal. A compression factor is incorporated into the cost function to control the compression degree of the error signal, and an automated adjustment strategy is proposed to balance convergence speed and robustness of the algorithm. Finally, an improved variable step size strategy is introduced to further enhance the algorithm’s performance. Simulation results demonstrate that, compared to other algorithms, the proposed NAFxatanLMS algorithm exhibits superior convergence speed and noise reduction ratio.