Gudermannian-based Active Impulsive Noise Control Algorithm: Design and performance analysis

In active noise control (ANC) systems, the conventional filtered-x least mean square (FxLMS) algorithm suffers from performance degradation in impulsive-noise environments. To address this problem, a robust filtered-x least Gudermannian (FxLGD) algorithm is proposed by incorporating a Gudermannian-based nonlinear saturation transformation that compresses the residual noise into the FxLMS framework. Based on the Gaussian-mixture model to characterize the impulsive noise, we analyze the mean-square transient evolution of the FxLGD algorithm and obtain a closed-form to predict its steady-state behavior. To further improve performance in both convergence speed and residual error, a variable-parameter FxLGD algorithm is developed by taking advantage of the logarithmic mapping with respect to the residual error. Simulation results under various impulsive-noise scenarios have verified the proposed theoretical analysis as well as that the proposed algorithms achieve faster convergence, lower residual error, and better robustness than the compared algorithms. In addition, the experiment on a real single-channel pipeline ANC system further confirms their effectiveness.