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Active noise control (ANC) systems operating on adaptive algorithms endure instability in the presence of impulsive noise (IN). Therefore, this manuscript investigates the performance of such adaptive algorithms with online secondary path modeling (OSPM) in the presence of impulsive noise in non-stationary acoustic paths. Herein, we propose three new solutions based on the filtered x least mean absolute third (FxLMAT) algorithm for OSPM with IN. Our first solution utilizes the FxLMAT algorithm in the control filter of ANC, achieving improved modeling accuracy, good convergence, and better stability than the already existing variants of the filtered x least mean square (FxLMS) solutions. However, our proposed FxLMAT based solution exhibit slow convergence and is not robust in time-varying acoustic paths. Therefore, we propose a modified FxLMAT (MFxLMAT) algorithm to enhance the robustness of the FxLMAT solution. However, the proposed MFxLMAT still lacks good convergence. Henceforth, we introduce our third solution, i.e., a variable step size filtered x robust normalized LMAT (VSSFxRNLMAT) algorithm that almost acquires the same performance as that of the already existing filtered x recursive least square (FxRLS) family-based solutions. Simulation results are provided which show that our proposed VSSFxRNLMAT solution outperforms the already existing algorithms in terms of noise and vibration reduction, robustness, and convergence. Moreover, a comparative analysis based on the computational complexity of some well known existing as well as our proposed solutions is provided, which shows that our proposed VSSFxRNLMAT has almost the same complexity as that of the existing techniques.

Robust and Least Complex Online Secondary Path Estimation in Broadband Feed-Forward Active Control of Impulsive Noise Using FxLMAT Family