Robust multi-reference adaptive gain FxLMS algorithm for active impulsive noise control

The multi-reference least mean square (MR-FxLMS) algorithm achieves significant advantages over the traditional single-reference feed-forward FxLMS algorithm. Nevertheless, the MR-FxLMS algorithm's performance may degrade in the presence of impulsive noise. To enhance its robustness, the robust multi-reference adaptive gain Filtered-x-Logerf-LMS (RMAG-FxLe-LMS) algorithm is proposed, which consists of three parts. Firstly, a novel cost function is formulated by incorporating a nonlinear transformation within the logarithmic function, leading to the introduction of the robust multi-reference FxLMS algorithm. Subsequently, to improve the accuracy of the estimated error, the secondary error calculation (SEC) and the adaptive gain factor are introduced. Then, the stability performance and computational complexity are analyzed. The experiments were conducted to validate the effectiveness of the proposed algorithm under varying impulse noise intensities and real-world noise conditions. Simulation results show that the proposed RMAG-Fxle-LMS achieves 5-10 dB performance improvement over previous algorithms under different noise inputs.