On Developing a Robust Filtered-Reference RLS Algorithm and its Application for ANC Systems Targeting Impulsive Noise Sources

This paper develops a robust filtered-reference recursive least squares (RLS) algorithm for active noise control (ANC) systems targeting impulsive sources. The developed algorithm is based on a previous work exploiting an objective function showing robustness to tackle impulsive sources. The update equation in the previous algorithm incorporates a fixed step-size as a learning parameter. Furthermore, the forgetting factor (signifying the memory of least squares adaptation) is kept constant as in the traditional RLS algorithm. This paper first develops a generalized sigmoid activation function computed on the basis of internally generated error signal in the ANC system. The activation function is tuned such that it stays close to unity during the transient state and decays towards zero at the steady-state. This allows to tune the step-size as well as the forgetting factor such that the step-size parameter (the forgetting factor) is adjusted to a large value (small value) during the transient state to improve upon the convergence speed. On the other hand, the step-size parameter (the forgetting factor) is automatically tuned to a small value (large value) as the ANC system approaches the steady-state. Therefore, the proposed algorithm completely solves the trade-off situation. Extensive numerical simulations have been carried out which show the effective performance of the proposed algorithm.