Developing a New Filtered-X Recursive Least Squares Adaptive Algorithm Based on a Robust Objective Function for Impulsive Active Noise Control Systems

It is well-known that performance of the classical algorithms for active noise control (ANC) systems severely degrades when implemented for controlling the impulsive sources. The objective of this paper is to propose a new recursive least squares (RLS) algorithm (and its variant) for being implemented in the framework of ANC systems. The proposed RLS-based adaptive algorithm employs an objective function designed to achieve robustness against the impulse type sources. The derivation of the algorithm is quite straightforward; however, a few modifications have been incorporated to address the application at hand. In order to improve upon the numerical stability issue of RLS-based adaptation, it is suggested to employ smoothing while updating the inverse correlation matrix. Furthermore, it is proposed to introduce a step size in the update equation of the adaptive algorithm. This results in the fixed step-size modified filtered-x (MFx) robust RLS (FSS-MFxRRLS) algorithm. As expected, a fixed value step size results in a trade-off situation for convergence speed and steady-state misalignment. In order to address this issue of a trade-off situation, the idea of a convex combined step size (CCSS) is introduced into the adaptive procedure to develop the CCSS-MFxRRLS algorithm. When the ANC is started, the CCSS strategy (automatically) selects a large-valued step size to achieve a fast initial convergence. As the ANC system converges at the steady-state, the CCSS is automatically tuned to a small value which improves the steady-state performance of the proposed CCSS-MFxRRLS algorithm. Extensive simulations have been designed to mimic many scenarios for practical applications of ANC for impulsive sources. The simulation results demonstrate that the proposed CCSS-MFxRRLS algorithm is very effective in many practical scenarios involving ANC of impulsive sources.