Robust adaptive filtering algorithms based on the half‐quadratic criterion

Abstract

Recently, robust adaptive filtering algorithms have attracted the interest of researchers and have been extensively studied. However, most of these methods suffer from the non-convexity of their performance surfaces, which results in reduced convergence rate and filtering accuracy. To address this problem, we present a novel robust half-quadratic criterion (HQC) adaptive filtering algorithm by utilizing a convex cost function. In contrast with conventional methods, the proposed HQC can introduce a more effective performance surface, allowing a gradient-based strategy to provide significant performance improvements in convergence speed and robustness against impulsive noise. Furthermore, to enhance the performance of the HQC adaptive filter, a variable step-size (VSS) version, the VSS-HQC algorithm, has also been introduced. Using the energy conservation method, the theoretical expressions for the transient, steady-state, and tracking performance analysis of the proposed HQC algorithm are studied under the Gaussian noise assumption. Then, we examined the theoretical analysis of the HQC using various numerical simulations for system identification to validate the findings. Finally, we compared the performance of the HQC and VSS-HQC algorithms to their competitors in both Gaussian noise and non-Gaussian noise scenarios through numerical experiments.