A Family of Constrained Robust Adaptive Filtering Algorithms Based on the Logarithmic Criterion

Recently, robust constrained adaptive filtering algorithms have garnered significant research attention and have been the subject of extensive investigations. Most of these methods utilize specific error nonlinearity cost functions, which have demonstrated superiority over traditional methods based on the least mean squared (LMS) error cost function, particularly in environments contaminated with Gaussian and non-Gaussian noises. This paper introduces a generalized family of constrained robust least mean logarithmic square (CRLMLS) algorithms that optimize error nonlinearity called a relative logarithmic cost function. The proposed method offers a tradeoff between robustness and computational complexity when compared to other recent competitive methods. Using an energy conservation approach, we establish a sufficient condition for mean-square stability. Additionally, we analyze the steady-state mean-square deviation (MSD) performance of the standard CRLMLS algorithm under both Gaussian and non-Gaussian noise distributions. We validate the effectiveness of the proposed algorithms through numerical simulations in various impulsive noise scenarios, focusing on applications in system identification and beamforming.