Abstract
<title>Abstract</title> <p>The zero-attraction based least mean square (LMS) algorithms have gained popularity for sparse system identification due to their low computational complexity and easy implementation. This paper introduces a new sparsity aware function based on Pseudo-Huber Loss (P-HL) namely modified P-HL (MP-HL). This loss function is designed to enhance the sparsity promotion while maintaining smoothness and differentiability for stable adaptation.This is then utilized to develop novel sparsity aware zero attraction-based MP-HL LMS (ZA-MP-HL-LMS) adaptive filter. The proposed adaptive filter integrates zero-attraction mechanisms with the conventional LMS to effectively identify sparse systems.The paper also presents bound on the learning rate, ensuring convergence in both the mean and mean square error sense. Additionally, mean and mean square error (MSE) theoretical analysis and state state MSE, mean square deviation error are also performed. Finally, guidance on the selection of zero attraction parameter to ensure steady state MSE lesser than LMS and computational complexity analysis is also provided. Simulation results demonstrate that the proposed algorithms outperform the state of the art approaches in the system identification examples.</p>