Robust zero-point attraction least mean square algorithm on near sparse system identification

The newly proposed l₁ norm constraint zero-point attraction least mean square algorithm (ZA-LMS) demonstrates excellent performance on exact sparse system identification. However, ZA-LMS has less advantage against standard LMS when the system is near sparse. Thus, in this study, firstly the near sparse system (NSS) modelling by generalised Gaussian distribution is recommended, where the sparsity is defined accordingly. Second, two modifications to the ZA-LMS algorithm have been made. The l₁ norm penalty is replaced by a partial l₁ norm in the cost function, enhancing robustness without increasing the computational complexity. Moreover, the ZA item is weighted by the magnitude of estimation error which adjusts the ZA force dynamically. By combining the two improvements, Dynamic Windowing ZA-LMS (DWZA-LMS) algorithm is further proposed, which shows better performance on NSS identification. In addition, the mean-square performance of DWZA-LMS algorithm is analysed. Finally, computer simulations demonstrate the effectiveness of the proposed algorithm and verify the result of theoretical analysis.