Hermite polynomial based affine projection Blake Zisserman algorithm for identification of robust sparse nonlinear system

Several adaptive filters have recently incorporated the Maximum Versoria criteria (MVC) and Blake Zisserman techniques to demonstrate their resilience to impulsive noise and non-Gaussian interference. In scenarios involving nonlinear system identification expressing sparse characteristics, the performance of these algorithms degrade when dealing with colored input signals. This manuscript presents the design of a nonlinear adaptive algorithm in the presence of impulsive noise by integrating a Hermite function polynomial in the functional link network, incorporating the Blake Zisserman function as a robust function. Additionally, this script introduces a zero-attracting affine projection Blake Zisserman-based Hermite functional link network (ZAB-HFLN) to model a nonlinear sparse system with impulsive or non-Gaussian noise disturbances, associated with the input as a colored signal. The l1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_1$$\end{document} regularization term is utilized in the algorithm to effectively model the system along with a sparsity parameter in this approach. Furthermore, a re-weighted ZAB-HFLN (RZAB-HFLN) is incorporated in this study, which integrates a log sum regularization parameter into the cost term function. This addition addresses the challenge of withstanding changing sparsity levels in the desired nonlinear system. The experimental outcomes clearly demonstrate the effectiveness and performance of the proposed algorithm in representing nonlinear systems, particularly when considering the input as colored signals. In addition, the nonlinear acoustic feedback paths of a behind-the-ear (BTE) hearing aid are also modelled employing the proposed techniques.