Kernel Filter Proportionate Normalized Least Mean Square Algorithm for Nonlinear Sparse Systems

An effective nonparametric model for creating adaptive nonlinear filtering (ANF) algorithms is provided by kernel methods. These algorithms were developed based on different kernels like Gaussian and Laplacian. Moreover, in practical applications, nonlinear systems are also sparse in nature. So, the filter proportionate normalized least mean square (FPNLMS) algorithm was developed for such sparse nonlinear systems. In this paper to have an effective ANF algorithm, the Gaussian kernel method is used with the FPNLMS algorithm providing a novel kernel FPNLMS (KFPNLMS) algorithm for sparse environments is developed. The system identification problem is solved using the KFPNLMS method, which performs as expected when the convergence analysis is done.