Adaptive Filtering Algorithms Under Mixed Kernels And Maximum Correntropy

Adaptive filter(AF),as an effective random signal processing tool,has been used in various fields of information society.The research of adaptive filter algorithm is an active topic in the field of signal processing.Adaptive filtering algorithms can be catagoried into two major categories,including linear adaptive filtering algorithms and nonlinear adaptive filtering algorithms.The classical adaptive filter algorithms include least mean square algorithm(LMS),kernel least mean square algorithm(KLMS),kernel affine projection algorithm(KAPA),etc.Kernel adaptive filter(KAF)is a typical representative of nonlinear AF.In kernel adaptive filtering algorithms,the choice of kernel function is extremely important.There are many kinds of available kernel functions,such as Gaussian kernel(GK)function,Laplace kernel(LK)function,exponential kernel function and polynomial kernel function.The most widely used kernel function is Gaussian kernel function.In this paper,we propose a mixed kernel function and a mixed kernel least mean square algorithm(KLMS-MK)based on the mixed kernel function.Most existing adaptive filtering algorithms are derived under the mean square error criterion(MSE),which is optimal in the presence of Gaussian noise.However,this assumption failed to simulate the behavior of non-Gaussian noise in practice.As a robust nonlinear similarity measure in kernel space,the correntropy has received more and more attention in the field of machine learning and signal processing.In particular,the maximum correntropy criterion(MCC)has been successfully applied to signal processing.The default kernel function in the correntropy is the Gaussian kernel function.Of course,this is not the best choice.The generalized maximum correntropy criterion(GMCC)has been applied to adaptive filter algorithms as a generalization of MCC.This paper focuses on the cost function of adaptive filtering algorithm,and the main work mainly includes the following two aspects:(1)We propose a mixed kernel function to replace the Gaussian kernel function in KLMS.We use the mixed kernel function to perform theoretical derivation in KLMS and propose KLMS-MK.The convex combination method is applied to the KLMS kernel function.KLMS-MK has the advantages of both Gaussian kernel and Laplace kernel.In KLMS-MK,the convex combination of mixing parameters is automatically adjusted by the stochastic gradient descent method.At the same time,we also prove the convergence of the mixed parameter.In KLMS-MK,KLMS-MK extends traditional single-kernel functions to multi-kernel functions,which leads to the improvement of convergence rate and MSE.(2)We propose affine projection algorithms based on maximum correntropy.First of all,the related theory of maximum correlation entropy is introduced,including: definition,correlation properties of maximum correlation entropy and related adaptive filtering algorithms.Secondly,we mainly study APA and KAPA based on the maximum correntropy,and derive their weight updating methods.Simulation results validate the efficiency of the proposed algorithm.