On The Robustness Of Kernel Adaptive Filter Algorithms

As a new type of adaptive filter,Kernel adaptive filter(KAF)has a wide range of applications in signal processing.Its working principle is to use kernel trick to transform the original data into RKHS(reproducing kernel Hilbert space)which is an efficient and practical nonlinear filtering method to solve nonlinear problems.At present,the research of KAF mainly starts from three aspects: cost function(also can be said as error criterion),filter structure and control network growth.Among them,the cost function can be divided into second-order,low-order,high-order,entropy,and logarithm according to its statistical characteristics.The filtering structure is mainly divided into two types: feedforward and feedback.As for the control of network growth,due to the application of KAF,there will be a large amount of calculation,and the storage requirements of the device are high.In order to solve this problem,researchers have proposed many different types of sparse methods.It is mainly divided into two types: sample sparsity and structure sparsity.Sample sparsity uses threshold rule to filter samples at the expense of filter performance,and uses fixed network size to approximate kernel function for structure sparsity.Both kinds of sparsity methods can achieve the purpose of controlling network growth.This paper focuses on the above research direction of KAF,as follows:Firstly,in order to improve the robustness of the algorithm and achieve higher filtering accuracy,this paper proposes the Cauchy loss function by adding Gaussian kernel to Cauchy kernel loss function,then some important properties are introduced.On the basis of the theoretical support,the minimum Cauchy kernel loss criterion is proposed.Firstly,we propose the minimum Cauchy kernel loss algorithm(MCKL),then we develop it to kernel space,and propose the multikernel minimum Cauchy kernel loss algorithm(MKMCKL)combined with the multikernel theory.The proposed MKMCKL algorithm can effectively resist impulse noise,including robustness to large outliers,and can freely select kernel parameters.Furthermore,we further optimize the algorithm in terms of sparsification.A relatively idealized vector quantization method is selected in the sample sparseness method,and considering the shortcomings of the vector quantization method itself,combined with the sliding window method,a sparse multikernel minimum Cauchy kernel loss algorithm is proposed which can be effectively applied to time-varying systems.This method fully combines the advantages of two types of sparse methods,and has little effect on the convergence performance of the algorithm itself,which is within an acceptable range.Last,improve the algorithm by combining optimization criteria and error criteria.On the basis of the Cauchy kernel loss,combined with the generalized Gaussian distribution,the generalized Cauchy kernel loss is developed,and some important attributes are introduced,and then the minimum generalized Cauchy kernel loss criterion is proposed.In order to further improve the robustness of the algorithm to outliers,a recursive method was introduced,and a recursive generalized Cauchy kernel loss algorithm(KRGCKL)was proposed.This algorithm shows more robust filtering performance against mixed non-Gaussian noise.