Research On The Algorithms Of Combined Kernel Adaptive Filters

As an important part of statistical signal processing,adaptive filter(AF)has been widely used and developed in signal processing and localization.In signal processing,AF can adjust the system parameters adaptively with the change of the input signal without the estimation of the noise and signal parameters in advance.Kernel adaptive filter(KAF)is a kind of nonlinear filter which approximates the function by kernel method.It is also another form of AF in kernel Hilbert space.The inner product of in the input space of KAF can be effectively realized by the kernel method in reproducible kernel Hilbert space(RKHS).So far,kernel adaptive filter is the best method in nonlinear signal processing.However,its complex filter structure leads to high time complexity,which seriously restricts practical application.In the aspect of networksize control,there are two methods: sample sparsification and structure sparsification.The sample sparsification method simplifies the filter structure by vector quantization criteria and novel criteria to reduce the complexity.The structure sparsification can obtain the mapping function of the high-dimensional feature space by approximating the kernel function,so the dimension of feature space can be set arbitrarily.However,all the sparse methods reduce the complexity at the expense of filtering performance.The traditional sparse kernel filter algorithm has a high computational efficiency with a low filtering accuracy.In this paper,the combined kernel adaptive filter(CKAF)is designed to make full use of the cooperative work of kernel adaptive subfilters,so as to make up for the shortcomings of traditional KAF accuracy.In the case of lower time complexity,CKAF can achieve similar filter accuracy as traditional KAF.In the same time complexity,CKAF has better filtering performance.This paper improves the traditional nuclear filter from the following three aspects.(1)Control the linear increasing size of the kernel filter: Based on nearest-instancecentroid-estimation(NICE)and clustering methods,the original complex KAF is divided into several approximately independent subfilters,and the subfilters are used alternately according to the distance between the input data and the sample.The samples obtained by this method are closer to the current input data than those obtained by the traditional sample sparsity method,so as to obtain better filtering effect.(2)Increase the sparsity efficiency of the kernel filter: Although the Nystr?m method in the structural sparsification method can set the structure size of the filter in advance,the Gram matrix used in the calculation of high-dimensional feature mapping is full of invalid values which approximates to zero,and the position of invalid values is irregular.In this paper,NICE is used to optimize the sampling process in Nystr?m method,so as to ignore the calculation with the invalid value in Gram matrix.And thus,the calculation efficiency is improved.(3)Increase the filtering performance of the kernel filter: CKAF based on multiple random Fourier mappings is proposed in this paper.Firstly,input data are mapped into different high-dimensional feature Spaces which is similar to the kernel Hilbert space,and then the mapped data are sent into different sub-filters respectively.Finally,the results of each sub-filter is superposed,so as to improve the performance of traditional kernel filters.This paper also proposes a simple structure based on multiple random Fourier mapping CKAF,that is,the data mapped to different high-dimensional feature Spaces are first superposed and then processed by a single filter to reduce the computational complexity.