The Research On Kernel Adaptive Filtering Algorithms

The kernel adaptive filtering has shown a good performance in dealing with nonlinear problems,which has attracted the attention of scholars at home and abroad.It is a hotspot in signal processing.This thesis mainly researches the kernel adaptive filtering algorithms.Firstly,the mathematical basis and important properties of kernel method are introduced in detail,and the theoretical basis of kernel adaptive filtering algorithm is explained.The kernel least mean square algorithm(KLMS)is the simplest one in kernel adaptive filtering algorithms.Its derivation process and parameter selection methods are given.Then,two kinds of kernel adaptive filtering algorithms under Gaussian noise are proposed.Block parallelism is applied to KLMS,and the block kernel least mean square algorithm(BKLMS)is derived and proposed.Because the computational complexity of KLMS will increase with the increase of iteration times,it is effective to accelerate the running speed by using multiple input signal vectors to compose the data blocks.The gradient is estimated by using multiple input signals and error signals,so that to improve the accuracy of gradient estimation.The complexity analysis and computer simulation results show that BKLMS has lower computational complexity and better steady-state performance than KLMS.The decorrelation and the normalization are applied into KLMS,and the decorrelated kernel least mean square algorithm(DKLMS)is obtained.Decorrelation can effectively solve the problem of slow convergence speed caused by high correlation of input data.The simulation results show that the DKLMS algorithm has faster convergence speed and better steady-state performance than KLMS.Finally,three kernel adaptive filtering algorithms under ?-stable distribution noise are proposed.Kernel least mean P-norm algorithm(KLMP)is proposed by combining the least mean P-norm algorithm(LMP)with the kernel method.BKLMS is extended under ?-stable distribution noise environment,and the block kernel least mean P-norm algorithm(BKLMP)is proposed.The affine projection algorithm is applied into KLMP,and the kernel affine projection P-norm algorithm(KAPP)is derived and proposed.Simulation results show that,KLMP,BKLMP and KAPP have good impulse noise suppression,and KAPP algorithm exhibits faster convergence.The steady-state performance of KAPP with block structure is better than BKLMP,and BKLMP algorithm has lower computational complexity through using parallel block than KAPP algorithm.