Research Of The Kernel Adaptive Filtering Algorithm Under Impulse Noise

Kernel adaptive filtering is better applied to deal with nonlinear problems which has attracted the extensive attention and research.This thesis mainly researches kernel adaptive filter algorithmsc by using set-membership filtering theory,vector quantization method,etc.to reduce complexity of algorithms and increase performance of anti-impulsive noise.First of all,the basic theories of kernel adaptive filtering,Alpha stable distribution and set-membership filtering are briefly introduced.Then,three kinds of kernel set-membership filtering algorithms are proposed.Combining the famed kernel trick and the SMBNLMS algorithm,the Kernel SMBNLMS(KSMBNLMS)algorithm is presented.The KSMNLMS algorithm uses single constraint set to control the update of weight vector,and the KSMBNLMS algorithm uses two constraint sets to control the update of weight vector which can improve the estimation accuracy.Due to the degeneracy of performance of KSMNLMS and KSMBNLMS under Alpha stable distribution noise,the kernel SMNLMP(KSMNLMP)and kernel SMBNLMP(KSMBNLMP)algorithm are presented by making use of set-membership filtering theory.The simulation results of nonlinear channel equalization in set-membership filtering algorithms show that KSMBNLMS has better equalization results than KSMNLMS,KSMNLMP and KSMBNLMP respectively has better equalization results than KSMNLMS and KSMBNLMS,KSMBNLMP has the best equalization results.Thirdly,five kinds of anti-impulse adaptive filtering algorithms are proposed.In order to improving the performance of anti-impulse noise when deal with nonlinear problem under Alpha stable distribution noise,the famed kernel trick,the set-membership filtering theory and vector quantization method are used to the anti-impulse noise algorithm(AIA),so a kernel anti-impulse noise algorithm(KAIA),a kernel set-membership AIA algorithm(KSMAIA)and quantization KAIA(QKAIA)are proposed.The simulation results of the nonlinear channel equalization show that KAIA is better than the kernel normalized least mean square algorithm(KNLMS)and the kernel sign algorithm(KSA),the stable MSE and complexity of the KSMAIA and QKAIA algorithm are lower than KSMNLMS,the accurate of QKAIA is higher than KSMAIA,but the complexity of QKAIA is higher than KSMAIA.In order to improve the performance of anti-impulsive noise of above algorithms,the input signal is preprocessed through using nonlinear mapping,and then normalized KSMAIA and QKAIA are presented.The simulation results of nonlinear channel equalization show that the input preprocessing can enhance the performance of the algorithms,the equalization performance of NKSMAIA and NQKAIA are better than that of KSMAIA and QKAIA,respectively,and NQKAIA algorithm is the best when is used to dealing with the anti-impulse noise.Finally,a kernel recursive least mean p-norm(KRLMP)algorithm is proposed.The performance of the kernel recursive least square(KRLS)algorithm under the Alpha stable distribution is degraded,so KRLMP algorithm is proposed by using kernel method and matrix inversion lemma.The simulation results of MG time series prediction show that the KRLMP algorithm has the best anti-impulse noise ability than KRLS algorithm and kernel recursive maximum correntropy(KRMC)algorithm compared with recursive algorithms.