Research On The Kernel Least Mean Square-type Algorithm Under The Non-gaussion Noise Enviroment

In the linear system,the traditional adaptive filtering algorithm shows a good computational power.However,the practical application involves many nonlinear problems,and the linear adaptive filtering algorithm has poor tracing performance.As a powerful tool to extend the linear system model to the nonlinear application field,the kernel method has been widely applied to the design of nonlinear adaptive filter.In the existing kernel adaptive filtering algorithms,the kernel least mean square(KLMS)algorithm has attracted more and more attention because of its simple structure,strong approximation ability and relatively low computational complexity.However,the kernel least mean square algorithm is deduced in the white Gaussian noise environment.Under the non-Gaussian impulse noise,the tracking performance of the algorithm is seriously deteriorated,which also limits the application of the kernel least mean square error algorithm in practice.Therefore,this paper studies the stability and convergence speed of the kernel least mean square-type algorithm in the non-Gaussian impulse noise environment.The main research contents are as follows:1.Aiming at the problem of insufficient convergence performance of the kernel least mean square algorithm in non-Gaussian impulse noise environment,W.Liu et al.proposed the kernel maximum correlation criterion(KMCC)algorithm against non-Gaussian impulse noise interference.When the impulse noise is disturbed,the filter weight coefficient of the KMCC algorithm is almost not updated,which ensures the stability of the algorithm.However,compared with the KLMS algorithm,the KMCC algorithm has a slower convergence speed.Therefore,this paper combines KLMS and KMCC algorithm,then proposes a new hybrid algorithm.The simulation results show that the hybrid algorithm has the ability to resist the impulse noise similar to the KMCC algorithm,and also has the characteristics of fast convergence similar to the KLMS algorithm.2.Aiming at the problem of insufficient stability and mixed parameter selection of the algorithm which combines KLMS and KMCC algorithm,this paper proposes the kernel least logarithmic absolute difference(KLLAD)algorithm.The algorithm can automatically switch between KLMS and symbol-type algorithms by the change of the size of the prediction error to ensure the robustness of the algorithm and the convergence rate,while avoiding the selection of mixed parameters.The simulation results show that the KLLAD algorithm has better stability and faster convergence rate than the hybrid algorithm of KLMS and KMCC.Moreover,in order to further improve the convergence rate of the algorithm,KLLAD and KLMS are combined to deduce a new hybird algorithm in this paper.The simulation results show that the algorithm has a better ability to resist the impulse noise interference than the KLMS algorithm,and it has a faster convergence rate than the KLLAD algorithm.