Research On Kernel Fractional Lower Power Adaptive Filtering Algorithm Against Non-Gaussian Impulsive Interference

In the linear systems,the input-output has a simple linear relationship,the traditional linear adaptive filtering algorithm has a good ability to track linear systems.However,when the algorithm suffers the relationship that the input-output is nonlinear,the tracking performance of the linear adaptive filtering algorithm deteriorates.As an effective method for finding nonlinear relationships hidden in unknown nonlinear systems,the kernel method has been applied to the design of nonlinear adaptive filters.The traditional kernel adaptive filtering algorithm has attracted extensive attention due to its simple structure and low computational complexity.However,since the traditional kernel adaptive filtering algorithm is mainly subjected to Gaussian white noise during the derivation,the ability of the algorithm to track the unknown nonlinear system will be greatly reduced under the interference of non-Gaussian impulse noise.This thesis studies how to improve the ability of kernel adaptive filtering algorithm to resist impulse noise interference.The main research contents are as follows:Firstly,aiming at the performance degradation of traditional kernel adaptive filtering algorithm under non-Gaussian impulse noise,the kernel fractional lower power adaptive filtering algorithm(KFLP)is derived by combining fractional low-order statistical error criterion.The algorithm utilizes the advantageous characteristics of the reciprocal coefficient of the instantaneous estimation error in the weight update formula,so that the algorithm's weight vector will automatically stop updating when the instantaneous estimation error suddenly increases,thus eliminating the influence of impulse noise on the weight vector.Experimental simulation results by nonlinear system identification show that the KFLP algorithm not only has better stability under the non-Gaussian impulse noise than the kernel least mean square(KLMS)algorithm,but also has a faster convergence speed than the kernel maximum correntropy criterion(KMCC)algorithm.Secondly,The KFLP algorithm is essentially a low-order norm class algorithm with slow convergence speed in the tracking process.This thesis proposes an S-KFLP algorithm that combines the S-curve function with the KFLP algorithm.The algorithm achieves resistance to impulse noise by using the nonlinear saturation characteristics of the S-curve function.On the other hand,the weight vector is not updated to resist the interference of the impulse noise algorithm.Moreover,since the S-KFLP algorithm can improve the convergence speed of the algorithm by adjusting the steepness parameter,the S-KFLP algorithm has a faster convergence speed than the KFLP algorithm.The convergence condition of S-KFLP algorithm and the mean square error of the algorithm in steady state are obtained by theoretical analysis of the convergence and stability of S-KFLP algorithm.The simulation experiments of nonlinear system identification show that the proposed S-KFLP algorithm not only has good ability to resist impulse noise interference,but also has faster convergence speed than KMCC and KFLP algorithms.