Research On Affine Projection Adaptive Filtering Algorithm Based On Wilcoxon

The adaptive filter has the ability to process signals in a time-varying unknown environment,and is therefore widely used in many fields such as system identification,noise cancellation,echo cancellation,adaptive channel equalization,and the like.As an important part of adaptive filter,adaptive filtering algorithm has always been a research hotspot in the field of signal processing.Affine Projection Algorithm?APA?is one of the most important adaptive filtering algorithms.It is a generalization of the Normalized Least Mean Square?NLMS?algorithm and is reused by input data.Reducing the influence of the correlation of the input signal on the algorithm,and then effectively improving the convergence performance of the algorithm.However,the non-Gaussian noise widely existing in the actual environment will destroy the performance of the traditional affine projection algorithm based on thel₂norm optimization criterion.As an important means of robust estimation,Wilcoxon norm can be introduced into the adaptive filtering algorithm to achieve the purpose of suppressing non-Gaussian noise.In this thesis,the non-Gaussian signal processing theory,APA algorithm and robust estimation theory are deeply studied.An improved strategy is proposed for the problem that the traditional APA algorithm is resistant to non-Gaussian noise interference.Specifically,by weighting the weighted Wilcoxon norm instead of the weightedl₂norm as the cost function,the update equation of the Affine Projection Algorithm based on Wilcoxon norm?WAPA?is derived,and the double symbol operator is introduced into the updated equation to effectively suppress Non-Gaussian noise;Secondly,the step function is introduced to improve the adaptability of the algorithm to the environment.Finally,a Variable Step-Size Sign-Sign Wilcoxon Affine Projection Algorithm based on Wilcoxon norm?Variable Sign-Sign WAPA?is formed.The algorithm not only preserves the finiteness of the APA algorithm to the relevant input signal,but also enhances the ability of the algorithm to suppress non-Gaussian interference,and can automatically adjust the step factor to ensure the robustness of the algorithm.A large number of simulation experiments show that compared with some existing APA-like algorithms and robust adaptive filtering algorithms,the proposed algorithm has significant advantages in convergence speed,steady-state offset,and environmental adaptability.