Research On Adaptive Filtering Algorithm Based On Delay Error

In recent decades,adaptive filters have been widely applied to system identification,channel equalization,signal enhancement and prediction.Adaptive filtering algorithms determine the performance of adaptive filters.The researches on adaptive filtering algorithm have become one of the most active research directions in the field of signal processing,therefore it is a consistent pursuit for researchers to find an adaptive filtering algorithm with fast convergence speed,low steady-state error,high convergence precision and low computational complexity.The classical adaptive filtering algorithms are mainly studied based on mean square error criterion which can get the optimal solution under Gaussian noise,but in reality,the noise exhibits non-Gaussian characteristics.The adaptive filtering algorithms based on mean square error criterion degrades significantly under non-Gaussian noise,therefore many adaptive filtering algorithms based on other criterion are proposed to solve the filtering problem under non-Gaussian noise.This thesis mainly conducts the following researches:Firstly,the background,research meaning,development and application of adaptive filtering algorithm are briefly introduced.The non-Gaussian noise is divided into subGaussian noise and super-Gaussian noise,and the filter is algorithmically modeled.The Wiener filter principle,gradient-descent method and the existing adaptive filtering algorithms which are simulated under non-Gaussian noise are introduced.Secondly,the concept of delay error is proposed based on the criterion of existing adaptive filtering algorithms.The delay error is applied to mean square error criterion and the mean square delay error algorithm is proposed.The mean square delay error algorithm is verified by simulation under non-Gaussian noise.The mean error stability and mean square error performance are analyzed.In order to optimize the robustness of mean square delay error algorithm under super-Gaussian noise,a generalized mean square delay error algorithm is proposed and verified by simulation.Then the delay error is applied to the cost function of various existing adaptive filtering algorithms.The proposed algorithms based on delay error and the existing algorithms are compared under non-Gaussian noise to verify the validity of the delay error for the algorithm.Finally,the mean square error have closed-form solution,that is,the Wiener solution.However,closed-form solution similar to the Wiener solution can not obtained for many existing adaptive filtering algorithms.Inspired by fixed-point algorithms,a twostep closed-form solution estimatation method is proposed to estimate the closed-form solution of the existing algorithm.The first step is estimating error based on the Wiener solution,and the second step is to obtain the fixed-point algorithm and substitute the error estimatation of the first step into the fixed-point algorithm to obtain the closed-form solution estimatation of the algorithm.The closed-form solution comparison under nonGaussian noise is carried out to verify the validity of the two-step closed-form solution estimatation method.