Research On Recursive Adaptive Filtering Algorithm Based On Information Entropy In Non-Gaussian Noise Environment

As we all know,the structure design of filter has always been an important research hotspot in the field of signal processing.Among them,adaptive filter is widely used in echo cancellation,system identification and other engineering fields,because it does not require a priori knowledge of input information,and can have strong adaptability to unknown environment.However,due to the increasingly complex environment of the system,the traditional adaptive filtering algorithm also has some new problems: such as the influence of non-Gaussian noise commonly existing in practical application,and the time-varying noise displayed in the transmission channel of some communication systems.Therefore,in order to improve the filtering characteristics of adaptive filter and broaden its adaptive range,it is necessary to construct a more robust filtering algorithm.To solve this problem,based on information theory,this thesis combines information entropy criterion with recursive least squares algorithm,and puts forward some robust adaptive filtering algorithms that can deal with non-Gaussian noise in the environment.The key research contents of this thesis are as follows:Facing the problem that the traditional filtering processing calculation based on secondorder statistical characteristics can only produce optimal performance in Gaussian environment,this thesis presents a recursive minimum error entropy algorithm based on the minimum error entropy criterion and a recursive mixture q Gaussian minimum error entropy algorithm based on the mixture q Gaussian generalized minimum error entropy criterion.The former uses the minimum error entropy criterion to replace the minimum mean square error as the adaptive criterion.Combined with the recursive least square algorithm,a recursive minimum error entropy algorithm with recursive form is deduced and proposed,and the convergence analysis is made.The simulation results show that the algorithm will show better filtering characteristics than the least mean square error algorithm in the non-Gaussian noise environment.The latter uses the q Gaussian density function to replace the ordinary Gaussian function.According to the idea of mixture entropy,a recursive mixture q Gaussian minimum error entropy algorithm with recursive form is also deduced and proposed.The convergence analysis also proves the stability of the algorithm,and the algorithm simulation and physical verification experiments show that the algorithm can obtain better performance under the interference of non-Gaussian noise.According to the problem that the traditional adaptive filtering algorithm using the minimum error entropy criterion can not deal with the time-varying noise and hybrid noise in the environment under the condition of fixed kernel size,an adaptive kernel size recursive minimum error entropy algorithm based on Kullback-Leibler divergence is proposed.The algorithm not only ensures the robustness of the original recursive minimum error entropy algorithm,but also greatly expand the application range of the algorithm.Relevant simulation experiments also confirm the effectiveness of the algorithm.This thesis,based on the entropy criterion derived from information theory and combined with recursive least squares algorithm,proposes recursive minimum error entropy algorithm,recursive mixture q Gaussian minimum error entropy algorithm and adaptive kernel size recursive minimum error entropy algorithm.The algorithm simulation and physical verification results show that the proposed methods have good robustness under the conditions of non-Gaussian noise and time-varying noise.