Research On Efficient And Robust Adaptive Filtering Theory And Algorithms In Complex Environments

After half a century of development,adaptive filtering theory has become an important part of modern signal processing,and is widely used in communication systems,audio processing,noise control,power systems,biomedical engineering and other fields.However,Adaptive filtering algorithms still face many challenges for increasingly complex application environments.Most of the conventional adaptive algorithms are derived based on the minimum mean square error criterion or the least squares method.Although these algorithms have good performance in Gaussian environments,they are highly susceptible to divergence in non-Gaussian noise environments,especially when disturbed by impulse noise,they are very prone to divergence,which prevents the adaptive filter from working properly.In addition,most of the research on adaptive algorithm mainly focuses on linear finite impact response(FIR)filters,which suffer from problems such as weak nonlinear processing capability.In order to make up for these shortcomings to improve the efficiency of adaptive algorithms,this dissertation investigates the complex adaptive filter based on widely linear model,the application of fractional order calculus in adaptive filtering algorithms,and the distributed adaptive filtering algorithm based on graph signals,which are summarized as follows:Firstly,this dissertation investigates the complex adaptive filter based on widely linear model,and summarizes the current existing complex adaptive filtering algorithms.A series of explorations have been carried out to address the problem that existing complex adaptive algorithms face performance degradation or even fail to converge in non-Gaussian environments,especially when disturbed by impulsive noise.First,inspired by the M-estimate adaptive filtering methods in the real domain,we propose a class of robust widely linear complex least mean M-estimate adaptive filtering algorithms and further derive their normalized versions.Then,the performance of the proposed algorithm is theoretically analyzed to prove the effectiveness of the algorithm.Finally,simulation experiments are conducted to demonstrate that the proposed algorithm has obvious advantages in non-Gaussian environments.Then,we continue the research on complex adaptive filters for widely linear model,focusing on enhancing the robustness of the algorithm in non-Gaussian environments.In this paper,the hyperbolic secant function is introduced into the widely linear adaptive filter for the first time,and a robust widely linear complex adaptive filtering algorithm is successfully developed.In addition,this paper provides a comprehensive analysis of the performance of the proposed algorithm,including mean value convergence,mean square transient behavior and mean square steady-state behavior.Finally,simulation experiments demonstrate that the proposed algorithm has obvious advantages in non-Gaussian environments.Meanwhile,the accuracy of the theoretical performance analysis is also verified.In addition,adaptive filtering algorithms based on fractional order calculus are intensively studied.Several classical fractional-order adaptive filtering algorithms are reviewed.Then,the fractional-order adaptive filtering algorithm proposed by Sayed et al.is analyzed in terms of mean-square transient behavior and mean-square steady-state error,which improves the inadequacy of its theoretical performance analysis in the existing literature,and provides a more comprehensive exposition of the performance characteristics of the algorithm.a more robust fractional-order M-estimate adaptive filtering algorithm is derived in this paper,and and simulation experiments are conducted in system identification and acoustic echo cancellation.Finally,distributed adaptive filters based on graph signals are investigated in this dissertation.In order to enhance the nonlinear processing capability of FIR graph filters,a novel functional link graph adaptive filtering model is designed by combining a low complexity function link network,which has a stronger nonlinear processing capability compared with the original graph adaptive filter.In addition,based on the proposed graph adaptive filtering model,a new graph diffusion least mean square algorithm is further derived and its convergence performance is analyzed.Finally,the effectiveness of the proposed model and algorithm is verified by several typical nonlinear unknown systems.In summary,with the goal of improving the robustness and efficiency of classical adaptive filtering algorithms,this dissertation investigates the complex adaptive filter based on a widely linear model,the fractional-order adaptive filtering algorithm,and the distributed adaptive filter based on graph signals,respectively.The results improve the robustness of the adaptive filtering algorithms for processing non-Gaussian signals and enhance the ability to process nonlinear systems,and also expand the application system of adaptive filtering algorithms.