Research On Adaptive Filtering Algorithm Based On Maximum Versoria Criterion In The Presence Of Non-Gaussian Noise

Adaptive filters are widely used in engineering fields such as system identification,channel equalization,and speech echo cancellation.Adaptive filtering algorithm plays a core role in the adaptive filter design.The research of adaptive filtering algorithm in the presence of non-Gaussian noise is one of the most active topics in the field of adaptive signal processing.In the presence of non-Gaussian noise,the design of adaptive filtering algorithms with fast convergence speed,little steady-state error,low computational complexity and strong robustness,has been one of the goals of both academia and industry.Therefore,this thesis focuses on the Maximum Versoria Criterion(MVC)algorithm and proposes several robust algorithms to overcome the shortcomings of existing linear and nonlinear adaptive filtering algorithms in non-Gaussian noise environments.The main contribution includes the following aspects:(1)Nonlinear adaptive filtering algorithms: 1)A new kernel adaptive filtering algorithm,Kernel Maximum Versoria Criterion(KMVC),in which the kernel method is introduced into the MVC algorithm,is presented to overcome the shortcomings of the Generalized Kernel Maximum Correntropy(GKMC)algorithm,such as large exponential computation and steady-state error.Moreover,the convergence performance is analyzed for the proposed KMVC algorithm.Simulation results of nonlinear frequency doubling show that the KMVC algorithm has strong robustness against various non-Gaussian noises by choosing different shape parameters,and has lower exponential computation and steady-state error than the GKMC algorithm.2)In addition,the online quantization method is introduced into the KMVC algorithm,and accordingly the quantized KMVC(QKMVC)algorithm is proposed to address the issue that the network size of the KMVC algorithm increases linearly with the number of input data.Simulation results show that the QKMVC algorithm can effectively restrain the growth of network structure without significant loss of the algorithm performance.(2)Linear adaptive filtering algorithms: 1)In order to improve the tracking performance of Convex Combination Maximum Correction Criterion(CMCC)algorithm in non-stationary environments,the multi-convex combination strategy is introduced into the Maximum Correntropy Criterion(MCC)algorithm.Correspondingly,a Multi-convex Combination Maximum Correntropy Criterion(MCMCC)algorithm is proposed.Simulation results of linear system identification show that compared with the CMCC algorithm,the MCMCC algorithm has stronger tracking ability in non-stationary environments and can track weight change at different speeds.2)In addition,considering the disadvantages of MCMCC algorithm with large exponential computation and steady-state error,the multi-convex combination strategy is introduced into the MVC algorithm,and a multi-convex combination MVC(MCMVC)algorithm is presented.Simulation results show that compared with MCMCC algorithm,the MCMVC algorithm has lower exponential computation and steady-state error while guaranteeing tracking performance.