Research On Adaptive Filtering Algorithms Under Alpha Stable Distributed Environments

The Gaussian distribution model has been widely used in the field of signal processing because it has a comprehensive theoretical framework,simplifies engineering applications,and avoids non-linear problems.However,a large number of studies have shown that there are many impulsive noises and interferences in real-world applications.Examples include radar detection,power communication,atmospheric environment,underwater acoustic waves,seismic surveys,biomedicine,and econometrics.Such non-Gaussian impulsive characteristics can significantly deteriorate the performance of signal processing algorithms developed based on the Gaussian distribution model,even make them fail to work.As a class of non-Gaussian models,thestable distribution model can adequately describe heavy-tailed distributions,and is receiving increasing attention in the field of robust signal processing.The impulsive noise modeled by thestable distribution may severely restrict the applications of traditional adaptive filtering algorithms in signal processing.Examples include system identification,channel equalization,regression,and time-series prediction.To address the problems above,in this thesis,I investigate robust adaptive filtering algorithms under thestable distributed noise environment.The main contributions of this thesis are as follows:1.Since the sign function only extracts the sign of signals,it can effectively suppress impulsive noise,and hence,the l₁-norm criterion has been widely used in robust adaptive filtering algorithms.Because the correntropy induced metric?CIM?can be regarded as an excellent smooth approximation of l₀-norm,it has received more and more attention in sparse adaptive filtering algorithms.In this thesis,based on the combination of l₁-norm criterion and CIM,a robust affine projection proportional adaptive filtering algorithm,named as CI-M-IP-APSA,is proposed for sparse system identification under impulsive noise environments.Besides,a simplified CI-M-IP-APSA with lower computational complexity is derived by using the Taylor expansion of CIM.The abridged version can effectively reduce the computational complexity of the original algorithm while preserving the excellent performance of CI-M-IP-APSA.2.As an extension of the maximum correntropy?MC?criterion,the generalized MC?GMC?criterion has an excellent ability to suppress non-Gaussian noise.The robust adaptive filtering algorithm based on the GMC criterion is receiving strong interests in signal processing.In this thesis,based on GMC,a fixed-point adaptive filtering algorithm is proposed,and is named as FP-GMC.In addition,based on the Banach fixed-point theorem,a sufficient condition guaranteeing the convergence of FP-GMC is derived.Two online versions of FP-GMC are obtained by using the sliding window method and the recursive strategy,respectively.These two algorithms are named as SW-GMC and RGMC.The basic RGMC is derived with some approximations,which can slow down its convergence rate in non-stationary situations.An adaptive convex combination RGMC algorithm,called as AC-RGMC,is proposed to overcome this issue.Moreover,to further improve the convergence rate of AC-RGMC in non-stationary environments,a simple and efficient weight transfer strategy is developed for AC-RGMC.3.As a kind of excellent nonlinear modeling method,kernel adaptive filtering?KAF?algorithm has been widely studied in nonlinear regression and time-series prediction.In this thesis,based on weighted output information and MC,a robust kernel recursive filtering algorithm is proposed and named as KRMC-W.In addition,replacing MC in KRMC-W by GMC,a new KAF,kernel recursive generalized maximum correntropy algorithm?KRGMC?,can be derived.KRGMC realizes better filtering performance than KRMC-W.However,the main drawback of KAF is that the functional representation of classical kernel-based algorithms grows linearly with the number of processed data samples,which results in increased memory and computational complexity.To overcome this issue,in this thesis,a vector projection?VP?method in the reproducing kernel Hibert space?RKHS?is proposed.And,VP is applied to KRMC-W,leading to a sparsified KAF called as projected KRMC-W?PKRMC-W?.The algorithms mentioned above are analyzed and compared in extensive simulation experiments.The simulation results show that the proposed algorithms can achieve excellent filtering accuracy and convergence rate in system identification under impulsive noise environments.