Research On Adaptive Filtering Algorithm Based On Total Least Square Method

Adaptive signal processing has been widely used in systems identification,echo cancellation,active noise control,and beamforming.However,the classic adaptive filtering algorithms such as the least mean square(LMS)algorithm,the recursive least squares(RLS)algorithm,and the affine projection(AP)algorithm are all based on the assumption that input signal being completely accurate,and noise only exists in the output signal.However,in the actual environment,due to the existence of sampling errors,artificial errors,and tool errors,it may sometimes be impractical to have a completely accurate input signal.In this case,the mentioned classic adaptive algorithm will produce biased estimates,and its convergence performance will be seriously deteriorated.Since the beginning of the 20 th century,in order to improve the convergence performance of the classical adaptive filtering algorithm in the presence of both input and output signals with observation errors,several fitting methods have been studied in detail.One of the important solutions is the total least squares(TLS)method.This paper proposes several improved total least squares algorithms for different working environments.First,this article outlines the classic LMS and RLS algorithms and explains how the TLS algorithm works.Then,for the problem that the performance of the TLS algorithm is severely deteriorated in the impact noise environment,this paper proposes a total least mean M-estimate(TLMM)adaptive algorithm that can resist impact noise by combining the M-estimation function.The convergence conditions of the new algorithm are also studied in this paper,and the range of step sizes for stable operation is obtained.In addition,in order to solve the contradiction between fast convergence and steady state error of the algorithm,this paper uses variable step size strategy to further accelerate the convergence speed of the algorithm.Finally,the convergence performance of the new algorithm is verified by simulation experiments.Secondly,for the problem of sparse system identification,this paper uses three different zero-attraction factors to improve the two kinds of robust adaptive algorithms: the maximum total correntropy(MTC)and the proposed total least mean M-estimate(TLMM)in this paper.The convergence performance of the new algorithm in sparse systems is greatly improved,and the advantages of the improved algorithm under sparse systems are confirmed by simulation experiments.Finally,this paper reviews and analyzes existing distributed total least squares algorithms,and proposes a diffusion recursive total least squares algorithm by using diffusion strategies and inverse power iteration in distributed adaptive networks.The mean and mean square performance of the algorithm are studied,and the theoretical value of steady-state mean square deviation is obtained.In addition,this paper uses the dichotomous coordinate descent(DCD)to reduce the computational complexity of the diffusion recursive total least squares algorithm.Finally,computer simulation experiments verify the convergence performance of the algorithm and the accuracy of the theoretical analysis.