Research On Distributed Robust Least Mean Square Algorithms Over Adapative Networks

Distributed adaptive filtering is an extension of adaptive filtering algorithms on distributed network,whose purpose is to solve the distributed estimation problem with cooperating nodes distributed in a geographic region.Adaptive filtering algorithms are the core of distributed adaptive filtering.The diffusion least mean square(DLMS)algorithm based on the mean square error(MSE)criterion is widely used due to its simple structure and good estimation performance.The traditional DLMS algorithms rely on the assumption that the background noise obeys the Gaussian distribution.However,DLMS algorithms will have severely deteriorated performances or even be divergent when impulsive noise occurs in the network.The thesis studies the robust DLMS algorithm under impulsive noise environment.The topic selection has research significance and application value.Firstly,based on two typical impulsive noise models,Alpha stable distribution and Bernoulli-Gaussian distribution,we analyze the impact of impulsive noise on DLMS algorithm.Simulation results illustrate that even a small amount of impulsive noise will cause serious performance degradation of DLMS algorithms.In order to solve the problem that the performance of the DLMS algorithm is seriously degraded under the impulsive noise environment,we propose a dynamic-threshold-Huberbased diffusion least mean square(DTH-DLMS)algorithm.The proposed algorithm adopts the Huber criterion to design the cost function combining both the estimation performance of the MSE criterion and the robustness of the mean absolute error(MAE)criterion.Simultaneously,for the problem of threshold selection in Huber criterion,a dynamic threshold setting method based on output error retention is proposed.The nodes detect the occurrence of impulsive noise by the threshold,so that the algorithm can dynamically distinguish between normal data and outliers that contaminated by impulsive noise during the iteration process,and deal with these two kinds of data respectively in corresponding update manner.Simulation results show that the proposed DTH-DLMS algorithm effectively combines the superiority of the MSE and the MAE criteria,and achieves good estimation performance while combating impulsive noise interference effectively.To avoid the trouble caused by the threshold selection in the Huber criterion,we propose a Log-Cosh-based variable step-size diffusion least mean square(LCVS-DLMS)algorithm.The proposed algorithm uses the Log-Cosh function as a relative cost measure to design the cost function,and performs hyperbolic tangent constraints on the output errors in the adaptive step to achieve robustness to the impulsive noise.Simultaneously,autocorrelation processing is performed on the gradient parameter to further eliminate the influence of impulsive noise.In addition,based on the autocorrelation of gradient parameter,a variable step-size setting method under impulsive noise environment is proposed to improve the contradiction between the convergence rate and steady-state error with a fixed step-size.Simulation results show that the proposed LCVS-DLMS algorithm has fast convergence and small steady-state error under both Gaussian noise and impulsive noise environments.Two distributed adaptive filtering algorithms proposed in this thesis improve the robustness of the DLMS algorithm against impulsive noise interference effectively,and have a good application prospect in complex noise environment where both Gaussian noise and impulsive noise exist.