Research On Robust Distributed Affine Projection Adaptive Estimation Algorithms

Adaptive network is composed of a group of nodes with adaptive and learning ability.These nodes interact at the local level and propagate information in the whole network to estimate and infer tasks in a distributed way.Since the adaptive network of the diffusion strategy is scalable and robust to node and link failures,the distributed algorithm based on diffusion network has been extensively studied by researchers.In recent years,domestic and foreign scholars have carried out a lot of research and proposed corresponding distributed algorithms for a series of problems such as colored signal input,impulsive noise interference,variable step-size strategy,multitask network.When the input signal of the network node is colored signal,the distributed AP algorithm shows faster convergence speed as compared to the traditional distributed LMS algorithm.However,when the diffusion adaptive network node is disturbed by impulsive noise,the distributed AP algorithm has poor convergence performance.Therefore,this paper mainly studies the robustness and convergence of the distributed AP algorithm under impulsive noise interference.The main research work is summarized as follows:1)In order to improve the estimation performance of distributed diffusion AP algorithm(DAPA)under impulsive noise interference.In this paper,the Gaussian kernel function is introduced into the local cost function of diffusion network,and then the diffusion AP algorithm based on maximum correntropy criterion(MCC)algorithm,namely DAPMCC algorithm,is derived by using the stochastic gradient method.Secondly,the mean performance,mean square performance,steady-state performance and computational complexity of DAPMCC algorithm are analyzed.Finally,simulation results verify the convergence performance and robustness of the proposed DAPMCC algorithm under impulsive noise interference,and accurately verify the theoretical steady-state MSD.2)In order to derive another robust DAPA,this paper defines a robust local cost function based on the diffusion network and M-estimate function,and then solves the minimization of distributed estimation problem,thus a diffusion AP based on M-estimate(DAPM)algorithm is proposed.Secondly,in order to verify the convergence performance of the proposed algorithm,this paper analyzes the mean convergence of the proposed DAPM algorithm,and obtains the convergence range of the learning step-size.Aiming at the limitation of the fixed step-size of DAPM algorithm,a variable step-size DAPM algorithm is proposed to improve the convergence performance of the algorithm.Finally,the simulation verified that the DAPM algorithm not only has strong anti-interference ability,but also has a faster convergence speed and lower steady-state error.3)In multitask distributed estimation,in order to improve the estimation performance of distributed multitask diffusion AP algorithm(MD-APA)under impulsive noise interference,two robust MD-APAs are proposed by using MCC and M-estimate function respectively.i.The Gaussian kernel function is introduced into the local cost function of the multitask network,and derive the MCC-based multitask diffusion AP(MD-APMCC)algorithm through the stochastic gradient method.Then,the method of adaptive kernel width is adopted to further improve the distributed estimation performance of the MD-APMCC algorithm.In addition,the convergence of the proposed MD-APMCC algorithm is analyzed,mainly including mean analysis,mean square analysis and steady-state analysis,so as to the convergence range of the learning step-size and the theoretical steady-state MSD are obtained.ii.By using the M-estimate function in multitask network,this paper proposes another robust MD-APA,namely the MD-APM algorithm.Then,the convergence of the proposed MD-APM algorithm is analyzed,including mean analysis,mean square analysis and steady-state analysis,so that the convergence range of the learning step-size and the theoretical steady-state MSD are obtained.Simulation experiment results show that the two robust MD-APAs proposed in this paper not only have strong anti-interference ability,but also have fast convergence speed and small steady-state error,and the theoretical steady-state MSD is accurately verified by simulation.4)The application of distributed robust DAPA in acoustic echo cancellation under impulsive noise is studied.This paper mainly introduces the generation of echo,the basic principle of acoustic echo canceller(AEC)and the basic principle of distributed echo cancellation.In the application of acoustic echo cancellation,the simulation experiment results show that the proposed robust DAPA not only has strong anti-interference ability,but also has fast convergence speed and good echo cancellation effect.