Distributed Affine Projection Algorithm Based On Wilcoxon Norm

The distributed adaptive filtering algorithm is a kind of adaptive signal processing capability through each node in the distributed network.Through the adaptive signal processing ability of each node in the distributed network,the parameters of interest can effectively estimated.It has been widely used in wireless sensor networks,target detection,and other fields.Among them,distributed affine projection algorithm(DAPA)is one of the important research branches.This kind of algorithms can still converge rapidly when the input signal is highly correlated.The disadvantage of DAPA is that it has weak ability to suppress non Gaussian noise with pulse characteristics,and the contradiction between convergence speed and steady-state error caused by fixed step size is also large.For this reason,this article has carried on the effective improvement through the thorough research to the DAPA algorithm.Firstly,the Wilcoxon norm in the theory of robust statistics is studied deeply.According to its core of scoring function,the sign function is used as a new scoring function,forming a new expression of Wilcoxon norm,replacing the L2 norm in DAPA algorithm as a new cost function,deriving a new updating equation,and realizing the suppression of non Gaussian noise in the iterative process.Secondly,in order to further improve the convergence speed of the algorithm,this thesis normalizes the residual part of the renewal equation through the sign function;then,considering the limitation of fixed step size,through the derivation of variable step function,the control of error signal to step is realized by iterative method,that is to select a smaller step size in the initial stage to improve the convergence speed.Thus,a new algorithm named variable step size sign distributed Wilcoxon affine projection is formed.Finally,through reasonable assumptions,this thesis makes a detailed theoretical analysis on the convergence performance and mean square sense of the proposed VSS-DWAPA algorithm,and compares the complexity of the proposed VSS-DWAPA algorithm with the existing diffusion adaptive filtering algorithm.Theoretical analysis and simulation results show that the proposed VSS-DWAPA algorithm has better convergence performance,steady-state performance and tracking performance than some existing diffusion adaptive filtering algorithms.