General Mixed-Norm-Based Diffusion Adaptive Filtering Algorithm for Distributed Estimation Over Network

A diffusion general mixed-norm (DGMN) algorithm for distributed estimation over network (DEoN) is proposed. The standard diffusion adaptive filtering algorithm with a single error norm exhibits slow convergence speed and poor misadjustments under specific environments. To overcome this drawback, the DGMN is developed by using a convex mixture of p and textit q norms as the cost function to improve the convergence rate and substantially reduce the steady-state coefficient errors. Especially, it can be used to solve the DEoN under Gaussian and non-Gaussian noise environments, including measurement noises with long-tail and short-tail distributions, and impulsive noises with α-stable distributions. In addition, the analysis of the mean and mean square convergence is performed. Simulation results show the advantages of the proposed algorithm with mixing error norms for DEoN.