Robust Multi-Task Diffusion Least Mean M-Estimate Adaptive Algorithm and Its Performance Analysis

Abstract

Multi-task diffusion LMS (MDLMS) is an useful algorithm to infer multiple related parameter vectors concurrently through the cooperation of nodes among clusters. However, it must be pointed out that its optimal estimation can only be realized under Gaussian noise. In practical applications, this ideal noise environment is not easy to meet. For example, there will be some impulsive noise interference. At this time, it is urgent to propose a robust multi-task algorithm against impulsive noise. The modified Huber (MH) function is considered in the new robust multi-task algorithm (i.e., multi-task diffusion least mean M-estimate (MDLMM)) proposed in this brief since its simple structure and outstanding effect of restraining impulsive interference. After that, we analyze the mean and mean square performance of the MDLMM algorithm, and give the stability conditions (in the sense of mean and mean square) and the closed-form expressions of theoretical transient and steady-state network mean square derivation (NMSD) under some assumptions. Numerical simulations verify the accuracy of the theoretical analysis results and the superiority of MDLMM over other robust multi-task algorithms.