Performance Analysis of the Robust Diffusion Normalized Least Mean ${p}$ -Power Algorithm

The diffusion least-mean p-power algorithm is presented for distributed estimation in impulsive noise environments, which aims to minimize the p-norm of the error. However, it suffers from slow convergence rate. In this brief, we propose a diffusion normalized least-mean p-power algorithm (DNLMP), motivated by the normalized-based algorithms. To further improve the performance of the DNLMP algorithm, a robust DNLMP (RDNLMP) algorithm is developed for distributed estimation. The RDNLMP algorithm considers the error signal in normalization factor, and therefore can diminish the significance of outliers under impulsive noise environments. Moreover, the steady-state analysis of the RDNLMP algorithm is provided. Both performance analysis and numerical simulations are given to verify the proposed algorithms.