Diffusion Minimum Generalized Rank Norm Over Distributed Adaptive Networks: Formulation and Performance Analysis

Abstract

Least squared error cost function based conventional diffusion strategies are not robust against outliers in both the desired and input data. In most of the practical scenarios, both the input and desired data contain impulsive noise along with Gaussian noise. The presence of outliers in the measured (input/desired) data can be treated as the impulsive noise. A novel diffusion generalized rank norm algorithm is developed in this article, which is robust against outliers in both input and desired data. The proposed method does not rely on any prior assumption regarding the distribution of the data. The performance analysis of the proposed algorithm is analyzed using asymptotic linearity relation between null and alternative hypotheses of generalized rank norm gradient. Simulation based experiments are carried out to validate the robustness of the proposed algorithm. Another diffusion high breakdown estimator algorithm is proposed, which attains ${\text{50}{\%}}$ breakdown in both input and desired data space.