A Novel Family of Robust Incremental Adaptive Algorithms for Distributed Estimation Based on Bregman Divergence

Distributed estimation in the wireless sensor network (WSN) faces severe challenges when outliers are present in the desired data. Conventional estimation techniques such as the block-least-mean-square (BLMS) algorithm have been designed to perform well in the presence of Gaussian noise. However, the performance of these conventional techniques degrades significantly in the presence of outliers in the desired data. In this letter, a novel family of incremental distributed estimation techniques for WSN based on the Bregman divergence measure is proposed, which are named as incremental Kullback–Leibler-divergence-based BLMS algorithm, incremental Itakura–Saito-divergence-based BLMS algorithm, incremental Amari-alpha-divergence-based BLMS algorithm, and incremental beta-divergence-based BLMS algorithm. The local stability analysis shows the upper bound of the step size for the tractable analysis. Simulation results show that the proposed Bregman-divergence-based incremental algorithms perform better compared to the incremental BLMS algorithm in terms of the mean-square deviation.