Robust Algorithms against Impulsive Noise for Distributed Estimation over Adaptive Networks

Abstract

In this dissertation, we study the problem of distributed estimation over adaptive networks, in which numerous sensor nodes over a network cooperate to estimate a common parameter from noisy measurements. In particular, our main concern is to develop robust distributed estimation algorithm that is insensitive to impulsive noise. To achieve fast and accurate estimation performance in real-world applications where impulsive noise presents, two robust algorithms are proposed.

Before presenting the proposed algorithms, we provide backgrounds that are helpful for understanding the proposed algorithms. First, the diffusion LMS algorithm which is one of the most popular distributed estimation algorithms is introduced. Next, the conventional robust algorithms in the literature are introduced. Several main approaches to obtain robustness are described to provide a brief survey of the conventional robust algorithms.

Next, we introduce a new robust algorithm for distributed estimation problem over adaptive networks. Motivated by the fact that each node can access to multiple spatial data, we propose to discard the data contaminated by impulsive noise and to process only the clean data. Under the assumption that impulsive noise is successfully detected, we propose a cost function that considers only the uncontaminated data. The derived algorithm is the diffusion LMS algorithm that has variable weighting coefficients depending on impulsive noise detection, which leads both to robustness and to good estimation performance. A method to detect impulsive noise is also presented. Simulation results show that the proposed algorithm has good estimation performance in an environment that is subject to impulsive noise, and outperforms the conventional robust algorithms.

Lastly, we introduce another new robust distributed estimation algorithm. We propose a cost function that is based on a switched-norm with variable threshold parameter for distributed estimation algorithm. The derived algorithm is the diffusion LMS algorithm that has a variable adaptation coefficient, which provides both robustness and outstanding estimation performance. Furthermore, we present performance analysis of the proposed algorithm, in which a useful approximation is also introduced. In simulations, the proposed algorithm achieves outstanding estimation performance even in the presence of impulsive noise, and our theoretical model is highly accurate.