Tackling heavy-tailed noise in distributed estimation: Asymptotic performance and tradeoffs

TL;DR

This paper introduces a robust distributed estimation algorithm for heavy-tailed noise environments, demonstrating convergence, asymptotic normality, and tradeoffs between noise characteristics and network topology.

Contribution

It proposes a novel consensus+innovation estimator with nonlinearities to mitigate heavy-tailed noise effects in distributed systems.

Findings

Almost sure convergence of the estimator

Asymptotic normality established

Tradeoffs between noise levels and network topology analyzed

Abstract

We present an algorithm for distributed estimation of an unknown vector parameter $\boldsymbol{\theta}^\ast \in {\mathbb R}^M$ in the presence of heavy-tailed observation and communication noises. Heavy-tailed noises frequently appear, e.g., in densely deployed Internet of Things (IoT) or wireless sensor network systems. The presented algorithm falls within the class of \emph{consensus+innovation} estimators and combats the effect of the heavy-tailed noises by adding general nonlinearities in the consensus and innovations update parts. We present results on almost sure convergence and asymptotic normality of the estimator. In addition, we provide novel analytical studies that reveal interesting tradeoffs between the system noises and the underlying network topology.