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

We present an algorithm for distributed estimation of an unknown vector parameter θ<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∗</sup> ∈ ℝ<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sup> 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 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.