Nonlinear consensus+innovations under correlated heavy-tailed noises: Mean square convergence rate and asymptotics

TL;DR

This paper develops a distributed estimator for consensus+innovations in networks with heavy-tailed, correlated noise, proving its convergence, asymptotic normality, and sublinear MSE rate, applicable in dense IoT scenarios.

Contribution

It introduces a nonlinear consensus+innovations estimator that handles correlated, infinite-variance noise, with theoretical guarantees and practical validation.

Findings

Estimator achieves almost sure convergence.

Estimator exhibits asymptotic normality.

Sublinear mean squared error convergence rate.

Abstract

We consider distributed recursive estimation of consensus+innovations type in the presence of heavy-tailed sensing and communication noises. We allow that the sensing and communication noises are mutually correlated while independent identically distributed (i.i.d.) in time, and that they may both have infinite moments of order higher than one (hence having infinite variances). Such heavy-tailed, infinite-variance noises are highly relevant in practice and are shown to occur, e.g., in dense internet of things (IoT) deployments. We develop a consensus+innovations distributed estimator that employs a general nonlinearity in both consensus and innovations steps to combat the noise. We establish the estimator's almost sure convergence, asymptotic normality, and mean squared error (MSE) convergence. Moreover, we establish and explicitly quantify for the estimator a sublinear MSE convergence rate. We then quantify through analytical examples the effects of the nonlinearity choices and the noises correlation on the system performance. Finally, numerical examples corroborate our findings and verify that the proposed method works in the simultaneous heavy-tail communication-sensing noise setting, while existing methods fail under the same noise conditions.