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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 and identically distributed 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 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. [ABSTRACT FROM AUTHOR]

We consider distributed recursive estimation of an unknown vector parameter θ* ∈ RM in the presence of impulsive communication noise. That is, we assume that interagent communication is subject to an additive communication noise that may have heavy-tails or is contaminated with outliers. To combat this effect, within the class of consensus+innovations distributed estimators, we introduce for the first time a nonlinearity in the consensus update. We allow for a general class of nonlinearities that subsumes, e.g., the sign function or componentwise saturation function. For the general nonlinear estimator and a general class of additive communication noises--that may have infinite moments of order higher than one--we establish almost sure convergence to the parameter θ*. We further prove asymptotic normality and evaluate the corresponding asymptotic covariance. These results reveal interesting tradeoffs between the negative effect of "loss of information" due to incorporation of the nonlinearity and the positive effect of communication noise reduction. We also demonstrate and quantify benefits of introducing the nonlinearity in high-noise (low signal-to-noise ratio) and heavy-tail communication noise regimes. [ABSTRACT FROM AUTHOR]