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.

翻译：我们考虑在重尾感知与通信噪声环境下，共识+创新类型的分布式递归估计问题。允许感知噪声与通信噪声存在相互相关性，但时间上独立同分布（i.i.d.），且两者可能均具有高于一阶的无穷矩（即具有无穷方差）。这类重尾、无穷方差噪声在实际应用中高度相关，例如在密集物联网（IoT）部署场景中已被证实存在。本文提出一种分布式共识+创新估计器，通过在共识步与创新步中引入通用非线性函数来抑制噪声影响。我们证明了该估计器的几乎必然收敛性、渐近正态性以及均方误差（MSE）收敛性。进一步，我们明确量化了估计器亚线性MSE收敛速率。通过解析示例，我们分析了非线性函数选择与噪声相关性对系统性能的影响。最后，数值实验验证了理论发现，并表明所提方法在通信-感知噪声同时呈现重尾特性的场景下有效，而现有方法在相同噪声条件下失效。