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：摘要：本文考虑在存在重尾感知与通信噪声时，共识+创新类型的分布式递归估计问题。我们允许感知噪声与通信噪声相互相关，且时间上独立同分布，并可能具有高于一阶的无限矩（即无限方差）。此类重尾、无限方差噪声在实际中高度相关，例如在密集物联网部署中已被证实存在。我们提出一种共识+创新分布式估计器，在共识步与创新步中均采用一般非线性函数以抑制噪声。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收敛性。此外，我们明确量化了该估计器的次线性均方误差收敛速率。通过解析示例，我们进一步量化了非线性函数选择与噪声相关性对系统性能的影响。最后，数值实验验证了我们的结论，并表明所提方法在同时存在重尾通信与感知噪声的场景下有效，而现有方法在相同噪声条件下失效。