论文标题
相关的重尾噪声下的非线性共识+创新：均方根收敛速率和渐近性
Nonlinear consensus+innovations under correlated heavy-tailed noises: Mean square convergence rate and asymptotics
论文作者
论文摘要
我们考虑在存在重尾感应和通信噪声的情况下，共识+创新类型的分布式递归估计。我们允许传感和通信噪声相互关联，而独立分布相同（i.i.d。），并且它们可能都具有高于一个高于一个的无限级时矩（因此具有无限差异）。这种重型，无限变化的噪声在实践中非常相关，例如在密集的物联网（IoT）部署中发生。我们开发了共识+创新分布式估计器，该估计值在共识和创新步骤中采用一般的非线性来打击噪声。我们建立了估计量的几乎确定的收敛，渐近正态性和平方误差（MSE）收敛。此外，我们为估计值建立并显式量化了sublinear MSE收敛速率。然后，我们通过分析示例量化非线性选择的影响以及噪声相关性对系统性能的影响。最后，数值示例证实了我们的发现，并验证了所提出的方法是否在同时进行重尾通信传感噪声设置中起作用，而现有方法在相同的噪声条件下失败。
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.
