传感器网络中的分布参数估计：非线性观测模型和不完全通信
Distributed Parameter Estimation in Sensor Networks: Nonlinear Observation Models and Imperfect Communication
摘要：
研究了具有非线性观测模型和传感器间通信噪声的传感器网络中分布式静态参数（矢量）估计问题。介绍了\emph{separably estimable}观测模型，将线性集中估计的可观测性条件推广到非线性分布估计。研究了可分离估计模型下的两种分布式估计算法$\mathcal{NU}$（及其线性对应的$\mathcal{LU}$）和$\mathcal{NLU}$。它们的更新规则结合了一个\emph{consensus}步骤（其中每个传感器通过对其邻居的状态进行加权平均来更新状态）和一个\emph{innovation}步骤（其中每个传感器处理其本地电流观测）。这使得\textit{consensus + innovations}类型的三种算法与传统的共识算法有很大的不同。本文证明了一致性（所有传感器几乎肯定达到共识，并收敛到真正的参数值），效率和渐近无偏性。对于$\mathcal{LU}$和$\mathcal{NU}$，它证明了渐近正态性，并提供了收敛速度保证。这三种算法的特点是适当选择衰减权序列。算法$\mathcal{LU}$和$\mathcal{NU}$的随机逼近理论的框架进行了分析，算法$\mathcal{NLU}$表现出混合的时间尺度行为和有偏扰动，它的分析需要一个不同的方法，在本文中开发。
英文摘要：
The paper studies distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and noisy inter-sensor communication. It introduces \emph{separably estimable} observation models that generalize the observability condition in linear centralized estimation to nonlinear distributed estimation. It studies two distributed estimation algorithms in separably estimable models, the $\mathcal{NU}$ (with its linear counterpart $\mathcal{LU}$) and the $\mathcal{NLU}$. Their update rule combines a \emph{consensus} step (where each sensor updates the state by weight averaging it with its neighbors' states) and an \emph{innovation} step (where each sensor processes its local current observation.) This makes the three algorithms of the \textit{consensus + innovations} type, very different from traditional consensus. The paper proves consistency (all sensors reach consensus almost surely and converge to the true parameter value,) efficiency, and asymptotic unbiasedness. For $\mathcal{LU}$ and $\mathcal{NU}$, it proves asymptotic normality and provides convergence rate guarantees. The three algorithms are characterized by appropriately chosen decaying weight sequences. Algorithms $\mathcal{LU}$ and $\mathcal{NU}$ are analyzed in the framework of stochastic approximation theory; algorithm $\mathcal{NLU}$ exhibits mixed time-scale behavior and biased perturbations, and its analysis requires a different approach that is developed in the paper.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
