非线性耦合传感器网络的分散极大似然估计
Decentralized Maximum Likelihood Estimation for Sensor Networks Composed of Nonlinearly Coupled Dynamical Systems
摘要：
在本文中，我们提出了一个分散的传感器网络计划能够达到全局最优的最大似然（ML）估计，通过自同步的非线性耦合动力系统。网络的每个节点由一个传感器和一个以本地测量值初始化的一阶动力系统组成。邻近节点相互交互，交换它们的状态值，并且最终估计与每个动态系统的状态导数相关联。我们推导出耦合机制的条件，保证如果网络观察到一个共同的现象，每个节点收敛到全局最优ML估计。证明了当耦合强度超过给定阈值时，同步状态是全局渐进稳定的。作用于一个单一的参数，耦合强度，我们展示了如何，在非线性耦合的情况下，网络行为可以从一个全球共识系统切换到一个空间集群系统。最后，我们展示了网络拓扑结构对网络可扩展性的影响，并通过仿真结果验证了我们的理论研究结果。
英文摘要：
In this paper we propose a decentralized sensor network scheme capable to reach a globally optimum maximum likelihood (ML) estimate through self-synchronization of nonlinearly coupled dynamical systems. Each node of the network is composed of a sensor and a first-order dynamical system initialized with the local measurements. Nearby nodes interact with each other exchanging their state value and the final estimate is associated to the state derivative of each dynamical system. We derive the conditions on the coupling mechanism guaranteeing that, if the network observes one common phenomenon, each node converges to the globally optimal ML estimate. We prove that the synchronized state is globally asymptotically stable if the coupling strength exceeds a given threshold. Acting on a single parameter, the coupling strength, we show how, in the case of nonlinear coupling, the network behavior can switch from a global consensus system to a spatial clustering system. Finally, we show the effect of the network topology on the scalability properties of the network and we validate our theoretical findings with simulation results.
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