Decentralized Maximum Likelihood Estimation for Sensor Networks Composed of Nonlinearly Coupled Dynamical Systems

TL;DR

This paper introduces a decentralized sensor network approach where nodes, modeled as nonlinear dynamical systems, self-synchronize to achieve a globally optimal maximum likelihood estimate of a shared phenomenon, with proven stability and scalability.

Contribution

It presents a novel decentralized scheme using nonlinear coupling for sensor networks to reach ML estimates through self-synchronization, with stability analysis and simulation validation.

Findings

Global asymptotic stability when coupling exceeds threshold

Network behavior can switch from consensus to clustering

Topology affects scalability and performance

Abstract

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.