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

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.

Synchronization in complex networks of phase oscillators: A survey

“…Since alternating current (AC) circuits are naturally modeled by equations similar to (1), some electric applications are found in structure-preserving (Bergen and Hill, 1981;Sauer and Pai, 1998) and networkreduced power system models (Chiang et al, 1995;Dörfler and Bullo, 2012b), and droop-controlled inverters in microgrids (Simpson-Porco et al, 2013). Algorithmic applications of the coupled oscillator model (1) include limit-cycle estimation through particle filters (Tilton et al, 2012), clock synchronization in decentralized computing networks (Simeone et al, 2008;Baldoni et al, 2010;, central pattern generators for robotic locomotion (Aoi and Tsuchiya, 2005;Righetti and Ijspeert, 2006;Ijspeert, 2008), decentralized maximum likelihood estimation (Barbarossa and Scutari, 2007), and human-robot interaction (Mizumoto et al, 2010). Further envisioned applications of oscillator networks obeying equations similar to (1) include generating music (Huepe et al, 2012), signal processing (Shim et al, 2007), pattern recognition (Vassilieva et al, 2011), and neuro-computing through micromechanical (Hoppensteadt and Izhikevich, 2001) or laser (Hoppensteadt and Izhikevich, 2000;Wang and Ghosh, 2007) oscillators.…”

Parameter Estimation Over Noisy Communication Channels in Distributed Sensor Networks

“…As stated above, any linear combination of the initial sensor values can be asymptotically achieved in a distributed form via collaborative exchanges of local information, although in a time-varying setting the number of available exchanges will determine the level of alignment of the quantities (58) and (59). As expected, if the number of exchanges without channel noise goes to infinity, the performance of the network approaches that of a centralized observer [72].…”

“…On the other hand, it is also possible to use filtering to fight noise (see e.g. [59]) although this causes strict consensus not be achievable. Figure 15 shows the evolution of the values in the four node network shown in Figs.…”

Vulnerability Analysis of Satellite-based Synchronized Smart Grids Monitoring Systems

“…The synchronized functions are executed by equipping each PMU by a dynamical system (oscillator) initialized by local information. The oscillators of nearby PMU are mutually coupled by proper local coupling strategies derived from the mathematics of populations of mutually coupled oscillators [38]. This bio-inspired paradigm allows all the PMU to reach consensus on general functions of the variables sensed by all the PMUs.…”