Distributed Decision Through Self-Synchronizing Sensor Networks in the Presence of Propagation Delays and Asymmetric Channels

TL;DR

This paper introduces a distributed algorithm enabling sensor networks to reach globally optimal decisions despite propagation delays and asymmetric channels, using self-synchronization and graph-based modeling.

Contribution

It provides necessary and sufficient conditions for consensus, including exponential convergence criteria, and proposes a double-step mechanism to eliminate bias without channel estimation.

Findings

Consensus achieved with exponential speed under bounded delays if the network is quasi-strongly connected.

Delay effects introduce bias in the final decision, which can be mitigated.

The proposed double-step mechanism provides unbiased estimates with minimal complexity.

Abstract

In this paper we propose and analyze a distributed algorithm for achieving globally optimal decisions, either estimation or detection, through a self-synchronization mechanism among linearly coupled integrators initialized with local measurements. We model the interaction among the nodes as a directed graph with weights (possibly) dependent on the radio channels and we pose special attention to the effect of the propagation delay occurring in the exchange of data among sensors, as a function of the network geometry. We derive necessary and sufficient conditions for the proposed system to reach a consensus on globally optimal decision statistics. One of the major results proved in this work is that a consensus is reached with exponential convergence speed for any bounded delay condition if and only if the directed graph is quasi-strongly connected. We provide a closed form expression for the global consensus, showing that the effect of delays is, in general, the introduction of a bias in the final decision. Finally, we exploit our closed form expression to devise a double-step consensus mechanism able to provide an unbiased estimate with minimum extra complexity, without the need to know or estimate the channel parameters.