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

TL;DR

This paper introduces a distributed algorithm enabling sensor networks to reach globally optimal decisions despite propagation delays and nonreciprocal channels, by analyzing synchronization conditions and bias correction methods.

Contribution

It provides necessary and sufficient conditions for consensus in directed networks with delays and offers a bias correction approach for optimal decision-making.

Findings

Consensus is achieved if and only if the network is quasi-strongly connected.

Propagation delays introduce a bias in the final decision.

A closed-form expression for the consensus allows bias correction 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 dependent on the radio interface and we pose special attention to the effect of the propagation delays 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 achieved for any bounded delay condition if and only if the directed graph is quasi-strongly connected. We also provide a closed form expression for the global consensus, showing that the effect of delays is, in general, to introduce a bias in the final decision. The closed form expression is also useful to modify the consensus mechanism in order to get rid of the bias with minimum extra complexity.