Algorithms for regional source localization

TL;DR

This paper develops algorithms using the MAP criterion for regional source localization with sensor networks, analyzing their asymptotic correctness and geometric properties, and validating performance through simulations under noise.

Contribution

It introduces algorithms for source localization that work with complete and limited sensor communication, proving asymptotic correctness and exploring geometric detection properties.

Findings

Algorithms asymptotically find the correct region with three or more sensors.

Performance improves as noise decreases.

Certain geometric conditions allow detection with a single sensor.

Abstract

In this paper we use the MAP criterion to locate a region containing a source. Sensors placed in a field of interest divide the latter into smaller regions and take measurements that are transmitted over noisy wireless channels. We propose implementations of our algorithm that consider complete and limited communication among sensors and seek to choose the most likely hypothesis. Each hypothesis corresponds to the event that a given region contains the source. Corrupted measurements are used to calculate conditional posteriors. We prove that the algorithms asymptotically find the correct region almost surely as long as information is available from three or more sensors. We also study the geometric properties of the model that make it possible in some situations to detect the correct region with a unique sensor. Our simulations confirm that the performance of algorithms with complete and limited information ameliorates with decreasing noise.