Detection Capabilities of Randomly-Deployed Sensor Fields

Distributed sensor fields have recently gained popularity as a means for detecting intruders moving through a protected area of the ocean. We characterize the detection capabilities of a network of randomly-deployed sensors with varying sensing capabilities. We develop a framework for analytically approximating the probability that such a sensor field detects a constant course target moving through the region as a function of the number of sensors deployed and the statistical properties that govern the sensing range. Analytical and empirical results indicate that, when the total sensing area is fixed, a set of smaller distributed sensors can achieve significantly improved detection performance relative to a single large sensor. We also study the relationship between coverage of a region of interest and likelihood of detecting a constant course intruder moving through that region. We derive expressions for the average number of sensors required to achieve a prescribed likelihood of detection and level of coverage and conclude that detection and coverage are fundamentally different characterizations of the capabilities of a sensor field. In fact, the number of sensors required to achieve a particular detection level may be several orders of magnitude smaller than that required to achieve the same level of coverage.