Optimal Sensor Distribution for Maximum Exposure in A Region with Obstacles

Abstract — Sensor networks have been envisioned to enhance the ability of human beings in observing the environment and understanding the world. A potential application of a sensor network is to detect the presence or absence of a target in a region of interest. Many heuristics have been proposed in literature for placing sensors to achieve better coverage in the monitored region. However, none of them guarantee an optimal sensor deployment especially when there are obstacles in the region. Unlike the prior work, this paper focuses on the problem of determining the optimal sensor distribution in a region with or without obstacles. The detection performance is characterized using a metric called “exposure”, which is defined as the least probability of detecting a target over all possible target locations subject to a fixed false alarm probability. A linear programming based approach is proposed to find the optimal sensor distribution by maximizing the exposure in a given region with or without obstacles. The optimal sensor distribution can also be used as weights of sensor measurements taken at different locations for decision-making. I