Optimal Sensor Deployment for Value-Fusion Based Detection

In many wireless sensor networks based detection and surveillance applications, the goal is to deploy sensors in an an area of interest such that certain false alarm and detection requirements are satisfied. Additionally, data fusion methods can be used to combine information from multiple sensors in order to enhance the ability of the network to meet the detection/false alarm requirements. In this paper, we pose the following question: Given a finite number of sensors that have the ability to cooperate via data fusion, what is the best way to deploy the sensors in order to meet the detection requirements in a mean squared sense, while maintaining a specified false alarm probability. Unlike prior efforts that rely on heuristics to address the deployment question, we present an optimal control theory based sensor deployment approach. Here, we model the system as a linear quadratic regulator with the deployment locations serving as control parameters. We quantify the effect of placing a sensor (and its ability to cooperate with other sensors) on the overall detection probability in order to develop an analytical solution. Using simulation results, we illustrate that our proposed approach is far superior in performance relative to existing methods in terms of minimum number of sensors needed to satisfy detection and false alarm requirements.