Optimal Control-Based Strategy for Sensor Deployment

In sensor network-based detection/surveillance, one of the first challenges to address is the optimal deployment of sensors such that detection requirements are satisfied in a given area. Specifically, we pose the following question: Given a finite number of sensors, what is the best way to deploy these sensors in order to minimize the squared difference between achieved and required detection/miss probabilities? In this paper, we develop a novel optimal control theory based formulation of this sensor deployment problem. Exploiting similarities between the problem at hand and the linear quadratic regulator, an analytical solution is derived and tested. Unlike prior efforts that rely purely on heuristics, the proposed optimal control framework provides a theoretical basis for the resulting solution. As the complexity of the optimal control based solution is high, we develop a low-complexity approximation called Max_Deficiency algorithm. Using simulation results, we show that the proposed algorithms outperform existing methods by using 10% to 30% fewer number of sensors to satisfy detection requirements.