Optimal Placement of a Moving Sensor Network for Track Coverage

The problem of optimizing the configuration of a moving sensor network deployed to detect moving targets is formulated using optimal control theory. A cost function of the Lagrange type is obtained through a computational geometry approach to measure the space of line transversals for k of the n sensors by formulating an integral function of the sensors locations, where k is the number of required detections. Then, the cost function is optimized subject to the sensors dynamics expressed by a state-space model. The method is demonstrated for a surveillance application that involves sonobuoys deployed on the ocean´s surface to detect underwater targets within a specified region of interest and over a desired period of time. It is shown that a state-space model of the sonobuoy dynamics can be obtained from the steady-state solution of Stokes´s problem and a current vector field obtained from oceanographic models or CODAR measurements. In this paper, a solution is presented for the case of non-maneuverable sensors that can be placed anywhere within the region of interest and move subject to the ocean´s current. The methodology can also be extended to maneuverable sensors with on-board control capabilities, such as, thrusters, or to acoustic sensors installed on underwater vehicles. The numerical simulations show that by taking into account the drift dynamics the cumulative coverage over a period of seven days can be increased by up to 85%.