Optimal multiple underwater target localization and tracking using two surface acoustic ranging sensors

In many scientific and commercial missions at sea, it is of crucial importance to localize one ore more targets underwater. This objective meets with difficulties due to the unavailability of GPS underwater and the high cost of the equipment classically used for target localization. For these reasons, there has been a surge of interest in the problem of range-based underwater target localization, defined as that of localizing a group of unknown (fixed/moving) targets resorting to surface vehicles (called trackers) equipped with sensors capable of measuring their distances to the targets. In this setup, the surface sensor nodes should be placed according to some optimality criterion aimed at maximizing the information available for target tracking. In addition, the number of sensor nodes should be kept to a minimum in order to avoid the use of a complex and expensive network of vehicles that must be positioned and controlled in a coordinated manner. Motivated by these considerations, in this paper we study the problem of multiple target localization using two trackers and present a constructive method to generate a family of optimal waypoints for the trackers. The use of two surface sensors is motivated by the fact that a single surface sensor does not provide enough positioning accuracy for multiple target localization simultaneously. For two and three targets, we provide a family of analytical solutions for optimal sensor node placements. Further, the proposed solutions can be extended to more than three targets under some well-defined constraints on the target configuration. The optimal sensor positions are derived by maximizing the determinants of appropriately defined Fisher information matrices associated with each of the targets. It is shown that the optimal sensor configuration thus obtained lends itself to an interesting and useful geometrical interpretation. Simulation examples illustrate the results derived.