Optimal sensor placement for underwater positioning with uncertainty in the target location

Worldwide, there has been increasing interest in the use of Autonomous Underwater Vehicles (AUVs) to drastically change the means available for ocean exploration and exploitation. Representative missions include marine habitat mapping, pipeline inspection, and archaeological surveying. Central to the operation of some classes of AUVs is the availability of good underwater positioning systems to localize one or more vehicles simultaneously based on information received on-board a support ship or a set of autonomous surface vehicles. In an interesting operational scenario the AUV is equipped with an acoustic pinger and the set of surface vehicles carry a network of acoustic receivers that measure the ranges between the emitter and each of the receivers. Motivated by these considerations, in this paper we address the problem of determining the optimal geometric configuration of an acoustic sensor network at the ocean surface that will maximize the range-related information available for underwater target positioning. It is assumed that the range measurements are corrupted by white Gaussian noise, the variance of which is distance-dependent. Furthermore, we also assume that an initial estimate of the target position is available, albeit with uncertainty. The Fisher Information Matrix and the maximization of its determinant are used to determine the sensor configuration that yields the most accurate “expected” positioning of the target, the position of which is expressed by a probabilistic distribution. It is shown that the optimal configuration lends itself to an interesting geometrical interpretation and that the “spreading” of the sensor configuration depends explicitly on the intensity of the range measurement noise, the probabilistic distribution that defines the target position, and the target depth. Simulation examples illustrate the key results derived.