Surface sensor networks for Underwater Vehicle positioning with bearings-only measurements

There is increasing interest in the use of Autonomous Underwater Vehicles (AUVs) to substantially improve the means available for ocean exploration and exploitation. A key element in the operation of certain 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 set of autonomous surface vehicles carries a network of acoustic units that measure the elevation and azimuth angles between the target 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 angle-related information available for underwater target positioning. It is assumed that the angle measurements are corrupted by white Gaussian noise, the variance of which is distance-dependent. Using the Cramer-Rao lower bound inequality, the trace of the inverse of the Fisher Information matrix (also called the Cramer-Rao Bound matrix) for the problem at hand is used to determine the sensor configuration that yields the minimum possible covariance of any unbiased target estimator. 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 measurement noise and the target depth. Simulation examples illustrate the key results derived.