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In this paper, we address the problem of determining the optimal geometric configuration of an acoustic sensor network that will maximize the angle-related information available for underwater target positioning. In the set-up adopted, a set of autonomous vehicles carries a network of acoustic units that measure the elevation and azimuth angles between a target and each of the receivers on board the vehicles. It is assumed that the angle measurements are corrupted by white Gaussian noise, the variance of which is distance-dependent. Using tools from estimation theory, the problem is converted into that of minimizing, by proper choice of the sensor positions, the trace of the inverse of the Fisher Information Matrix (also called the Cramer-Rao Bound matrix) to determine the sensor configuration that yields the minimum possible covariance of any unbiased target estimator. It is shown that the optimal configuration of the sensors depends explicitly on the intensity of the measurement noise, the constraints imposed on the sensor configuration, the target depth and the probabilistic distribution that defines the prior uncertainty in the target position. Simulation examples illustrate the key results derived.

The problem of determining the optimal geometric configuration of a sensor network that will maximize the range-related information available for multiple target positioning is of key importance in a multitude of application scenarios. In this paper, a set of sensors that measures the distances between the targets and each of the receivers is considered, assuming that the range measurements are corrupted by white Gaussian noise, in order to search for the formation that maximizes the accuracy of the target estimates. Using tools from estimation theory and convex optimization, the problem is converted into that of maximizing, by proper choice of the sensor positions, a convex combination of the logarithms of the determinants of the Fisher Information Matrices corresponding to each of the targets in order to determine the sensor configuration that yields the minimum possible covariance of any unbiased target estimator. Analytical and numerical solutions are well defined and it is shown that the optimal configuration of the sensors depends explicitly on the constraints imposed on the sensor configuration, the target positions, and the probabilistic distributions that define the prior uncertainty in each of the target positions. Simulation examples illustrate the key results derived.

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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.