This paper addresses the problem of optimal acoustic sensor placement for underwater target localization in 3-D using range measurements only. By adopting an estimation theoretical framework, the optimal geometric sensor formation that will yield the best achievable performance in terms of target positioning accuracy is computed by maximizing the determinant of an appropriately defined Fisher information matrix (FIM). For mathematical tractability, it is assumed that the measurements of the ranges between the target and a set of acoustic sensors are corrupted with white Gaussian noise. For the sake of completeness, an explicit analytical result for a generic n-sensor network is first obtained for the case when there is no uncertainty in the prior knowledge about the target position. The result is then extended to the practical case where the target is known to lie inside a region of uncertainty. The optimal sensor configuration thus obtained lends itself to an interesting and useful geometrical interpretation. In addition, the “spreading” of the configuration is shown to depend on the number of range measurements, target depth, and the probability distribution function that characterizes the prior knowledge about the target position. Results are also obtained for the problem of optimal sensor placement with constraints, namely, by considering that the sensors can be either located at the sea surface or distributed between the surface and the seabed. The connection between 2-D and 3-D scenarios is clarified. 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.

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.