Optimal Sensor Placement for Acoustic Underwater Target Positioning With Range-Only Measurements

Abstract

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.