Optimal Sensor Placement for Acoustic Range-Based Underwater Robot Positioning

This paper addresses the problem of optimal sensor placement for acoustic range-based underwater target positioning. In particular, we focus on the experimental set-up whereby target positioning is performed by measuring the ranges between the underwater target and a number of surface units equipped with acoustic ranging devices and GPS. With the objective of affording the reader a concise overview of the main theoretical challenges involved, this paper starts with a survey of previous work done in the area, including that of the authors. By casting the problem at hand in the form of a classical estimation problem we describe and solve the equivalent mathematical problem of maximizing the determinant of a conveniently defined Fisher Information Matrix (FIM). The latter is related to the Cramér-Rao Bound, which equals the smallest possible position estimation error variance that can possibly be achieved with any unbiased estimator. To further clarify the presentation, the details of Monte Carlo simulations in 2D and 3D with a selected target positioning algorithm are included to confirm the theoretical results numerically.