Single-beacon, range-based AUV localization systems work on the principle that a vehicle may find its position by maneuvering appropriately and acquiring measurements of its successive distances (ranges) to a stationary beacon deployed at a known location. This motivates the study of optimal trajectories to improve the accuracy of the vehicle's position estimate while respecting mission related criteria. In this work, the performance index used to compare different trajectories is the determinant of a properly defined Fisher Information Matrix (FIM). Assuming that heading measurements are available, the problem is studied in 2D, and a class of analytical and numerical solutions are derived. An approach to deal with the case where the initial position of the vehicle is known to lie in a region of uncertainty is also presented. Considering that depth measurements can be obtained, a 3D navigation algorithm consisting of an optimal trajectory planner and a minimum-energy estimator is proposed and its performance assessed via simulation of a practical scientific scenario.
Pedro, M., Moreno-Salinas, D., Crasta, N., & Pascoal, A. (2015). Underwater single-beacon localization: Optimal trajectory planning and minimum-energy estimation. IFAC-PapersOnLine, 28(2), 155–160. https://doi.org/10.1016/j.ifacol.2015.06.025