Optimal Motion Planning for Range-Based Marine Vehicle Positioning in the Presence of Unknown Currents

We address the problem of range-based marine vehicle positioning in the presence of unknown but constant ocean currents. The goal is to estimate the position of one or more vehicles from a sequence of range measurements to fixed or moving acoustic beacons with known locations. In contrast to most range-based positioning algorithms, we address the case where the currents are unknown and seek to estimate them explicitly as well. This increases the complexity of the problem at hand and raises interesting observability issues. In particular, the vehicles must undergo sufficiently exciting maneuvers so as to maximize the range-based information available for joint current/multiple vehicle position estimation. The main contribution of the paper is the computation of vehicle trajectories for range-based vehicle positioning system in the presence of constant, unknown currents by maximizing the determinant of a suitable Fisher information matrix (FIM), subject to collision avoidance and maneuvering constraints. A numerical solution is proposed for the general set-up of multiple vehicles and beacons. Analytical solutions are obtained for the case of one vehicle and one static beacon. The efficacy of the strategies proposed for vehicle trajectory optimization is shown by numerical simulations.