Underwater navigation in the presence of unknown currents based on range measurements from a single location

An underwater navigation algorithm is considered that enables an underwater vehicle to compute its trajectory in the presence of unknown currents by utilizing range measurements from a single known location. There exists a small set of trajectories for which the algorithm does not converge. By assessing local observability about potential vehicle trajectories, we characterize those trajectories that cannot be asymptotically estimated. The navigation algorithm is illustrated using computer simulation and a hardware experiment.