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Navigation technology is considered that enables an underwater vehicle to compute its trajectory in real-time by utilizing range measurements from a single known location. This concept is especially attractive for small underwater vehicles where more traditional navigation technology is prohibitive due to volume constraints. By assessing local observability of the underwater vehicle and available measurements about potential vehicle trajectories, we explicitly characterize those trajectories that can be asymptotically estimated. It is shown that all but a small class of trajectories can be estimated.