Observability analysis of 2D single beacon navigation in the presence of constant currents for two classes of maneuvers

We analyze the observability properties of an underwater vehicle (moving in 2D) performing single beacon navigation for two specific classes of maneuvers, whereby the vehicle measures its distance to a fixed transponder located at a known position using an acoustic ranging device. We show that in the presence of known ocean currents, the system is found to be globally observable for constant relative course and constant (nonzero) relative course rate inputs in the sense of Herman and Krener. On the other hand, with unknown ocean currents the system fails to be locally weakly observable with constant relative course but we characterize the set of indistinguishable states from a given initial position and ocean current configuration. Interestingly, observability can be achieved with constant (nonzero) relative course rate in the presence of unknown, constant ocean currents.