Range-Based Underwater Vehicle Localization in the Presence of Unknown Ocean Currents: Theory and Experiments

This paper addresses the problem of range-based autonomous underwater vehicle (AUV) localization in the presence of unknown ocean currents. In the setup adopted, the AUV is equipped with an attitude and heading reference system, a depth sensor, and an acoustic device that provides measurements of its distance to a set of stationary beacons. We consider the situation where the number of active beacons is not known in advance and may vary with time. The objective is to simultaneously localize the AUV and beacons, that is, to find their positions underwater. We start by deriving conditions under which it is possible to reconstruct the initial condition of the system under study. We consider the design model where the states evolve continuously with time, but the range measurements are only available at discrete instants of time, possibly in a nonuniform manner. For trimming maneuvers that correspond to AUV trajectories with constant linear and angular velocities expressed in the body frame, we show that if either the position of one of the beacons or the initial position of the AUV is known, then even without depth information the system is weakly observable (i.e., the set of states that are indistinguishable from a given initial configuration contains only a set of finite isolated points). If depth measurements are also available, then the system is observable even in the presence of unknown constant ocean currents. Equipped with these results, we then propose a novel observer for simultaneous AUV and beacon localization. The mathematical setup exploited borrows from minimum-energy estimation theory applied to continuous-time processes with discrete measurements, projection filters, and multiple-model estimation techniques. Convergence analysis of the resulting observer system yields conditions under which the estimation errors converge to a small neighborhood of the origin (whose size depends on the magnitude of the process and measurement noise). The results of field experiments with a robotic marine vehicle show the efficacy of the simultaneous AUV/multiple beacon localization system proposed.