Observability Analysis for AUV Range-only Localization and Mapping Measures of Unobservability and Experimental Results

We investigate the observability problem of the Simultaneous Localization and Mapping (SLAM) process of an Autonomous Underwater Vehicle (AUV) equipped with inertial sensors, a depth sensor, and an acoustic ranging device that provides relative range measurements to stationary beacons. For trimming trajectories (that is, when the motion of the AUV is in steady-state with constant linear and angular velocities expressed in the body-frame), we provide conditions under which it is possible to reconstruct the initial state of the resulting SLAM system (and in particular the position of the AUV). We show that the unobservable subspace UO restricted to the assumption that the position of one of the beacons or the initial position of the AUV is known, contains only the zero vector with exception of a distinct case where the UO is composed by a finite set of isolated points. Another problem that we also address in this paper is to understand (independently of the observer scheme) how difficult it is to accurately estimate the state of the system from the pair input/output measured signals. To this end, we compute explicitly the unobservability index and the estimation condition number that provide measures of the degree of unobservability. Simulation and experimental results with the Medusa robotic vehicle are presented and discussed.