Observability Analysis of 3D AUV Trimming Trajectories in the Presence of Ocean Currents Using Single Beacon Navigation

This paper addresses the observability properties of a 3D autonomous underwater vehicle (AUV) model in the presence of ocean currents, under the assumption that the vehicle can only measure its distance to a fixed transponder using an acoustic ranging device. In the set-up adopted, the AUV may undergo a wide range of maneuvers that are usually described as trimming trajectories. The latter are of paramount importance in flight dynamics and can be completely parametrized by three variables: i) linear body speed v, ii) flight-path angle γ, and iii) yaw rate ψ̇. We assume that v > 0, γ, and ψ̇ are constant but otherwise arbitrary (within the constraints of the vehicle capabilities) and examine the observability of the resulting system with the output (measured) variable described above. We adopt weaker definitions of observability that are akin to those proposed by Herman and Krener (Hermann and Krener, 1977) but reflect the fact that we consider specific kinds of maneuvers in 3D. We show that in the presence of known constant ocean currents the 3D kinematic model of the AUV that corresponds to trimming trajectories with nonzero flight path angle and yaw rate is observable. In case the latter conditions fail, we give a complete characterization of the sets of states that are indistinguishable from a given initial state. We further show that in the case of unknown constant ocean currents the model is locally weakly observable for yaw rate different from zero but fails to be locally weakly observable for zero yaw rate. In both the cases we give a complete characterization of the sets of states that are indistinguishable from a given initial state.