Observability analysis of 3D AUV trimming trajectories in the presence of ocean currents using range and depth measurements

We start with the single transponder case. For range measurements only, we show that in the absence of ocean currents the 3D kinematic model of an AUV undergoing trimming trajectories with nonzero flight-path angle and yaw rate is observable. In the case of non-zero but known ocean currents, identical results apply subject to the condition that the flight-path angle satisfies a current-related constraint. However, if the current is non-zero and unknown, the model is only weakly observable. The situation changes completely when both range and depth measurements are available. In this case, under the assumption that the yaw rate is different from zero, observability is obtained even when the flight-path angle is zero (vehicle moving in a horizontal plane) and there are non-zero unknown currents. These obvious advantages are lost if yaw rate is equal to zero, for in this case the model is only weakly observable. In all situations where the model is weakly observable we give a complete characterization of the sets of states that are indistinguishable from a given initial state. Finally, we show that the extended model that is obtained by considering multiple (at least two) transponders is observable in all situations if the yaw rate is different from zero.