Observability metric for the relative localization of AUVs based on range and depth measurements: Theory and experiments

This paper addresses the problem of observability of the relative motion of two AUVs equipped with velocity and depth sensors, and inter-vehicle ranging devices. We start by exploiting nonlinear observability concepts to analyze, using observability rank conditions, some types of relative AUV motions. Because rank conditions only provide binary information regarding observability, we then derive a specific observability index (metric) and study its dependence on the types of relative motions executed by the vehicles. In particular, it is shown that the degradation of observability depends on the range and angle between the relative velocity and position vectors. The problem addressed bears affinity with that of single beacon localization. For this reason, the results derived are validated experimentally in a equivalent, single beacon navigation scenario.