Observability analysis for single range localization

This paper presents an observability analysis for the single range localization problem of a second order kinematics model of an Autonomous Underwater Vehicle (AUV) possibly subject to a constant current. In particular, the AUV is modeled as a double integrator having as input the acceleration in an inertial reference frame and as output its distance to a stationary beacon. Since the range is a non linear function of the position, the single range observability problem is inherently nonlinear. Thus, to eventually design an observer, we assess observability conditions addressing two complementary issues: local weak observability of the nonlinear system and global observability referring to a linear time varying representation of the system derived through a `state augmentation´ method. The proposed methods for observability analysis is discussed in different case studies (e.g. 2D/3D, absence/presence of current) and the performances of the related state observers are illustrated throughout numerical simulations.