Underwater localization using single beacon measurements: Observability analysis for a double integrator system

This paper addresses the observability analysis for the single beacon localization problem of an Autonomous Underwater Vehicle (AUV) modeled as a double integrator where its input is the acceleration in an inertial reference frame and its output (measurement) is its range to a stationary beacon. The nonlinear map between range and position makes the range-based observability problem inherently nonlinear. The observability analysis here proposed addresses two complementary issues: the local weak observability for the nonlinear system, and the global observability for a linear time varying representation of the system derived through a state augmentation method. The proposed methods for observability analysis are discussed in different case studies (e.g. 2D/3D, absence/presence of current, and presence of additional sensors like a Doppler Velocity Logger or a depth gauge). Two different state observers, i.e., an Extended Kalman Filter for the nonlinear system, and a Kalman Filter for the system with augmented state are designed: their performances are analyzed through numerical simulations while validating the derived observability properties.