Observability analysis for single range localization

Abstract

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.

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

“…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, and their performances are illustrated throughout numerical simulations and compared referring to the derived observability properties. This work extends our preliminary paper Arrichiello et al (2015) by providing a more in-depth and formalized analysis of the system observability in the two different cases, and an extended number of case studies and comparison via numerical simulations.…”

SRIBO: An Efficient and Resilient Single-Range and Inertia Based Odometry for Flying Robots

“…In accumulated studies, observability analyses have been either carried out with a classical linearization procedure [8], [10], [11], or derived from modern control theories [9], [18], [26]. Such research commonly concludes that the observability can only be guaranteed when the accumulated excitation is linearly independent on different axes [4].…”

“…However, only using the IMU and UWB range measurements at a single time instance is insufficient to determine the position of a robot, and a sliding windows filtering (SWF) associated with observability analyses are necessary [8]. Such analyses are originated in the field of autonomous underwater vehicles [9], [10], and the results are seamlessly applied for flying robots [4], [6]. Typically, the vehicles or robots are modeled as double-integral systems, and corresponding observability matrices are evaluated either linearly or nonlinearly [9], [11].…”

“…Such analyses are originated in the field of autonomous underwater vehicles [9], [10], and the results are seamlessly applied for flying robots [4], [6]. Typically, the vehicles or robots are modeled as double-integral systems, and corresponding observability matrices are evaluated either linearly or nonlinearly [9], [11]. These works commonly conclude that the observability is guaranteed only when accumulating actuation in arbitrary two axes is not constant or linearly dependent on each other [6], [9].…”

Observability Conditions and Sensing Quality for Unicycle Systems with Constant External Forcing

“…This method also has the advantage of avoiding calculation of a state transition matrix and has been applied to studies of both linear and nonlinear observability [12]. The empirical observability Gramian has been used to determine optimal control, specifically with respect to a single ranging beacon [13], and to determine trajectories to prevent degenerate measurements [14].…”