UWB Indoor Global Localisation for Nonholonomic Robots with Unknown Offset Compensation

The problem addressed in this paper is the localisation of a mobile robot using a combination of on-board sensors and Ultra-Wideband (UWB) beacons. Specifically, we consider a scenario in which a mobile robot travels across an area infrastructured with a small number of UWB anchors. The presence of obstacles in the environment introduces an offset in the measurements of the distance between the robot and the UWB anchors causing a degradation in the localisation performance. By using a discrete-time formulation of the system dynamics, we show that, under mild condition, the trajectories can be observed and the offset can be estimated in a finite number of steps. Besides being interesting in its on right, the global observability results offer a clear pathway towards the definition of a new generation of estimation algorithms.