A robust methodology for mobile robot localisation, or relocation, is described, making use of airborne sonar. A linear array of three sequentially fired ultrasonic transducers is proposed for performing a full scan of the environment, whose map is assumed to be a priori given. A geometric approach to relocation is adopted: the segmentation algorithm is based on an extended Kalman filter for estimating the geometrical parameters of different targets and related uncertainty. The features characterised by minimal geometrical uncertainty are used by the matching algorithm to perform a least squares search for the displacement and rotation that best take the sensor-based map into coincidence with the a priori reference map. A few heuristics are provided to enhance data robustness. An effective pruning strategy finally leads to solutions of the relocation problem with sub-centimeter positional accuracies and orientational accuracies within one degree.>