Navigation of a mobile robot is conditioned on the knowledge of its pose. In observer-based localisation configurations its initial pose may not be knowable in advance, leading to the need of its estimation. Solutions to the problem of global localisation are either robust against noise and environment arbitrariness but require motion and time, which may (need to) be economised on, or require minimal estimation time but assume environmental structure, may be sensitive to noise, and demand preprocessing and tuning. This article proposes a method that retains the strengths and avoids the weaknesses of the two approaches. The method leverages properties of the Cumulative Absolute Error per Ray (CAER) metric with respect to the errors of pose hypotheses of a 2D LIDAR sensor, and utilises scan--to--map-scan matching for fine(r) pose estimations. A large number of tests, in real and simulated conditions, involving disparate environments and sensor properties, illustrate that the proposed method outperforms state-of-the-art methods of both classes of solutions in terms of pose discovery rate and execution time. The source code is available for download.