In this article a real-time method is proposed that reduces the pose estimate error for robots capable of motion on the 2D plane. The solution that the method provides addresses the recent introduction of low-cost panoramic range scanners (2D LIDAR range sensors whose field of view is 360∘), whose use in robot localisation induces elevated pose uncertainty due to their significantly increased measurement noise compared to prior, costlier sensors. The solution employs scan-to-map-scan matching and, in contrast to prior art, its novelty lies in that matching is performed without establishing correspondences between the two input scans; rather, the matching problem is solved in closed form by virtue of exploiting the periodicity of the input signals. The correspondence-free nature of the solution allows for dispensing with the calculation of correspondences between the input range scans, which (a) becomes non-trivial and more error-prone with increasing input noise, and (b) involves the setting of parameters whose output effects are sensitive to the parameters’ correct configuration, and which does not hold universal or predictive validity. The efficacy of the proposed method is illustrated through extensive experiments on public domain data and over various measurement noise levels exhibited by the aforementioned class of sensors. Through these experiments we show that the proposed method exhibits (a) lower pose errors compared to state of the art methods, and (b) more robust pose error reduction rates compared to those which are capable of real-time execution. The source code of its implementation is available for download.