Compact Digital Track Maps: Enhancing Train Traveller Information at the Crossing of Accuracy and Availability : A comparative analysis of algorithms for generating compact representations of railway tracks

Abstract: Trains are constrained to the railway tracks they operate on. This can be leveraged for absolute train positioning, where a train’s position can be mapped onto a digital track map (DTM). Extensive research has been dedicated to enhancing the accuracy of DTMs. However, certain practical applications necessitate compact DTMs that can be processed and transferred in real-time, thereby introducing a trade-off between accuracy and memory requirements. This study focuses on data reduction techniques for generating compact DTMs, presenting three distinct methods. Equidistantly sampled Cartesian coordinates are the input to all three methods as they employ different approaches: the linear method simplifies the polygonal chain that connects the coordinates, the spline method utilises smoothing B-splines for interpolation, and the geometric method interpolates the coordinates with a cubic spline and analyse the curvature to identify track segments and describe them geometrically. The performance of these methods is evaluated by their compactness in terms of the number of data fields needed, accuracy in representing track length, and the perpendicular distances between the ground truth track and the generated DTM. The compact DTM generation techniques are applied to three evaluation tracks specifically generated for this study, as well as two existing tracks in the Swedish railway network, each with distinct complexities and characteristics. On the evaluation tracks, the geometrical DTM excels when accuracy is prioritised. As greater perpendicular deviations are tolerated, the smoothed spline DTM method outperforms the other techniques in terms of compactness. The linear DTM method is superior when even greater perpendicular deviations are tolerated. On the existing tracks, the linear DTM method is outperforming the other methods in both accuracy and compactness, presumably because of limitations with the used data set. In conclusion, the choice of technique for generating compact DTMs depends on multiple factors, including the characteristics of the track and the desired level of accuracy.