Although Global Navigation Satellite Systems (GNSS) have been widely used in aviation, vehicle and marine navigation, and have also found non-safety railway applications, they still cannot be used in a standalone mode for safety critical railway applications. This is because GNSS suffers from the line-of-sight problem, namely, GNSS might be unavailable when trains run through the areas with low satellite visibility. A potential solution is to integrate satellite navigation measurements with other sensors such as a track database, INS or an augmentation system. This book is concerned with the evaluation of the potential role of a track database for this purpose. A rigorous mathematical model for the integration of GNSS with the track database is developed. The key feature of this model is its ability to model errors in both GNSS measurements and the track database to achieve realistic performance statistics for the combined system. Knowledge of the position of the railway lines turns positioning, in principle, into a one dimensional problem.