  Globally rising demand for transportation by rail is pushing existing
infrastructure to its capacity limits, necessitating the development of
accurate, robust, and high-frequency positioning systems to ensure safe and
efficient train operation. As individual sensor modalities cannot satisfy the
strict requirements of robustness and safety, a combination thereof is
required. We propose a path-constrained sensor fusion framework to integrate
various modalities while leveraging the unique characteristics of the railway
network. To reflect the constrained motion of rail vehicles along their tracks,
the state is modeled in 1D along the track geometry. We further leverage the
limited action space of a train by employing a novel multi-hypothesis tracking
to account for multiple possible trajectories a vehicle can take through the
railway network. We demonstrate the reliability and accuracy of our fusion
framework on multiple tram datasets recorded in the city of Zurich, utilizing
Visual-Inertial Odometry for local motion estimation and a standard GNSS for
global localization. We evaluate our results using ground truth localizations
recorded with a RTK-GNSS, and compare our method to standard baselines. A Root
Mean Square Error of 4.78 m and a track selectivity score of up to 94.9 % have
been achieved.
