The use of GNSS in the railway sector has been postulated on the notion of a Virtual Balise (VB). The VB-based positioning system works by setting a VB point on the railway track and determining the passage of the VB point using the position solution from the GNSS receiver. Although augmentation systems such as SBAS or GBAS are able to satisfy the integrity requirements of the aviation standards down to the 10-7 level, it is difficult to satisfy the high integrity requirements of the railway sector because firstly the railway users located on the ground are affected by the ground environment such as terrain, buildings and tunnels and secondly because the stringency of the railway sector requirements extends below the 10-9 level. This paper proposes a method to detect faults in the GNSS solution due to satellite failure or local effects. Firstly, requirements for the monitoring performance are carefully derived accounting for the specificities of GNSS, namely that the possibility of consecutive VB faults cannot be discounted. The second contribution of the paper is the proposed detection using both odometry and track geometry of the onboard system. This enables to monitor all three-dimensional solution error so that higher sensitivity for the fault detection can be achieved. Simulations have been performed with both single and dual (GPS, GALILEO) solutions. It has been found that the combinations of metrics are able to achieve very small missed detection probabilities for mean failure rates from 5.0m/s down to 0.03m/s for most dual constellation geometries. The detection performance of the odometer implementation varied according to the heading of the train. On the other hand, when odometry and track geometry are used together, all the three-directional monitors can obtain stable results regardless of the heading.