The train positioning systems using of the ATS (Automatic Train Stop) beacons on tilting train requires ATS beacon position and the on-board database to be updated continuously in accordance with each new ATS beacon location. Under the method proposed, track curvature data calculated by dividing the yaw rate of the carbody by the running speed are held in the on-board database, and the position of the train is detected on the basis of comparison of track curvature data during running. In this case, applying a spatial filter improves detection accuracy and reduces database update frequency. This paper presents the outline of the system and its detection accuracy.