The present invention addresses presence-on-track detection problems which can arise when performing positional correction using correction elements, in a wireless train-control system for managing trains present on track by transmitting, to an aboveground facility, train positions detected on-board. In an on-board device (20), a train position is measured by counting the rotational frequency of a tachometer generator (12), and an estimated range occupied by the train, said estimated range being where the train is likely to be present, is ascertained on the basis of the train position, and transmitted to an aboveground device (30). Furthermore, when an installation point of a correction element (50) is passed, the train position is corrected on the basis of a communication result with the correction element (50). In cases when the correction of the train position by the correction element (50) is correction in the rearward direction, the estimated range occupied by the train is ascertained on the basis of a train position immediately prior to correction, and transmitted, until an updated train position reaches the train position immediately prior to correction, and when the updated train position reaches the train position immediately prior to correction, the estimated range occupied by the train is thereafter ascertained on the basis of the updated train position, and transmitted.
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