A system mounted on a train, the system comprising an onboard control device, a train control on-board radio station, a public-radio-network on-board radio station and a train-information management device; the on-board control device being configured to obtain the train position on the basis of the running distance of the train, and to transmit, to a train-presence management device, train position information from the train control on-board radio station connected to the on-board control device via a train control radio base station, a base device, and a train control dedicated network; the train-information management device being configured to obtain the position of the train independently from the on-board control device, and to connect itself to the train control dedicated network and the train-presence management device via the public-radio-network on-board radio station, a public-radio-network base station, a public radio network, and a ground router, and then to transmit train position information to the train-presence management device, the train-information management device comprising: an intra-block position calculator configured to convert information on a kilometrage that indicates a position of the train into information on a block number and an intra-block position of a plurality of blocks into which a route of the train is divided and that are used when a train position is specified by a train radio system; and a communication device configured to communicate the information on the block number and the intra-block position to the train-presence management device on the ground side via the public-radio-network on-board radio station and over the public radio network. the on-board control device being configured to obtain the train position on the basis of the running distance of the train, and to transmit, to a train-presence management device, train position information from the train control on-board radio station connected to the on-board control device via a train control radio base station, a base device, and a train control dedicated network; the train-information management device being configured to obtain the position of the train independently from the on-board control device, and to connect itself to the train control dedicated network and the train-presence management device via the public-radio-network on-board radio station, a public-radio-network base station, a public radio network, and a ground router, and then to transmit train position information to the train-presence management device, the train-information management device comprising: an intra-block position calculator configured to convert information on a kilometrage that indicates a position of the train into information on a block number and an intra-block position of a plurality of blocks into which a route of the train is divided and that are used when a train position is specified by a train radio system; and a communication device configured to communicate the information on the block number and the intra-block position to the train-presence management device on the ground side via the public-radio-network on-board radio station and over the public radio network. an intra-block position calculator configured to convert information on a kilometrage that indicates a position of the train into information on a block number and an intra-block position of a plurality of blocks into which a route of the train is divided and that are used when a train position is specified by a train radio system; and a communication device configured to communicate the information on the block number and the intra-block position to the train-presence management device on the ground side via the public-radio-network on-board radio station and over the public radio network.