A kinematic positioning system configured to determine position coordinates of moving bodies by receiving positioning signals from positioning satellites, comprises an on-vehicle device configured to calculate the position coordinates of one of the moving bodies based on carrier wave phases of the positioning signals received from the positioning satellites, and a ground management device configured to transmit correction data used to calculate the position coordinates to the on-vehicle device in response to a request from the on-vehicle device. The on-vehicle device executes a first processing sequence of performing precise point positioning computation by acquiring precise orbit data of each positioning satellite from any of the positioning satellite and the ground management device, and calculating the position coordinates, and a second processing sequence of sending the ground management device a pseudorange concerning a positioning satellite selected from the positioning satellites, a carrier wave, and the position coordinates of the one moving body, performing the precise point positioning computation by acquiring the correction data from the ground management device, and calculating the position coordinates. The on-vehicle device selects the position coordinates having a smaller data error out of the position coordinates calculated in the first processing sequence and the position coordinates calculated in the second processing sequence as the position coordinates of the one moving body.