In a system that displays the existing position of an object caught by a camera on a map, the load on a user are reduced, and user-friendliness is increased.The position of an object in a camera image is converted into a position on a map with the use of conversion equations. The existing position of the object based on a result of the conversion is displayed on the map based on results of the conversion. The existence allowed region of the object on the map is set through a designation by the user. The parameters of the conversion equations are determined based on results of the conversion at respective times within a predetermined period of time and the set existence allowed region of the object so that trajectories of the object on the map fall within the existence allowed region.