Devices, methods, and programs identify a leading candidate point by calculating a cost for candidate points on a road, and match a vehicle position to the identified leading candidate point. The devices, methods, and programs acquire an estimated vehicle position based on dead reckoning navigation, acquire a GPS position of the vehicle, and set the candidate points for the vehicle position on nearby roads. The devices, methods, and programs calculate for each candidate point a normal cost of the candidate point with respect to the estimated position and a correction cost that corresponds to a value L1 (the value L1 being found by subtracting a width W of a road having the candidate point from a distance d between the GPS position and the candidate point), and identify the leading candidate point based on a total cost of the normal cost and the correction cost for each candidate point.