1. A navigation device that identifies a leading candidate point by calculating a cost for candidate points that are set on a road, and matches a vehicle position to the identified leading candidate point, the navigation device comprising: a controller that: acquires an estimated position of a vehicle based on dead reckoning navigation; acquires a GPS position of the vehicle based on GPS; sets the candidate points for the vehicle position on roads in the vicinity of the estimated position; calculates for each candidate point a normal cost of the candidate point with respect to the estimated position; calculates for each candidate point a correction cost that corresponds to a value L 1 , the value L 1 being found by subtracting a width W of the road from a distance d between the GPS position and the candidate point; and identifies the leading candidate point based on a total cost of the normal cost and the correction cost for each candidate point.