A collision determination apparatus includes an acquisition section, a setting section, a target object information detection section, a target object path prediction section, an own vehicle path prediction section, and a collision determination section. The acquisition section acquires detection information based on a reflected wave from a search device. The setting section sets filter characteristics of a filtering process used when the detection information is filtered. The target object information detection section detects a position of a target object using the filtered detection information. The target object path prediction section predicts a path of the target object based on changes in the position of the target object detected by the target object information detection section. The own vehicle path prediction section predicts a path of an own vehicle. The collision determination section makes a determination of a collision between the own vehicle and the target object. The setting section estimates a detectable time or a detectable distance in which the position of the target object can be detected in the path of the target object based on the position of the target object and the traveling condition of the own vehicle and sets the filter characteristics in accordance with the detectable time or the detectable distance that has been estimated.