1. A travel path estimation apparatus comprising: an acquisition section for acquiring a captured image of a periphery of a vehicle; an extraction section for extracting, from the captured image acquired by the acquisition section, characteristic points indicating vehicle lanes; a setting section for, based on a distribution of the characteristic points extracted by the extraction section, setting system noise expressing variation of travel path parameters when estimating travel path parameters related to a position or an angle of the vehicle itself with respect to a travel path for travel by the vehicle itself and related to a shape or a size of the travel path; and an estimation section for estimating the travel path parameters by probability signal processing using a discrete time signal based on the characteristic points extracted by the extraction section, a previous estimation result of the travel path parameters, and the system noise set by the setting section.