1. A wakefulness level estimation apparatus, comprising: an estimation portion that estimates a level of wakefulness of a subject person based on one of a wakefulness level estimation function, of which a variable is a wakefulness level correlation value of the subject person, and a difference between the wakefulness level correlation value of the subject person and a reference value of the wakefulness level correlation value; a stimulation detection portion that detects whether an awakening stimulation is externally applied to the subject person; and a correction portion that, when the stimulation detection portion detects that the awakening stimulation is applied to the subject person, performs a correction of one of the reference value of the wakefulness level correlation value and the wakefulness level estimation function, which is used for estimating the level of wakefulness of the subject person.