1. A position estimation apparatus comprising one or more processors configured to implement: a position estimation unit configured to estimate a position of a moving object driven on an arbitrary lane according to an image frame captured by a stereo camera provided in the moving object; a posture information acquisition unit configured to obtain first posture information of the moving object from the estimated position and second posture information of the moving object at a point of time of the stereo camera capturing the image frame; a position correction unit configured to calculate a first probability distribution for a position of the moving object by using the first posture information and the second posture information, configured to correct the estimated position based on the first probability distribution, configured to calculate a composite probability distribution using the first probability distribution and a second probability distribution which shows probabilities of the moving object being positioned in lane sections of the arbitrary lane from a lane probability distribution chart in which a lane width of the arbitrary lane is divided into a plurality of sections, and configured to re-correct the corrected estimated position based on the composite probability distribution.