A position estimation apparatus which estimates a position of a mobile object in a space includes: a measurement unit which measures, for each of points in a local space in proximity to the mobile object, a position and an attribute; an extractor which extracts position information and attribute information from a result of the measuring by the measurement unit, for each measurement voxel in a group of measurement voxels arrayed three-dimensionally in association with the local space; a map manager which manages position information and attribute information, for each map voxel in a group of map voxels arrayed three-dimensionally in association with the space represented by a map; and a position estimator which estimates a position of the mobile object, based on a position information approximation degree and an attribute information approximation degree.