1. A monitoring device for monitoring facility elements in a building, comprising: a three-dimensional measurement unit for measuring a three-dimensional shape in the periphery of the monitoring device; a self-localization estimation unit for estimating the self-localization of the monitoring device by collating the measured three-dimensional shape with a map for localization including the shapes and positions of structural objects inside the building excluding those (the shapes and positions) of the facility elements; a peripheral facility element extraction unit for extracting facility elements in the periphery of the estimated self-localization from a facility element collation map including the shapes and positions of the facility elements inside the building; a facility element candidate extraction unit for extracting the shape and position of a facility element candidate from the measured three-dimensional shape; a similarity evaluation unit for calculating a similarity between the shape and position of each of the facility elements in the periphery of the self-localization extracted from the facility element collation map and the shape and position of the facility element candidate extracted from the measured three-dimensional shape on the basis of the error distribution of the shape and position of the facility element in the periphery of the self-localization and the error distribution of the shape and position of the facility element candidate extracted from the measured three-dimensional shape; and a facility element identification unit for identifying which of the facility elements in the periphery of the self-localization extracted from the facility element collation map is the facility element candidate extracted from the measured three-dimensional shape on the basis of the calculated similarity.