This paper describes an algorithm for determining robot location from visual landmarks. This algorithm determines both the correspondence between observed landmarks (in this case vertical edges in the environment) and a stored map, and computes the location of the robot using those correspondences. The primary advantages of this algorithm are its use of a single geometric tolerance to describe observation error, its ability to recognize ambiguous sets of correspondences, its ability to compute bounds on the error in localization, and fast execution. The algorithm has been implemented and tested on a mobile robot system. In several hundred trials it has never failed, and computes location accurate to within a centimeter in less than 0.5 s.>