In this article we describe an algorithm for robot localization using visual landmarks. This algorithm determines both the correspondence between observed landmarks (in this case vertical edges in the environment) and a pre-loaded map, and the location of the robot from 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 performance. The current version of the algorithm has been implemented and tested on a mobile robot system. In several hundred trials the algorithm has never failed, and computes location accurate to within a centimeter in less than half a second.