An algorithm for robot localization using visual landmarks is described. This algorithm determines both the correspondence between observed landmarks (in this case vertical edges in the environment) and a preloaded 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 its fast execution. The current version of the algorithm has been implemented and tested on a mobile robot system. In several hundred trials the algorithm has not failed, and computes location accurate to within a centimeter in less than half a second.>