This paper describes a method by which range data from a sonar or other type of rangefinder can be used to determine the 2-dimensional position and orientation of a mobile robot inside a room. The plan of the room is modeled as a list of segments indicating the positions of walls. The method works by extracting straight segments from the range data and examining all hypotheses about pairings between the segments and walls in the model of the room. Inconsistent pairings are discarded efficiently by using local constraints based on distances between walls, angles between walls, and ranges between walls along their normal vectors. These constraints are used to obtain a small set of possible positions, which is further pruned using a test for physical consistency. The approach is extremely tolerant of noise and clutter. Transient objects such as furniture and people need not be included in the room model, and very noisy, low-resolution sensors can be used. The algorithm's performance is demonstrated using Polaroid Ultrasonic Rangefinder, which is a low-resolution, high-noise sensor.