Presents a rapid localization method for mobile robots. Localization, i.e., absolute position measurement, is an important issue since odometer errors render it impossible for any robot to precisely follow a specified trajectory, resulting in a growing difference between the actual configuration and the calculated configuration as the robot travels. Periodic localization is required to correct these errors. We propose a localization method using range sensor data which is based on simple geometric properties of the environment. In many common situations, information regarding the environment is provided a priori for path planning. During processing, the method proposed here utilizes this information to partition the workspace into sectors using simple visibility computations, and a small identifying label is computed for each sector. The localizer analyzes range sensor readings (distances) and extracts characteristic points, which are compared with the pre-computed sector labels to localize the robot, first to a sector, and then to a particular configuration within that sector. Advantages of this two step process are that it is computationally very simple, and that it allows precise localization without any landmarks from any configuration in the environment. This localization method also provides opportunities for the global navigation procedure to analyze and select trajectories in terms of their tolerance to localization errors.