We describe an efficient method for localizing a mobile robot in an environment with landmarks. We assume that the robot can identify these landmarks and measure their bearings relative to each other. Given such noisy input, the algorithm estimates the robot's position and orientation with respect to the map of the environment. The algorithm makes efficient use of our representation of the landmarks by complex numbers. The algorithm runs in time linear in the number of landmarks. We present results of simulations and propose how to use our method for robot navigation.

To navigate effectively, an autonomous agent must be able to quickly and accurately determine its current location. Given an initial estimate of its position (perhaps based on dead-reckoning) and an image taken of a known environment, our agent first attempts to locate a set of landmarks (real-world objects at known locations), then uses their angular separation to obtain an improved estimate of its current position. Unfortunately, some landmarks may not be visible, or worse, may be confused with other landmarks, resulting in both time wasted in searching for invisible landmarks, and in further errors in the agent's estimate of its position. To address these problems, we propose a method that uses previous experiences to learn a selection function that, given the set of landmarks that might be visible, returns the subset which can reliably be found correctly, and so provide an accurate registration of the agent's position. We use statistical techniques to prove that the learned selecti...