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