This work presents some methods to create local maps and to estimate the position of a mobile robot, using the global appearance of omnidirectional images. We use a robot that carries an omnidirectional vision system on it. Every omnidirectional image acquired by the robot is described only with one global appearance descriptor, based on the Radon transform. In the work presented in this paper, two different possibilities have been considered. In the first one, we assume the existence of a map previously built composed of omnidirectional images that have been captured from previously-known positions. The purpose in this case consists of estimating the nearest position of the map to the current position of the robot, making use of the visual information acquired by the robot from its current (unknown) position. In the second one, we assume that we have a model of the environment composed of omnidirectional images, but with no information about the location of where the images were acquired. The purpose in this case consists of building a local map and estimating the position of the robot within this map. Both methods are tested with different databases (including virtual and real images) taking into consideration the changes of the position of different objects in the environment, different lighting conditions and occlusions. The results show the effectiveness and the robustness of both methods.