This paper describes a navigation system implemented on a real mobile robot. Using simple sonar and visual sensors, it makes possible the autonomous construction of a dense topological map representing the environment. At any time during the mapping process, this system is able to globally localize the robot, i.e. to estimate the robot's position even if the robot is passively moved from one place to another within the mapped area. This is achieved using algorithms inspired by Hidden Markov Models adapted to the on-line building of the map. Advantages and drawbacks of the system are discussed, along with its potential implications for the understanding of biological navigation systems.