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This paper introduces a new approach to simultaneous localization and mapping (SLAM) that pursues robustness and accuracy in large-scale environments. Like most successful works on SLAM, we use Bayesian filtering to provide a probabilistic estimation that can cope with uncertainty in the measurements, the robot pose, and the map. Our approach is based on the reconstruction of the robot path in a hybrid discrete-continuous state space, which naturally combines metric and topological maps. There are two fundamental characteristics that set this paper apart from previous ones: 1) the use of a unified Bayesian inference approach both for the metrical and the topological parts of the problem and 2) the analytical formulation of belief distributions over hybrid maps, which allows us to maintain the spatial uncertainty in large spaces more accurately and efficiently than in previous works. We also describe a practical implementation that aims for real-time operation. Our ideas have been validated by promising experimental results in large environments (up to 30 000 m2, a 2 km robot path) with multiple nested loops, which could hardly be managed appropriately by other approaches.