This paper presents a new way to acquire occupancy grid maps with mobile robots. Virtually all existing occupancy grid mapping algorithms decompose the highdimensional mapping problem into a collection of onedimensional problems, where the occupancy of each grid cell is estimated independently of others. This induces conflicts that can lead to inconsistent maps. This paper shows how to solve the mapping problem in the original, highdimensional space, thereby maintaining all dependencies between

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... neighboring cells. As a result, maps generated by our approach are often more accurate than those generated using traditional techniques. Our approach relies on a rigorous statistical formulation of the mapping problem using forward models. It employs the expectation maximization algorithm for estimating maps, and a Laplacian approximation to determine uncertainty.