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Mapping and tracking in dynamic environments for autonomously-moving robots is still challenging, despite being essential tasks. They are often done separately using occupancy grids and established object tracking algorithms. In this work, an approach is presented that estimates a uniform, low-level, grid-based world model including dynamic and static objects, their uncertainties, as well as their velocities. It does not require existing object tracks to filter out data points not used for creating and updating the map. Nor does it require that measurements can be classified into belonging to a static or to a moving object. Promising results from experiments with an autonomous vehicle equipped with a laser scanner demonstrate the usefulness of the approach.