Building a model of the environment is essential for mobile robotics. It allows the robot to reason about its surroundings and plan actions according to its intentions. To enable safe motion planning it is vital to anticipate object movements. This paper presents an improved formulation for occupancy filtering. Our approach is closely related to the Bayesian Occupancy Filter (BOF) presented in. The basic idea of occupancy filters is to represent the environment as a 2-dimensional grid of cells holding information about their state of occupancy and velocity. To improve the accuracy of predictions, prior knowledge about the motion preferences is used, derived from map data that can be obtained from navigation systems. In combination with a physically accurate transition model, it is possible to estimate the environment dynamics. Experiments show that this yields reliable estimates even for occluded regions.