In this paper we present a new method to detect motion from mobile platforms using laser range data. Motion can be found as differences in successive scans. The main challenge in doing so from a mobile platform is to distinguish differences originating from the platforms own motion from those caused by objects moving in the robot's vicinity. We tackle this combining localization and data association based on an a-priori obtained map. Localization and data association is done using the EM-algorithm. Elements, which are not in the map, are singled out as outliers. Subtracting them over time provides motion information. To reduce the complexity of each iteration step we chose a feature-based environment model, which reduces the computation required to a fraction. We use simulations to test our method against a known ground-truth. Results based on real-world data from the exhibition Robotics@Expo.02 are used to evaluate the proposed method under real-world conditions in highly dynamic situations with several hundred visitors per hour.