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A key challenge for autonomous vehicles is to navigate in unseen dynamic environments. Separating moving objects from static ones is essential for navigation, pose estimation, and understanding how other traffic participants are likely to move in the near future. In this work, we tackle the problem of distinguishing 3D LiDAR points that belong to currently moving objects, like walking pedestrians or driving cars, from points that are obtained from non-moving objects, like walls but also parked cars. Our approach takes a sequence of observed LiDAR scans and turns them into a voxelized sparse 4D point cloud. We apply computationally efficient sparse 4D convolutions to jointly extract spatial and temporal features and predict moving object confidence scores for all points in the sequence. We develop a receding horizon strategy that allows us to predict moving objects online and to refine predictions on the go based on new observations. We use a binary Bayes filter to recursively integrate new predictions of a scan resulting in more robust estimation. We evaluate our approach on the SemanticKITTI moving object segmentation challenge and show more accurate predictions than existing methods. Since our approach only operates on the geometric information of point clouds over time, it generalizes well to new, unseen environments, which we evaluate on the Apollo dataset.