We present a LiDAR-based and real-time capable 3D perception system for automated driving in urban domains. The hierarchical system design is able to model stationary and movable parts of the environment simultaneously and under real-time conditions. Our approach extends the state of the art by innovative in-detail enhancements for perceiving road users and drivable corridors even in case of non-flat ground surfaces and overhanging or protruding elements. We describe a runtime-efficient pointcloud processing pipeline, consisting of adaptive ground surface estimation, 3D clustering and motion classification stages. Based on the pipeline's output, the stationary environment is represented in a multi-feature mapping and fusion approach. Movable elements are represented in an object tracking system capable of using multiple reference points to account for viewpoint changes. We further enhance the tracking system by explicit consideration of occlusion and ambiguity cases. Our system is evaluated using a subset of the TUBS Road User Dataset. We enhance common performance metrics by considering application-driven aspects of real-world traffic scenarios. The perception system shows impressive results and is able to cope with the addressed scenarios while still preserving real-time capability.