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New applications of mobile robotics in dynamic urban areas require more than the single-session geometric maps that have dominated simultaneous localization and mapping (SLAM) research to date; maps must be updated as the environment changes and include a semantic layer (such as road network information) to aid motion planning in dynamic environments. We present an algorithm for long-term localization and mapping in real time using a three-dimensional (3D) laser scanner. The system infers the static or dynamic state of each 3D point in the environment based on repeated observations. The velocity of each dynamic point is estimated without requiring object models or explicit clustering of the points. At any time, the system is able to produce a most-likely representation of underlying static scene geometry. By storing the time history of velocities, we can infer the dominant motion patterns within the map. The result is an online mapping and localization system specifically designed to enable long-term autonomy within highly dynamic environments. We validate the approach using data collected around the campus of ETH Zurich over seven months and several kilometers of navigation. To the best of our knowledge, this is the first work to unify long-term map update with tracking of dynamic objects.