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Dynamic obstacle avoidance is one crucial component for compliant navigation in crowded environments. In this paper we present a system for accurate and reliable detection and tracking of dynamic objects using noisy point cloud data generated by stereo cameras. Our solution is real-time capable and specifically designed for the deployment on computationally-constrained unmanned ground vehicles. The proposed approach identifies individual objects in the robot's surroundings and classifies them as either static or dynamic. The dynamic objects are labeled as either a person or a generic dynamic object. We then estimate their velocities to generate a 2D occupancy grid that is suitable for performing obstacle avoidance. We evaluate the system in indoor and outdoor scenarios and achieve real-time performance on a consumer-grade computer. On our test-dataset, we reach a MOTP of $0.07 \pm 0.07m$, and a MOTA of $85.3\%$ for the detection and tracking of dynamic objects. We reach a precision of $96.9\%$ for the detection of static objects.