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This is particularly challenging when the camera is also moving, entangling human and camera motion. To address these issues, we adopt a novel 5D representation (space, time, and identity) that enables end-to-end reasoning about people in scenes. Our method, called TRACE, introduces several novel architectural components. Most importantly, it uses two new \"maps\" to reason about the 3D trajectory of people over time in camera, and world, coordinates. An additional memory unit enables persistent tracking of people even during long occlusions. TRACE is the first one-stage method to jointly recover and track 3D humans in global coordinates from dynamic cameras. By training it end-to-end, and using full image information, TRACE achieves state-of-the-art performance on tracking and HPS benchmarks. 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