An accurate and uncertainty-aware 3D human body pose estimation is key to enabling truly safe but efficient human-robot interactions. Current uncertainty-aware methods in 3D human pose estimation are limited to predicting the uncertainty of the body posture, while effectively neglecting the body shape and root pose. In this work, we present GloPro, which to the best of our knowledge the first framework to predict an uncertainty distribution of a 3D body mesh including its shape, pose, and root pose, by efficiently fusing visual clues with a learned motion model. We demonstrate that it vastly outperforms state-of-the-art methods in terms of human trajectory accuracy in a world coordinate system (even in the presence of severe occlusions), yields consistent uncertainty distributions, and can run in real-time. Our code will be released upon acceptance at https: $I$ Igithub. coml smartroboticslab/GloPro.