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Estimating 3D human poses from a monocular video is still a challenging task. Many existing methods' performance drops when the target person is occluded by other objects, or the motion is too fast/slow relative to the scale and speed of the training data. Moreover, many of these methods are not designed or trained under severe occlusion explicitly, making their performance on handling occlusion compromised. Addressing these problems, we introduce a spatio-temporal network for robust 3D human pose estimation. As humans in videos may appear in different scales and have various motion speeds, we apply multi-scale spatial features for 2D joints or keypoints prediction in each individual frame, and multi-stride temporal convolutional networks (TCNs) to estimate 3D joints or keypoints. Furthermore, we design a spatio-temporal discriminator based on body structures as well as limb motions to assess whether the predicted pose forms a valid pose and a valid movement. During training, we explicitly mask out some keypoints to simulate various occlusion cases, from minor to severe occlusion, so that our network can learn better and becomes robust to various degrees of occlusion. As there are limited 3D ground-truth data, we further utilize 2D video data to inject a semi-supervised learning capability to our network. Moreover, we observe that there is a discrepancy between 3D pose prediction and 2D pose estimation due to different pose variations between video and image training datasets. We, therefore propose a confidence-based inference stage optimization to adaptively enforce 3D pose projection to match 2D pose estimation to further improve final pose prediction accuracy. Experiments on public datasets validate the effectiveness of our method, and our ablation studies show the strengths of our network's individual submodules.