Applications providing automated coaching for physical training are increasing in popularity, for example physical therapy. These applications rely on accurate and robust pose estimation using monocular video streams. State-of-the-art models like BlazePose excel in real-time pose tracking, but their lack of anatomical constraints indicates improvement potential by including physical knowledge. We present a real-time post-processing algorithm fusing the strengths of BlazePose 3D and 2D estimations using a weighted optimization, penalizing deviations from expected bone length and biomechanical models. Bone length estimations are refined to the individual anatomy using a Kalman filter with adapting measurement trust. Evaluation using the Physio2.2M dataset shows a 10.2 percent reduction in 3D MPJPE and a 16.6 percent decrease in errors of angles between body segments compared to BlazePose 3D estimation. Our method provides a robust, anatomically consistent pose estimation based on a computationally efficient video-to-3D pose estimation, suitable for automated physiotherapy, healthcare, and sports coaching on consumer-level laptops and mobile devices. The refinement runs on the backend with anonymized data only.