Markerless video-based golf-stick motion analysis using Kalman filtering and Rauch-Tung-Striebel smoothing

Abstract

Relevance. Quantitative assessment of golf-stick motion matters for sport biomechanics, coaching, rehabilitation, and virtual-reality training. Laboratory marker-based capture is precise but impractical for routine field use, whereas markerless monocular video still suffers from noise, missed detections, foreshortening, and perspective scale variation. Aim of the article. The aim is to develop and evaluate a reproducible markerless workflow that converts heterogeneous golf-stick video into interpretable kinematic indicators with explicit comparison of raw, filtered, and smoothed trajectories. Objectives. Objectives are to formalize filtering and smoothing; stabilize dynamic pixel-to-metre scaling; export path-quality and phase indicators; and quantify between-session dispersion while reporting diagnostic sensitivity, ablation, and keyframe-timing checks. Methods. The implemented pipeline uses offline MediaPipe-based landmarks, median pre-filtering, a constant-velocity Kalman filter with residual-adaptive measurement noise and physical gating, Rauch–Tung–Striebel smoothing, despiking with bounded polynomial smoothing, and dynamic scale calibration from the detected stick length with an assumed physical reference length. Apparent two-dimensional speed, acceleration, jerk, curvature, path efficiency, tempo, phase durations, and a smoothness index are exported. Evaluation covered all available heterogeneous field sessions under the scientific filtering profile. Scientific novelty. Novelty lies in coordinating these components in one reproducible workflow with transparent stage comparison and a clear split between implemented processing and planned external validation. Practical significance. Ordinary smartphone video can yield interpretable swing-quality indicators for research, coaching, and virtual-reality training without motion-capture hardware, if values are treated as apparent monocular two-dimensional estimates rather than laboratory ground truth. Results. All sessions were processed successfully. Smoothness index and path efficiency had the lowest between-session coefficients of variation, while peak derivative and phase metrics were highly dispersed. Keyframe-timing errors were large and are not accepted as accuracy evidence; sensitivity and ablation outputs remain computational diagnostics only. Conclusions. Global path-quality metrics are comparatively less dispersed than peak derivatives under heterogeneous capture, but measurement validity is unconfirmed until paired test–retest designs and independent spatial references are available.