IMU Error Propagation in Position Reconstruction and Its Mitigation Through Task-Informed Dual-IMU Constrained Optimization: Application to Golf Putting

Inertial measurement units (IMUs) are promising low-cost tools for golf putting analysis, but accurate putter trajectory reconstruction remains limited by sensor errors, sensor fusion tuning, and drift accumulation during numerical integration. This study aimed to analyze error propagation in a standard IMU-based reconstruction pipeline, in which orientation is estimated to remove gravity from the accelerometer signal, followed by double integration to obtain velocity and position. In addition, a constrained redundant optimization pipeline (CROP) is proposed to improve reconstruction accuracy. CROP exploits the redundant information provided by two IMUs mounted on the same rigid body, together with task-informed kinematic constraints, to optimize residual accelerometer and gyroscope bias compensation terms and sensor fusion parameters for each recording. An amateur golfer performed 23 putting strokes with two IMUs mounted on the putter shaft and head, respectively, while a stereophotogrammetric system served as a reference. Results were compared with the standard pipeline tuned with different parameter configurations. Overall, compared with the best parameter configuration of the standard pipeline, CROP reduced the median RMS error of the velocity and position norms by about 40%, from 16.5 to 9.9 cm/s, and 63%, from 23.2 to 8.5 cm, respectively. These findings indicate reduced drift and improved trajectory reconstruction, although further improvements are required for accurate field use.