Uncertainty estimation in marker-based motion capture of the tennis serve

Marker-based motion capture (MoCap) systems are widely used to analyse human movement. However, they are affected by measurement uncertainties, particularly marker placement errors (MPE) and soft tissue artefacts (STA). Here, we quantify the individual and combined effects of these two sources of uncertainty on joint angles and angular velocities in the case of the tennis serve. A Monte-Carlo approach was used to simulate 3000 perturbed marker trajectories for each uncertainty source and their combination. We applied a random offset for MPE, while sinusoidal perturbations were used to simulate for STA. The resulting joint kinematics were compared across all degrees of freedom. Confidence intervals (5-95 %), root mean square deviation (RMSD) and Minimal Detectable Changes (MDC) were calculated for key biomechanical variables. Results showed that STA predominantly affected angular velocities, while MPE had a greater impact on joint angles. The combined simulation consistently produced the largest variability, with mean confidence intervals ranging from 5.1° to 30.8° for joint angles and from 70.5°.s^-1 to 248.5°.s^-1 for joint angular velocities, and RMSD values ranging from 1.6° to 8.4° for joint angles and from 16.8°.s^-1 to 68.0°.s^-1 for joint angular velocities. To our knowledge, this is the first quantification of MPE and STA effects on ballistic movement kinematics. These results provide critical reference values, enabling more accurate comparisons across subjects and studies while accounting for measurement uncertainties.