## 2 Materials and Methods
### Data Processing  
All data were processed using MATLAB (version 2023a, The MathWorks Inc., Natick, MA, USA). The raw GNSS outputs (vertical position, latitude, and longitude) were sampled at 100 Hz. To remove high-frequency noise while preserving the fundamental signal characteristics related to running kinematics, we applied a zero-phase 4 th-order Butterworth low-pass filter with a cutoff frequency of 5 Hz. This cutoff was selected based on a Fourier analysis of the vertical velocity signal, revealing dominant frequency components corresponding to the athletes' \(SF\)s. Such a cutoff has been employed in previous studies examining vertical oscillations during running [28]. Filtering was applied identically to the vertical position and horizontal coordinates (latitude and longitude). After filtering, we derived the vertical velocity by differentiating the vertical position. Two RTK GNSS-based step detection methods were then implemented. Method 1 (vertical position minima) identifies mid-stance events by finding the minima in the vertical position profile (Figure 2A). The time interval between successive minima defines the step time, from which the \(SF\) is obtained as \(SF=1/\)(_step time_). The horizontal displacement between consecutive minima provides the \(SL\), and the _running velocity_ is computed as \(velocity=SL\times SF\). Method 2 (vertical velocity minima) aligns step detection with an identifiable biomechanical event: IC (Figure 2B). Minima in the vertical velocity trace correspond to IC, allowing direct measurement of step times and subsequent calculation of the \(SF\), \(SL\), and \(velocity\). Both methods rely on continuous GNSS solutions. In this study, the RTK GNSS provided real-time correction data, offering two solution statuses: 'Fix' (centimeter-level accuracy) and 'Float' (decimeter-level accuracy) [37; 38]. Float solutions are primarily caused by incomplete integer ambiguity resolution due to insufficient satellite visibility, signal multipath, or suboptimal environmental conditions [37; 38]. Most data were given the 'Fix' status, ensuring high positional accuracy. Additionally, segments of 'Float' solutions were noted for Subject A.  
Figure 1: Experimental measurement system. (**A**) Athlete wearing the measurement system, including an RTK GNSS receiver, an antenna, and IMUs. (**B**) RTK GNSS receiver stored in a waist pack. (**C**) Head-mounted GNSS antenna set-up, with a triple-band helical antenna connected via an SMA cable. (**D**) IMUs attached above the ankles for \(SF\) validation, with an additional unit on the headgear for synchronization. The IMU data were processed based on methodologies from the previous study [13]. The raw acceleration data from the IMUs were filtered using a zero-phase, 2 nd-order Butterworth low-pass filter with a cutoff frequency of 70 Hz. To account for variations in sensor orientation and movement artifacts, we calculated the resultant acceleration by combining the acceleration components from all three axes: \(Resultant\ Acceleration=\sqrt{a_{x}^{2}+a_{y}^{2}+a_{z}^{2}}\), where \(a_{x}\), \(a_{y}\), and \(a_{z}\) are the acceleration components along the \(x\), \(y\), and \(z\) axes, respectively. Gravity was not explicitly removed from these signals; the resultant acceleration approach inherently accounts for it [13]. IC events were detected using characteristic features in the resultant acceleration signal (Figure 2C,D). The accuracy of the IMU-derived IC timings was confirmed by calculating the mean absolute error (_MAE_) and standard deviation (_SD_) against reference data from the 3D video analysis (200 fps). Consistent with a previous study [13], we excluded the first five steps from further temporal analyses due to the transient mechanics of the initial acceleration phase. The 3D video analysis provided the primary reference data for the running parameters. The videos were analyzed using WinAnalyze 2.8 software (Mikromak, Berlin, Germany), which is widely used in sports analysis [39; 40].