## 2 Materials and Methods
### Data Analysis
\begin{table}
\begin{tabular}{c c} \hline \hline
**VICON** & **GNSS** \\ \hline \hline Raw coordinates: & \([x_{raw},\ y_{raw}]\) \\ where \(x_{raw},\ y_{raw}\) are the raw Vicon coordinates. \\ \hline \hline Filtered coordinates: & \(\left[x_{fill},\ y_{fill}\right]=[F(x_{raw}),F(y_{raw})]\) \\ where \(x_{fill},\ y_{fill}\) are the filtered coordinates. The filtering process (\(F\)) is a fourth-order (zero 120) low pass Butterworth filter with a cut-off frequency of 6 Hz, performed on the raw coordinates (\(x_{raw},\ y_{raw}\)) \\ \hline Distance between samples: & \\ \(Dp_{(i)}=\sqrt{\left(x_{fill\ (i+1)}-x_{fill\ (i)}\right)^{2}+\left(y_{fill\ (i+1)}-y_{fill\ (i)}\right)^{2}}\) \\ where \(Dp\) is the distance between the samples calculated of the filtered coordinates (\(x_{fill},\ y_{fill}\)); \(i\) is the index of a sample in the 100 Hz data. \\ \hline Total distance: & \\ \(D_{(i)}=\sum{(j=1\ {\rm{to}}\ i)\ Dp_{(i)}}\) & \\ where \(D\) is the cumulative sum of the distance between samples (\(Dp\)). & \\ \hline Speed (first-order central difference method): & Raw speed data: \\ \(S_{(j)}=\frac{(D_{(i+1)}-D_{(i-1)})}{2t}\) & \(W_{raw}\) \\ where \(S\) is the speed calculated of the distance (\(D\)) and the sample rate of the Vicon data (\(t\) = 0.01 s) & where \(W_{raw}\) is the raw Doppler-shift speed data of the GNSS, completely unfiltered by any software. \\ \hline Filtered speed: & Filtered speed: \\ \(S_{fill}=G(S)\) & \(Q_{fill}=Z(W_{raw})\) \\ where \(S_{fill}\) is the filtered speed data. The filtering process (\(G\)) is a fourth-order (zero lag) low pass Butterworth filter with a cut-off frequency of 2 Hz, performed on the speed (\(S\)) & where \(Q_{fill}\) is the filtered raw speed data. The following filters were tested for \(Z\): \\ \hline \hline \end{tabular}
\begin{tabular}{c c} \hline \hline Acceleration (first-order central difference method): & Acceleration (central difference method): \\ \(A_{(i)}=\frac{(S_{fill\ (i+1)}-S_{fill\ (i-1)})}{2t}\) & \(B_{(i)}=\frac{(Q_{fill\ (i+1)}-Q_{fill\ (i-1)})}{2t}\) \\ where \(B\) is the acceleration data calculated of the filtered speed (\(Q_{fill}\)) and the sample rate of the GNSS data (\(t\) = 0.1 s). \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Data processing steps performed in order on the Vicon data (raw coordinate data until acceleration data) and on the GNSS data (raw speed data until acceleration data). practitioners and researchers. The downsampling process is detailed in Table 3. The raw GNSS Doppler-shift speed data were processed using three different smoothing techniques (I) a fourth-order (zero lag) low pass Butterworth filter (cut-off frequencies ranging from raw to 4.9 Hz, steps of 0.1 Hz), (II) exponential smoothing (smoothing constant ranging from 0.1 to 0.9, steps of 0.1), and (III) moving average (sliding window ranging from 0.2 s to 2.0 s, steps of 0.1 s). The boundaries of all smoothing parameters (e.g., cut-off frequencies ranging from raw to 4.9 Hz) were set to their maximum possible values to experiment with all potential options for the smoothing techniques (maximal smoothing to minimal smoothing). A small step size of 0.1 for each smoothing boundary was set to allow for more options in testing, helping identify the best possible combination of smoothing technique and smoothing parameter. These three techniques were chosen as they are widely used techniques for smoothing time-series acceleration data, each with distinct characteristics that balance noise reduction and signal preservation in dynamic acceleration data [7; 15]. Smoothing the raw Doppler-shift speed data before deriving the acceleration data will ensure that any noise present in the speed data will not be increased due to deriving. Details on the used smoothing techniques and processing steps of the GNSS data can be found in Table 2. Next to the custom smoothed GNSS data, GNSS manufacturer smoothed acceleration data and raw GNSS acceleration data (calculated with the central difference method on the raw GNSS Doppler-shift speed data) were also used.