# Kinematic Determination of the Aerial Phase in Ski Jumping
## 2 Materials and Methods
### dGNSS Measurement  
In each data collection, the same dGNSS method was applied, in which the head trajectories of the athletes were captured using a dGNSS with a receiver (Alpha-G3T, Javad, CA, USA) in a backpack and an antenna (G5 Ant-2 AT1, Antcom, Torrance, CA, USA) mounted on the helmet, as shown in Figure 2. The antenna mounting point can be considered a reasonable representation of the athlete as a point mass as soon as the ski jumper has reached a steady posture, but not during the take-off and landing phases [35].  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**ID**} & \multirow{2}{*}{**Place**} & **Hill Size** & **Athletes** & \multirow{2}{*}{**Gender**} & **Perf. Level** & **Jumps** \\  & & **(m)** & **(\#)** & & & **(\#)** \\ \hline HS77 & Einsieden (CH) & 77 & 6 & Female/Male & Junior & 12 \\ HS106 & Midstubakken (N) & 106 & 8 & Male & WC/COC & 38 \\ HS117 & Einsieden (CH) & 117 & 2 & Male & Junior & 10 \\ HS140 & Lillehammer (N) & 140 & 3 & Male & WC/COC & 33 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Information on hill size, number of athletes, gender, performance level (WC/COC: World Cup and Continental Cup level), and number of jumps measured for the four different data collections conducted in this study.  
Figure 2: Ski jumpers with the dGNSS antenna mounted on their helmets and the receivers in backpacks that were carried under the ski jumping suit. Picture from [35].  
A GNSS base station with antenna (GrAnt-G3T, Javad, San Jose, CA, USA) and receiver (Alpha-GST, Javad, San Jose, CA, USA) was positioned in close proximity to the invnn (short-baseline dGNSS). GNSS signal reception through the GNSS antenna requires a direct line of sight to the satellites and is therefore constrained to being mounted on the head of the ski jumper. Both the athlete's GNSS and the base station GNSS logged GPS/GLONASS dual frequency (L1/L2) signals at 50 Hz. Raw GNSS data were downloaded from the GNSS receivers and dGNSS solutions were calculated in post-processing. Geodetic dGNSS post-processing was done using the software Justin (Javad, San Jose, CA, USA) and was applied to the raw GNSS data to calculate kinematic carrier phase double difference position solutions [36], which were exported in a Cartesian coordinate system (UTM32N), and rotated in to a local coordinate system with the origin at the invn edge with \(x\) along the horizontal axis of the jump and \(y\) along the vertical axis. For the analysis, jumps were only used when the dGNSS solution managed to fix the integer ambiguities in the dGNSS solution yielding a typical global position error of \(\pm 0.05\) m. Jumps with periods of dGNSS float solutions (typically yielding one order of magnitude larger errors [36]) were discarded from the analysis.  
The raw dGNSS positions were filtered with a weighted cubic spline filter, where position error estimates from the geodetic dGNSS processing were applied as weights [38; 39]. Position, velocity, and acceleration were derived from the dGNSS position--time data. The \(LD\)-ratio was calculated as a coefficient from the horizontal and vertical acceleration components. For more detailed information about the calculation of parameters, the reader is referred to [PERSON] et al. [35]. The derived position, velocity, and acceleration data were filtered with different cut-off frequency settings using a second order Butterworth filter, as stated in Appendix A. These were used to test the sensitivity of filter settings for the identification of the steady glide phase as described in Section 3. Parameter calculation, filtering, and the following analysis were conducted in Matlab R2021a.