## 2 Methods
### GNSS Methods Simulation  
A GNSS antenna (Antcom G5 Ant-2 AT1, 160 g) was mounted on the helmet of the athlete and was connected to a GPS/GLONASS dual frequency (L1/L2) receiver (Javad Alpha-G3T, 430 g, L: 148 mm \(\times\) H: 85 mm \(\times\) D: 35 mm) carried in a cushioned backpack (Figure 1) and recording position signals at 50 Hz. Two GNSS base stations were mounted close to the start of the course and were equipped with antennas (Javad GrAnt-G3T) and Javad Alpha-G3T receivers.  
Figure 1: **(Left)** Magnification of the antenna installation on the skier’s helmet. (Photos: [PERSON]). **(Right)** An alpine skier equipped with the GNSS system. The antenna was mounted on the helmet and connected to a receiver, which was carried in a cushioned backpack.  
Accurate absolute global positions of the GNSS base stations were calculated using reference data from the Austrian Positioning Service (APOS, Wien, Austria) and the geodetic post-processing software Justin (Javad). All GNSS measurements were determined in the WGS84 (Universal Transverse Mercator zone 32, Northern Hemisphere) coordinate system. The skier's GNSS antenna trajectory was computed using the geodetic post-processing software Justin in double difference mode. When the post-processing software Justin was unable to fix ambiguities (integer ambiguities), float ambiguities (real number ambiguities) were calculated using the chosen frequencies (L1 or L1 and L2) and satellite systems (GPS or GPS and GLONASS). No cascading from L1 and L2 to L1 was used.  
The kinematic position solutions were computed for five different GNSS methods (Table 1). Method \(A\) was a differential phase solution that included both GPS and GLONASS satellite signals and the signal frequencies L1 and L2. Method \(B\) was similar to method \(A\), but using frequency L1 only. Method \(C\) was similar to method \(A\) except that GPS signals only were used. Method \(D\) was similar to \(C\) but using frequency L1 only. Method \(E\) was a non-differential code solution using only GPS code signals (the software was choosing among the code signals P1, P2, C2, C5 and C/A. In order to simulate measurement environments with different grades of satellite signal obstruction, each GNSS method was computed for circular elevation angles of 10\({}^{\circ}\), 30\({}^{\circ}\) and 40\({}^{\circ}\) on top of the masking caused by the topography. The elevation angles were adjusted in the post-processing software. All signals (direct or indirect) of satellites with an elevation angle smaller than the 10\({}^{\circ}\), 30\({}^{\circ}\) or 40\({}^{\circ}\) cut-off elevation angle were left out from the solution computation. Hence, 5 methods were used with 3 different satellite signal obstruction conditions each. The method names are written in italic (_A_-_E_), while the position vectors of the skier trajectory are written in italic and bold (_A_-_E_).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**GNSS**} & \multicolumn{2}{c}{**Frequency**} & \multicolumn{2}{c}{**Processing**} \\ \cline{2-7}  & **GPS** & **GLONASS** & **L1** & **L2** & **Differential** & **Non-Differential** \\ \hline \(A\) & X & X & X & X & X & \\ \(B\) & X & X & X & & X & \\ \(C\) & X & & X & X & X & \\ \(D\) & X & & X & & X & \\ \(E\) & X & & Code & & & X \\ \hline \hline \end{tabular}
\end{table}
Table 1: Composition of the 5 GNSS methods applied in study 1 and 2.  
Figure 2: Animation of an alpine skier in the giant slalom course surrounded by the reference points of the reference measurement system at gate number 7 (Photo: [PERSON]).