## 3 Results and Discussion
### Discussion  
The current study produced the following main findings: (1) For the periods when solutions were computed the spatial differences were smallest for method \(A\), followed by \(C\), \(B\), \(D\) and \(E\); (2) The period of time for which no differential solution could be computed was shortest for method \(A\) and increased for methods \(B\), \(C\) and \(D\) respectively; (3) Methods \(A\), \(B\) and \(C\) were approximately equally accurate for the 10\({}^{\circ}\) condition; (4) Time to fix integer ambiguities was shortest for method \(A\) followed by methods \(C\), \(B\) and \(D\). The elevation angles 10\({}^{\circ}\), 30\({}^{\circ}\) and 40\({}^{\circ}\) were chosen to simulate realistic signal obstruction conditions for WC alpine ski racing. Positioning dilution of precision (PDOP) was determined by forerunners skiing 19 real WC races, using method \(A\). The measurements in the WC races revealed that PDOP of 1.5 to 2.0 occurred 76% of the time, PDOP between 2 and 5 for 19% of  
Figure 5: Results of study 2: Histograms of the position difference norms (XYZ) between the trajectories of methods _A–E_ (_A–E_) and the reference trajectory (_A_10_) for the elevation masking conditions 10\({}^{\circ}\), 30\({}^{\circ}\) and 40\({}^{\circ}\). NaN on the horizontal axis indicates the amount of time when no solution could be computed. Black bars indicate fixed solutions, white bars indicate float solutions. NaN indicates that the system was unable to compute a solution. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & \multicolumn{3}{c}{**Maximal XYZ [m]**} & \multicolumn{3}{c}{**Maximal XY [m]**} & \multicolumn{3}{c}{**Maximal Z [m]**} \\ \cline{2-10}
**Elev. Angle** & **10\({}^{\circ}\)** & **30\({}^{\circ}\)** & **40\({}^{\circ}\)** & **10\({}^{\circ}\)** & **30\({}^{\circ}\)** & **40\({}^{\circ}\)** & **10\({}^{\circ}\)** & **30\({}^{\circ}\)** & **40\({}^{\circ}\)** \\ \hline Method \(A\) & - & 3.44 & 8.18 & - & 1.25 & 5.43 & - & 3.34 & 6.12 \\ Method \(B\) & 2.00 & 17.88 & 50.20 & 1.30 & 11.70 & 8.09 & 1.83 & 16.78 & 49.69 \\ Method \(C\) & 1.30 & 5.63 & 10.26 & 0.82 & 2.39 & 3.52 & 1.05 & 5.50 & 9.64 \\ Method \(D\) & 4.69 & 6.13 & - & 1.86 & 3.84 & - & 4.55 & 5.47 & - \\ \hline \end{tabular}
\end{table} 
Table 11: _Cont._the time and PDOP above 5 for approximately 5% of the time for method \(A\). These measures are in agreement with the findings of other studies [28,42]. During the experiment for this simulation a mean PDOP of 1.9 was found for an elevation angle of 30\({}^{\circ}\) and a mean PDOP of 7.8 for the 40\({}^{\circ}\) elevation angle condition. Hence, the 10\({}^{\circ}\) elevation angle condition represented conditions without any additional obstruction, as would be the case on glaciers for example, while the 30\({}^{\circ}\) and 40\({}^{\circ}\) conditions represented ordinary and extreme WC racing conditions, respectively. In order to be able to detect relevant functional differences, the accuracy requirements for position data in alpine skiing must be in the range of a few centimeters in slalom and giant slalom [33], but might be larger in the speed disciplines super-G and downhill. Hence, the results of study 1 and 2 showed that GNSS measurements in WC races should be accomplished using both GPS and GLONASS and frequency L1 and L2 (method _A_). If measuring in areas with little satellite signal obstruction, for example on glaciers, GLONASS or frequency L2 can probably be dropped, if high-end devices are used. However, under real WC competition conditions, where topography and trees are obstructing the satellite signal, both accuracy of the differential (fixed and float) solutions and the amount of differential solutions decreased, if either frequency L2 (method _B_) or GLONASS (method _C_) was dropped. Comparing method \(B\) and _C,_ the use of frequency L2 increased the accuracy of the integer fixed solutions in method \(C\) compared to method \(D\), possibly as a result of the reduction of disturbances in the ionosphere [42].