## 3 Results and Discussion
### Results
#### 3.1.2 Step 2
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & \multicolumn{3}{c}{**Number of Trajectories with**} & & & \\  & \multicolumn{3}{c}{**Fixed Solution**} & & & & \\
**Elev. Angle** & \(\mathbf{10^{\circ}}\) & \(\mathbf{30^{\circ}}\) & \(\mathbf{40^{\circ}}\) & \(\mathbf{10^{\circ}}\) & \(\mathbf{30^{\circ}}\) & \(\mathbf{40^{\circ}}\) \\ \hline Method \(A\) & 12 & 12 & 12 & \(0.06\pm 0.10\) & \(0.06\pm 0.06\) & \(0.56\pm 1.52\) \\ Method \(B\) & 12 & 12 & 9 & \(1.1\pm 1.1\) & \(13.58\pm 20.50\) & \(43.70\pm 20.24\) \\ Method \(C\) & 12 & 10 & 7 & \(0.34\pm 0.88\) & \(4.62\pm 11.12\) & \(27.94\pm 66.18\) \\ Method \(D\) & 12 & 8 & - & \(19.96\pm 2.26\) & \(51.54\pm 46.54\) & - \\ Method \(E\) & - & - & - & - & - & - \\ \hline \end{tabular}
\end{table} 
Table 7: The number of trajectories (out of 12) for which a fixed ambiguities solution was computed at least once during the run is shown on the left. The duration from GNSS measurement start to the instant a fixed ambiguities solution was computed for the first time is shown on the right. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & \multicolumn{3}{c}{**Fixed**} & & & & **Float (Method \(A\)-\(D\))** & & & \\  & \multicolumn{3}{c}{**Fixed**} & & & & **Code (Method \(E\))** & & & \\
**Elev. Angle** & \(\mathbf{10^{\circ}}\) & \(\mathbf{30^{\circ}}\) & \(\mathbf{40^{\circ}}\) & \(\mathbf{10^{\circ}}\) & \(\mathbf{30^{\circ}}\) & \(\mathbf{40^{\circ}}\) & \(\mathbf{10^{\circ}}\) & \(\mathbf{30^{\circ}}\) & \(\mathbf{40^{\circ}}\) \\ \hline Method \(A\) & 100 & 100 & 87 & 0 & 0 & 13 & 0 & 0 & 0 \\ Method \(B\) & 99 & 78 & 8 & 1 & 22 & 61 & 0 & 0 & 31 \\ Method \(C\) & 100 & 81 & 33 & 0 & 4 & 14 & 0 & 15 & 54 \\ Method \(D\) & 82 & 33 & 0 & 18 & 37 & 0 & 0 & 30 & 100 \\ Method \(E\) & & & & 100 & 85 & 36 & 0 & 15 & 64 \\ \hline \end{tabular}
\end{table} 
Table 8: The fraction of the entire run time during which fixed or float ambiguities (method \(A\)–\(D\)), code solution (method \(E\)) or no solution (NaN) was computed are given in % of the entire run time. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & \multicolumn{3}{c}{**Mean XYZ [m]**} & \multicolumn{3}{c}{**Mean XY [m]**} & & **Mean Z [m]** & \\ \cline{2-10}
**Elev. Angle** & \(\mathbf{10^{\circ}}\) & \(\mathbf{30^{\circ}}\) & \(\mathbf{40^{\circ}}\) & \(\mathbf{10^{\circ}}\) & \(\mathbf{30^{\circ}}\) & \(\mathbf{40^{\circ}}\) & \(\mathbf{10^{\circ}}\) & \(\mathbf{30^{\circ}}\) & \(\mathbf{40^{\circ}}\) \\ \hline Method \(A\) & - & 0.02 & 0.67 & - & 0.01 & 0.19 & - & 0.02 & 0.63 \\ Method \(B\) & 0.02 & 1.10 & 4.23 & 0.01 & 0.59 & 1.22 & 0.01 & 0.89 & 3.98 \\ Method \(C\) & 0.01 & 0.51 & 1.29 & 0.01 & 0.35 & 0.64 & 0.01 & 0.36 & 1.06 \\ Method \(D\) & 1.06 & 1.43 & NaN & 0.57 & 0.59 & NaN & 0.85 & 1.19 & NaN \\ Method \(E\) & 1.99 & 3.58 & 11.75 & 1.09 & 1.77 & 3.04 & 1.45 & 2.84 & 11.27 \\ \hline \end{tabular}
\end{table} 
Table 9: Mean, Median, SD and Maximum of the spatial differences between the skier trajectories _fixed and float_ solutions for method \(A_{2}\)–\(D_{2}\), the _code_ solution \(E_{2}\) and the solution of method \(A\) in the condition \(10^{\circ}\). XYZ represents the difference norm in 3 dimensions, XY the difference norm in the horizontal plane and Z in the vertical direction.