## 3 Results and Discussion
### Results
#### 3.1.1 Step 1
Angle** & **10\({}^{\circ}\)** & **30\({}^{\circ}\)** & **40\({}^{\circ}\)** & **10\({}^{\circ}\)** & **30\({}^{\circ}\)** & **40\({}^{\circ}\)** & **10\({}^{\circ}\)** & **30\({}^{\circ}\)** & **40\({}^{\circ}\)** \\ \hline Method \(A\) & 0.00 & 0.01 & 0.05 & 0.00 & 0.01 & 0.01 & 0.00 & 0.01 & 0.05 \\ Method \(B\) & 0.01 & 0.02 & 3.44 & 0.00 & 0.01 &The histograms shown in Figure 4 illustrate the norm of the spatial differences (XYZ) for fixed integer ambiguity (black bars) and real number float ambiguity (white bars) solutions along with the proportions of time when no solutions could be computed with the respective methods (NaN, white bars). For the condition of 10\({}^{\circ}\), all differential methods were able to fix integer ambiguities for the entire reference turn. Method \(D\) consisted of differences smaller than 5 cm and in the range of 2-3 m to 50% of total time each. Integer ambiguity was fixed for the entire time and hence, the differences in the order of meters must have occurred due to inappropriate integer fixing. Method \(E\) had no differences smaller than 0.5 m or larger than 10m. For the condition of 30\({}^{\circ}\), method \(A\) had only fixed integer \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & \multicolumn{3}{c}{**SD XYZ [m]**} & \multicolumn{3}{c}{**SD XY [m]**} & \multicolumn{3}{c}{**SD 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 \(A\) & 0.00 & 0.01 & 1.27 & 0.00 & 0.00 & 0.36 & 0.00 & 0.01 & 1.22 \\ Method \(B\) & 0.00 & 2.40 & 3.49 & 0.00 & 1.19 & 0.76 & 0.00 & 2.09 & 3.52 \\ Method \(C\) & 0.00 & 1.35 & 1.38 & 0.00 & 0.98 & 0.44 & 0.00 & 0.93 & 1.31 \\ Method \(D\) & 1.00 & 1.63 & NaN & 0.55 & 0.47 & NaN & 0.87 & 1.63 & NaN \\ Method \(E\) & 0.66 & 1.43 & 6.80 & 0.39 & 1.05 & 1.83 & 0.94 & 1.64 & 6.70 \\ \hline \multicolumn{10}{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 \(A\) & 0.00 & 0.06 & 4.28 & 0.00 & 0.02 & 1.01 & 0.00 & 0.05 & 4.16 \\ Method \(B\) & 0.02 & 8.07 & 26.90 & 0.01 & 4.21 & 5.04 & 0.02 & 7.50 & 26.48 \\ Method \(C\) & 0.03 & 4.50 & 5.84 & 0.02 & 3.25 & 1.68 & 0.03 & 3.11 & 5.60 \\ Method \(D\) & 2.44 & 5.04 & NaN & 1.41 & 1.80 & NaN & 2.17 & 5.03 & NaN \\ Method \(E\) & 4.53 & 9.27 & 24.67 & 3.02 & 5.33 & 7.85 & 4.20 & 9.15 & 24.40 \\ \hline \end{tabular}
\end{table} 
Table 4: _Cont._  
Figure 4: Histograms of the position difference norms (XYZ) between the trajectories of methods \(A\)–\(E\) (\(A_{I}\)–\(E_{I}\)) and the reference trajectory (\(P_{REF}\)) for the elevation masking conditions 10\({}^{\circ}\), 30\({}^{\circ}\) and 40\({}^{\circ}\). On the horizontal axis, NaN 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. ambiguity solutions and position difference mean and median were smaller than 5 cm. The fraction of the data without solution (NaN) was largest for method _D,_ followed by _E, C_ and \(B\). For method \(B\) and \(D\) approximately 80% and 70% of the differences respectively were smaller than 5 cm, while the remainders were in the order of meters. The reasons for the differences in the order of meters were caused both by sections of real number float ambiguity and sections of inappropriate integer fixing. Method \(E\) had most differences in the range of 2-15 m. For the condition of 40\({}^{\circ}\), the fraction of the data without solution (NaN) was largest for method \(D\) (no solution) followed by _E, C_, \(B\) and \(A\).