# Integrity Analysis for GPS-Based Navigation of UAVs in Urban Environment
## 3 Simulation
### Simulation Results
\begin{tabular}{c} **DOP** \\ **Type** \\ \end{tabular}  } & \multicolumn{6}{c}{**Percentage of DOP Values in a Given Ranges (\(\kappa\) = DOP Value)**} \\ \cline{3-10}  & & **x \textless{} 1** & **1 \textless{} x \textless{} 2** & **2 \textless{} x \textless{} 3** & **3 \textless{} x \textless{} 5** & **5 \textless{} x \textless{} 7** & **7 \textless{} x \textless{} 10** & **10 \textless{} x** & **N/A** \\ \hline \multirow{4}{*}{5\({}^{\circ}\)} & GDOP & 0 & 91.42 & 8.58 & 0 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & PDOP & 0 & 100 & 0 & 0 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & HDOP & 95.08 & 4.92 & 0 & 0 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & VDOP & 1.99 & 98.01 & 0 & 0 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & TDOP & 98.91 & 1.09 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{\({\mathbf{10}^{\circ}}\)} & GDOP & 0 & 56.25 & 43.75 & 0 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & PDOP & 0 & 78.99 & 21.01 & 0 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & HDOP & 73.81 & 26.19 & 0 & 0 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & VDOP & 0 & 96.97 & 3.03 & 0 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & TDOP & 79.13 & 20.87 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{\({\mathbf{15}^{\circ}}\)} & GDOP & 0 & 4.03 & 88.89 & 5.87 & 1.21 & 0 & 0 & 0 \\ \cline{2-10}  & PDOP & 0 & 27.53 & 70.68 & 1.79 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & HDOP & 50.81 & 49.19 & 0 & 0 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & VDOP & 0 & 82.82 & 15.39 & 1.79 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & TDOP & 23.65 & 74.50 & 1.06 & 0.75 & 0.04 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{\({\mathbf{20}^{\circ}}\)} & GDOP & 0 & 52.69 & 35.42 & 8.40 & 0.71 & 2.78 & 0 \\ \cline{2-10}  & PDOP & 0 & 1.45 & 72.72 & 20.62 & 1.89 & 2.72 & 0.60 & 0 \\ \cline{2-10}  & HDOP & 24.81 & 72.30 & 2.89 & 0 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & VDOP & 0 & 32.26 & 48.08 & 15.94 & 0.57 & 3.15 & 0 & 0 \\ \cline{2-10}  & TDOP & 2.23 & 73.95 & 13.59 & 6.76 & 1.94 & 1.53 & 0 & 0 \\ \hline \multirow{4}{*}{\({\mathbf{25}^{\circ}}\)} & GDOP & 0 & 7.42 & 41.97 & 20.47 & 13.35 & 12.60 & 4.19 \\ \cline{2-10}  & PDOP & 0 & 0 & 23.75 & 39.09 & 16.03 & 11.15 & 5.79 & 4.19 \\ \cline{2-10}  & HDOP & 5.67 & 66.79 & 19.29 & 6.67 & 0.93 & 0.39 & 0.26 & 0 \\ \cline{2-10}  & VDOP & 0 & 0.15 & 34.12 & 32.84 & 13.14 & 12.60 & 2.96 & 4.19 \\ \cline{2-10}  
As a complementary tool for integrity analysis, the time history of HDOP and VDOP coefficients during half-day simulation under different cut-off elevations can be used as shown in Figure 8. Horizontal dotted lines represent DOP-based indirect protection levels. The figure shows when, for how long and how often these protection levels are exceeded during the simulation period; therefore, a time-to-alert analysis can be conducted based on these graphs. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Cut-Off Elevation** & **HDOP-Based HPL** & **HPL (m)** & **VDOP-Based VPL** & **VPL (m)** \\ \hline
5\({}^{\circ}\) & 1.3373 & 7.7973 & 2.0839 & 12.1504 \\ \hline
10\({}^{\circ}\) & 1.6109 & 9.3925 & 2.5246 & 14.7199 \\ \hline
15\({}^{\circ}\) & 1.8723 & 10.9166 & 3.6817 & 21.4665 \\ \hline
20\({}^{\circ}\) & 2.7898 & 16.2662 & 9.5747 & 55.8262 \\ \hline
25\({}^{\circ}\) & 7.2001 & 41.9809 & N/A & N/A \\ \hline
30\({}^{\circ}\) & N/A & N/A & N/A & N/A \\ \hline \hline \end{tabular}
\end{table} 
Table 7: DOP-based Protection Levels. Figure 8: Time history of Horizontal DOP (HDOP) (**top**), Vertical DOP (VDOP) (**bottom**) during the simulated period. Below 20\({}^{\circ}\) cut-off elevation, both HDOP and VDOP coefficients are measurable for all time without any availability issues. Sharp increases in HDOP and VDOP values are observed above 20\({}^{\circ}\) and 25\({}^{\circ}\) cut-off elevations, respectively. Specified HPLs are not exceeded below 20\({}^{\circ}\) cut-off elevations.