# Integrity Analysis for GPS-Based Navigation of UAVs in Urban Environment
## 3 Simulation
### Simulation Results
Similarly, HDOP is always less than 2 and 3 for cut-off elevations at or below 15\({}^{\circ}\) and 20\({}^{\circ}\), respectively. At the 25\({}^{\circ}\) level, the probability of HDOP being higher than 5 is approximately 1.6%. Starting from a cut-off elevation of 30\({}^{\circ}\), availability issues begin to appear due to insufficient number of visible satellites. When analyzing vertical performance, we can see that VDOP coefficients are always less than 2 at 5\({}^{\circ}\) cut-off elevation without observable risk and with 3% risk at 10\({}^{\circ}\). VDOP at these cut-off elevations is always less than 3. At 15\({}^{\circ}\), VDOP remains below 5 with no integrity risk. At 20\({}^{\circ}\), while the risk is \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**GDOP**} & \multirow{2}{*}{**Error Type**} & \multicolumn{3}{c}{**Absolute Error Statistics**} \\ \cline{3-5}  & & **Mean (m)** & **67 th Percentile (m)** & **95 th Percentile (m)** \\ \hline \multirow{3}{*}{**1.69**} & Horizontal (HDOP = 0.75) & 1.5131 & 1.5864 & 1.7707 \\ \cline{2-5}  & Vertical (VDOP = 1.33) & 6.2144 & 6.3695 & 6.7599 \\ \cline{2-5}  & Position (PDOP = 1.53) & 6.3973 & 6.5574 & 6.9605 \\ \hline \multirow{3}{*}{2.90} & Horizontal (HDOP = 1.39) & 3.3590 & 3.6096 & 4.2403 \\ \cline{2-5}  & Vertical (VDOP = 2.26) & 5.0558 & 6.4321 & 9.8960 \\ \cline{2-5}  & Position (PDOP = 2.65) & 6.2087 & 7.4673 & 10.6350 \\ \hline \multirow{3}{*}{4.85} & Horizontal (HDOP = 1.80) & 3.4340 & 3.5286 & 3.7666 \\ \cline{2-5}  & Vertical (VDOP = 3.92) & 8.4715 & 10.3767 & 15.1717 \\ \cline{2-5}  & Position (PDOP = 4.32) & 9.3049 & 11.0302 & 15.3726 \\ \hline \multirow{3}{*}{7.09} & Horizontal (HDOP = 3.13) & 3.3777 & 3.5354 & 3.9325 \\ \cline{2-5}  & Vertical (VDOP = 5.13) & 10.9519 & 11.5978 & 13.2235 \\ \cline{2-5}  & Position (PDOP = 6.01) & 11.4723 & 12.0931 & 13.6559 \\ \hline \multirow{3}{*}{13.56} & Horizontal (HDOP = 5.78) & 24.3396 & 26.8177 & 33.0549 \\ \cline{2-5}  & Vertical (VDOP = 10.07) & 53.0153 & 55.6420 & 62.2532 \\ \cline{2-5}  & Position (PDOP = 11.61) & 58.3893 & 61.8051 & 70.4026 \\ \hline \multirow{3}{*}{31.96} & Horizontal (HDOP = 14.82) & 58.9134 & 68.3176 & 91.9872 \\ \cline{2-5}  & Vertical (VDOP = 22.89) & 96.7132 & 109.5804 & 141.9660 \\ \cline{2-5}  & Position (PDOP = 27.27) & 113.2787 & 129.1622 & 169.1396 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Position error statistics for different DOP levels. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Mean** & **Sigma** & **Corrected Sigma** & **95 th Percentile** & **99 th Percentile** & **99.99998 th Percentile** \\ \hline
1.9420 m & 0.7606 m & 0.7479 m & 3.1722 m & 3.6819 m & 5.8306 m \\ \hline \hline \end{tabular}
\end{table} 
Table 5: UERE of employed GNSS receiver. about 4% for VDOP = 5, VDOP = 7 can be guaranteed. When the cut-off elevation is at or above 25\({}^{\circ}\), vertical positioning availability issues start to be observed. Using these distributions of HDOP and VDOP, achievable protection levels can be derived following Equation (6) for each cut-off elevation, to be used as indirect integrity measures instead of the corresponding non-observable position errors. The 99.9998 th percentiles of HDOP and VDOP distributions for each cut-off elevation are accepted for this purpose. Calculated horizontal and vertical protection levels with less than \(2\times 10^{-7}\)/h integrity risk are shown in Table 7 along with the corresponding DOP-based indirect protection levels. It should be noted that some values were not defined during the simulation. Because of unavailability issues, HPL cannot be defined at 30\({}^{\circ}\), and VPL cannot be defined for 25\({}^{\circ}\) and 30\({}^{\circ}\) cut off elevations. These cut-off elevations represent essential integrity risks for flights of UAVs with single-mode GPS-based navigation in urban environments. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\ \begin{tabular}{c} **Cut-off** \\ **Elevation** \\ \end{tabular}  } & \multirow{2}{*}{