## 4 Simulation and Analysis
### Acceptable URA and \(P_{\text{sat}}\)  
To obtain an acceptable second group of parameters, the effect of a different second group of parameters on the integrity risk was further discussed. Based on the analysis, the change in \(P_{\text{sat}}\) had a negligible effect on global integrity performance. Therefore, we mainly focused on analyzing acceptable _URA_ under a different \(P_{\text{sat}}\). The 24 GPS + 27 BDS and 23 GPS + 26 BDS satellites (by removing one MEO satellite from GPS and BDS) were chosen as the baseline and depleted constellation configurations, respectively. The global coverage results are shown in Figure 4. The \(P_{\text{sat}}\) in the left, middle and right panels are set to \(10^{-3}\), \(10^{-4}\) and \(10^{-5}\), respectively. It can be observed from Figure 4 that the global coverage decreased with increasing _URA_. Due to the poorer satellite geometry, the coverage of the depleted constellation was always smaller than that of the baseline constellation. Table 3 shows acceptable _URA_ with different \(P_{\text{sat}}\) and integrity risk requirement. From Table 3, under the baseline constellation, _URA_ should be better than 0.88 and 1.14 m when \(P_{\text{sat}}\) is \(10^{-4}\) and \(10^{-5}\), respectively, such that more than 99.5% of global regions can satisfy the allocated integrity risk requirement of a single-satellite fault mode: 4.5 \(\times\)\(10^{-8}\). More than 95% of global regions can meet the integrity risk requirement of \(10^{-7}\) when \(P_{\text{sat}}\) is \(10^{-3}\) and _URA_ is smaller than 0.72 m. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multirow{2}{*}{**Value**} & \multirow{2}{*}{**Increased by \#**} & \multicolumn{4}{c}{**Worst-Case Integrity Risk**} & \multicolumn{4}{c}{**Coverage (99.5\%)**} \\ \cline{3-8}  & & & **Average** & **Maximum** & **Average** & **Maximum** & **IRreq =** & **IRreq =** \\  & & & **WIR** & _WIR_ & _dWIR_ & _dWIR_ & **9 \(\times\) 10\({}^{-8}\)** & **4.5 \(\times\) 10\({}^{-8}\)** \\ \hline \multirow{4}{*}{_URA_ (m)} & \multirow{2}{*}{\(1.0\)} & \(15\%\) & \(1.37\times 10^{-8}\) & \(4.65\times 10^{-6}\) & \(4.20\times 10^{-9}\) & \(1.43\times 10^{-6}\) & 98.17\% & 97.41\% \\  & & 30\% & \(3.14\times 10^{-8}\) & \(8.14\times 10^{-6}\) & \(8.70\times 10^{-9}\) & \(2.96\times 10^{-6}\) & 96.23\% & 94.82\% \\ \cline{2-8}  & \multirow{2}{*}{\(1.5\)} & \(15\%\) & \(2.92\times 10^{-7}\) & \(2.57\times 10^{-5}\) & \(9.62\times 10^{-8}\) & \(8.11\times 10^{-6}\) & 73.55\% & 69.22\% \\  & & 30\% & \(7.23\times 10^{-7}\) & \(3.57\times 10^{-5}\) & \(1.97\times 10^{-7}\) & \(1.67\times 10^{-5}\) & 63.01\% & 57.61\% \\ \cline{2-8}  & \multirow{2}{*}{\(2.0\)} & \(15\%\) & \(2.24\times 10^{-6}\) & \(5.07\times 10^{-5}\) & \(8.54\times 10^{-7}\) & \(1.53\times 10^{-5}\) & 41.51\% & 34.74\% \\  & & 30\% & \(4.84\times 10^{-6}\) & \(7.57\times 10^{-5}\) & \(1.73\times 10^{-6}\) & \(3.12\times 10^{-5}\) & 19.71\% & 12.60\% \\ \hline \multirow{4}{*}{\(P_{\text{sat}}\)} & \multirow{2}{*}{\(10^{-5}\)} & \(15\%\) & \(1.07\times 10^{-8}\) & \(1.82\times 10^{-6}\) & \(9.60\times 10^{-9}\) & \(8.12\times 10^{-7}\) & 97.79\% & 96.00\% \\  & & 30\% & \(1.21\times 10^{-8}\) & \(2.05\times 10^{-6}\) & \(1.97\times 10^{-8}\) & \(1.67\times 10^{-6}\) & 97.34\% & 95.78\% \\ \cline{2-8}  & \multirow{2}{*}{\(10^{-4}\)} & \(15\%\) & \(1.07\times 10^{-7}\) & \(1.82\times 10^{-5}\) & \(1.22\times 10^{-8}\) & \(2.25\times 10^{-6}\) & 90.45\% & 85.65\% \\  & & 30\% & \(1.21\times 10^{-7}\) & \(2.05\times 10^{-5}\) & \(2.43\times 10^{-8}\) & \(4.50\times 10^{-6}\) & 89.80\% & 84.67\% \\ \cline{2-8}  & \multirow{2}{*}{\(10^{-3}\)} & \(15\%\) & \(1.05\times 10^{-6}\) & \(1.79\times 10^{-4}\) & \(9.51\times 10^{-7}\) & \(8.03\times 10^{-5}\) & 72.91\% & 69.56\% \\  & & 30\% & \(1.19\times 10^{-6}\) & \(2.02\times 10^{-4}\) & \(1.95\times 10^{-6}\) & \(1.65\times 10^{-4}\) & 72.26\% & 68.91\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Global worst-case integrity risk performance and availability coverage with different _URA_ and \(P_{\text{sat}}\).