## 3 Integrity Monitoring Method of Space-Ground Integration
### Simulation Results and Sensitivity Analysis
#### 3.4.2 Simulation of GNSS Integrity Service Performance Under LEO Constellation Enhancement
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Constellations** & **BDS-3** & **GPS** \\ \hline User Range Accuracy (URA) & 2 m & 1 m \\ \hline User Range Error (URE) & \multicolumn{2}{c}{URE = 2/3 \(\times\) URA} \\ \hline Satellite Fault Rate (\(\text{R}_{\text{sat}}\)) & \(1\times 10^{-5}/\text{h}\) & \(1\times 10^{-5}/\text{h}\) \\ \hline Average Duration of Satellite Fault (\(\text{MTTN}_{\text{sat}}\)) & 1 h & 1 h \\ \hline Satellite Fault Probability (\(\text{P}_{\text{sat}}\)) & \(1\times 10^{-5}\) & \(1\times 10^{-5}\) \\ \hline Constellation Fault Rate (\(\text{R}_{\text{const}}\)) & \(6\times 10^{-5}/\text{h}\) & \(1\times 10^{-9}/\text{h}\) \\ \hline Average Duration of Constellation Fault (\(\text{MTTN}_{\text{const}}\)) & 1 h & 10 h \\ \hline Constellation Fault Probability & \(6\times 10^{-5}\) & \(1\times 10^{-8}\) \\ \hline \hline \end{tabular} Note: \(\text{P}_{\text{sat}}\) = \(\text{R}_{\text{sat}}\times\text{MTTN}_{\text{sat}}\), \(\text{P}_{\text{const}}\) = \(\text{R}_{\text{const}}\times\text{MTTN}_{\text{const}}\).  
\end{table} 
Table 10: GNSS constellation parameter settings for simulations. \begin{table}
\begin{tabular}{c c} \hline \hline
**User Range Accuracy, URA** & **0.3 m** \\ \hline User Range Error, URE & \multicolumn{2}{c}{URE = 2/3 \(\times\) URA} \\ \hline Satellite Fault Probability (\(\text{P}_{\text{sat, LEO}}\)) & Case 1 & \(\text{P}_{\text{sat, LEO}}\) = 1 \(\times\) 10\({}^{-5}\), \(\text{P}_{\text{const, LEO}}\) = 1 \(\times\) 10\({}^{-5}\) \\ \hline Satellite Fault Probability (\(\text{P}_{\text{sat, LEO}}\)) & Case 2 & \(\text{P}_{\text{sat, LEO}}\) = 1 \(\times\) 10\({}^{-4}\), \(\text{P}_{\text{const, LEO}}\) = 1 \(\times\) 10\({}^{-4}\) \\ \hline Constellation Fault Probability (\(\text{P}_{\text{const, LEO}}\)) & Case 3 & \(\text{P}_{\text{sat, LEO}}\) = 1 \(\times\) 10\({}^{-4}\), \(\text{P}_{\text{const, LEO}}\) = 1 \(\times\) 10\({}^{-3}\) \\ \hline  & Case 4 & \(\text{P}_{\text{sat, LEO}}\) = 1 \(\times\) 10\({}^{-3}\), \(\text{P}_{\text{const, LEO}}\) = 1 \(\times\) 10\({}^{-3}\) \\ \hline  & Case 5 & \(\text{P}_{\text{sat, LEO}}\) = 1 \(\times\) 10\({}^{-3}\), \(\text{P}_{\text{const, LEO}}\) = 1 \(\times\) 10\({}^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Simulation parameters for LEO satellites in the case where LEO satellites act as navigation satellites. at 99.5% availability are calculated for each user, denoted as HPL (0.995) and VPL (0.995), respectively. Finally, protection level world maps are generated and the global coverage results under CAT-I are computed. The pseudocode for this simulation process is shown in Figure 12.  
In this paper, the protection levels are calculated based on the advanced receiver autonomous integrity monitoring (ARAIM) [7]. It is worth mentioning that this work only considers the integrity performance of pseudorange-based positioning systems, in particular, single-point positioning. Most of the previous studies on BDS-3 integrity performance evaluation were also concentrated on single-point positioning for aviation applications and thus, the simulation analyses below can preliminarily demonstrate the integrity performance difference between the BDS-3 and the next-generation BDS (initial design). Given that carrier-phase positioning integrity will be of great significance for novel applications such as in the automotive industry, this topic will be investigated in our future work. The fundamental principles of ARAIM are briefly described as follows [40; 41; 42]: First, the fault modes that need to be monitored are determined. Each fault mode assumes that a specific subset of the satellites is faulted. For example, H\({}_{0}\) assumes all satellites are healthy, H\({}_{1}\) assumes GPS satellite 1 is faulted, H\({}_{10}\) assumes the GPS constellation is faulted, and H\({}_{21}\) assumes the GPS constellation and BeiDou satellite 1 are both faulted. The prior probability of each fault mode is determined based on the satellite fault probabilities and the constellation fault probabilities.