## 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  
Based on the LEO constellation configuration above, simulations are carried out to evaluate the integrity performance with LEO augmentation. Table 10 presents the preliminary parameter settings for the GNSS constellations. This paper analyzes the GNSS integrity service performance using the CAT-I navigation performance requirements as an example. The navigation performance requirements for CAT-I are shown in Table 1.  
Figure 11: PDOP world map for BDS-3 and LEO satellites. Figure 10: PDOP world map for BDS-3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number of Satellites That Track the Same GNSS Satellite from** & **Minimum** & **Average** & **Maximum** \\  & **the Constellation Below** & & \\ \hline BDS-3 & 15 & 18.2 & 21 \\ \hline GPS & 13 & 16.5 & 18 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: LEO coverage for GNSS satellite. Before comparing the integrity performance of the two schemes \"LEO as a space monitoring station\" and \"LEO as a navigation satellite\", the parameter settings for these two schemes are given first. If LEO satellites act as space monitoring stations, employing LEO satellites can help detect BeiDou satellite and constellation faults more quickly, thereby reducing the average duration of BeiDou satellite and constellation faults. This benefits from the fact that LEO satellites provide additional observations for BeiDou satellites and offer fast communication capability between LEO satellites and BeiDou satellites. This paper preliminarily assumes that employing LEO satellites can reduce the duration of BeiDou satellite and constellation faults by half, resulting in an average fault duration of 30 min. Therefore, the BeiDou satellite fault probability is set to \(5\times 10^{-6}\) and the BeiDou constellation fault probability is set to \(3\times 10^{-5}\) in this case. It is worth mentioning that in this case, users only utilize GNSS satellites for navigation and thus, the number of visible satellites is not affected by the introduction of LEO satellites. If LEO satellites act as navigation satellites, it is necessary to consider the parameters such as the URA, URE, satellite fault probability, and constellation fault probability for the LEO constellation. Table 11 presents the preliminary settings for these parameters. In this table, the URA for LEO satellites is set to 0.3 m [39]. Additionally, this paper considers multiple sets of parameters settings on LEO satellite fault probability and LEO constellation fault probability to provide a sensitivity analysis. To quantitatively display the integrity performance, this paper will provide protection level world maps and global coverage results under the CAT-I navigation performance requirements. The algorithms and simulation steps are as follows: first, a user grid is divided on the Earth's surface into 5-degree by 5-degree cells, with each grid point representing one user. For each user, the horizontal and vertical protection level (HPL and VPL) are calculated over a continuous period of 10 days, with a time step of 600 s, resulting in 1440 HPL and VPL values for each user. Based on this time series, the HPL and VPL