## 4 Simulation and Analysis
### Impact of URA and \(P_{\text{sat}}\)  
To explore the impact of the improved _URA_ and \(P_{\text{sat}}\) on the integrity risk, a global simulation was carried out based on Equations (7) and (8). We discussed the influence of the improved integrity parameters on integrity risk from three aspects: global worst-case integrity risk, global availability and variation of the global worst-case integrity risk error. The corresponding results are shown in Figures 1-3. When we analyzed the influence of the changes to _URA_ or \(P_{\text{sat}}\) on integrity performance, the other parameters remained unchanged. The top and bottom panels of (a) and (b) in Figures 1-3, respectively, represent selected parameters that increased by 15 and 30% from the true parameters. In panel (a), \(P_{\text{sat}}\) was set to \(10^{-4}\) and _URA_ varied in columns from left to right as 1.0, 1.5 and 2.0 m, respectively. In panel (b) of Figures 1-3, _URA_ was set to 1.5 m, and \(P_{\text{sat}}\) varied by column from left to right as \(10^{-5}\), \(10^{-4}\) and \(10^{-3}\), respectively. Figure 1: Global worst-case integrity risk with different _URA_ and \(P_{\text{sat}}\). (**a**) Global worst-case integrity risk with different _URA_; (**b**) Global worst-case integrity risk with different _P_sat. Figure 2: Global availability with different _URA_ and \(P_{\text{sat}}\). (**a**) Global availability with different _URA_; (**b**) Global availability with different _P_sat. As shown in Figure 1, the global integrity risk increased with _URA_ and \(P_{\text{sat}}\) growth. At equivalent deviation levels, _URA_ had a significantly greater impact on global integrity risk than did \(P_{\text{sat}}\). Figure 2 demonstrates that lower _URA_ and \(P_{\text{sat}}\) values led to higher global availability. A 30% increase in \(P_{\text{sat}}\) had a negligible effect on global availability, but an increase in _URA_ led to a substantial decrease in global availability. Figure 3 shows that an increase in _URA_ resulted in a more substantial impact on the global worst-case integrity risk error than that of \(P_{\text{sat}}\). However, in specific areas with poor geometry, such as North America, a \(P_{\text{sat}}\) increase resulted in a higher global worst-case integrity risk error compared to increased _URA_. Furthermore, in comparison to North and South America, the Asia-Pacific region demonstrated superior performance integrity due to a greater number of available IGSO satellites from BDS. Consequently, the regions featuring poorer geometry had higher vulnerabilities to _URA_ and \(P_{\text{sat}}\) changes. Better satellite geometry can be advantageous for reducing integrity losses resulting from improved _URA_ and \(P_{\text{sat}}\). Table 2 presents the global worst-case integrity risk performance and availability coverage for different _URA_ and \(P_{\text{sat}}\). Table 2 shows that the global average _WIR_, _dWIR_ and availability are significantly more affected by an increase in _URA_ than \(P_{\text{sat}}\). When IRreq = 4.5 \(\times\) 10\({}^{-8}\) and _URA_ increased by 15 to 30% from 1.5 m, the average _WIR_ and _dWIR_ increased by 4.31 \(\times\) 10\({}^{-7}\) and 1.01 \(\times\) 10\({}^{-7}\), respectively. As a consequence, global availability coverage decreased by 22.14%. When \(P_{\text{sat}}\) was 10\({}^{-4}\), an increase of 15 to 30% resulted in an increase of only 1.4 \(\times\) 10\({}^{-8}\) and 1.21 \(\times\) 10\({}^{-8}\) in average _WIR_ and _dWIR_, respectively, and global availability dropped by 0.98%. Under the same conditions, when \(P_{\text{sat}}\) was 10\({}^{-3}\), the impact of increased \(P_{\text{sat}}\) on average _WIR_ and availability was also not significant. However, the maximum _WIR_ and _dWIR_ increased by 2.3 \(\times\) 10\({}^{-5}\) and 8.74 \(\times\) 10\({}^{-5}\), respectively, which was higher than the maximum _WIR_ and _dWIR_ caused by an increase of 30% in _URA_ from 2.0 m. This indicated that changes in _URA_ had a significant impact on the integrity risk and availability of all regions worldwide.