# Impact Analysis of Satellite Geometry Variation on ARAIM Integrity Risk over Exposure Interval
## 4 Experiment and Analysis
### Evaluation of PHMI for Solution Separation Araim  
To analyze the impact of satellite geometry variations on the integrity performance of the ARAIM, three simulations were conducted under different situations of satellite geometry variation: the first simulation situation is the LPV-200 in a nominal situation, with an exposure interval time of 150 s. The second is the LPV-200 under a one-satellite outage situation. The third situation is RNP 0.1 phase, with an exposure interval time of 3600 s. For the one-satellite outage situation, a satellite was randomly selected as an outage within the exposure interval, and this outage lasted for 30 s. These settings are commonly employed to simulate ionospheric scintillation conditions [18]. The underlying vital assumptions and parameters specified in [13] are used to perform the simulations. The dual-frequency 24 GPS/Galileo nominal constellation with formal parameters was used, and the results were assessed for V-ARAIM (LPV-200) and H-ARAIM (RNP 0.1) operation, respectively. The global simulation was based on a 10\({}^{\circ}\)\(\times\) 10\({}^{\circ}\) user grid, for 24 h with a sampling interval of 10 min, which generated 144 samples per user grid. The cut-off  
Figure 6: Histogram of the tightness index of the proposed method under RNP-0.1 situation. The subfigure (**a,b**) indicates that \(\beta\) is 10 and 1000, respectively. Figure 7: Changes in satellite number and integrity risk in 1 h exposure interval. Pink squares indicate areas where the NES-based method is higher than the reference value. elevation angle was set as \(5^{\circ}\) to balance the observation accuracy and visible satellite. The availability of a grid point can be determined by calculating the ratio of epochs where the evaluated integrity risk is less than the required \(P_{\text{HMI,REQ}}\) to the total number of epochs during the simulation duration. The global availability coverage was used as the metric to reflect the global integrity performance, which was calculated as the ratio between the number of user grids with the integrity risk smaller than the required \(P_{\text{HMI,REQ}}\) and the total number of grids. In addition, we chose the minimum value to represent the integrity risk throughout the exposure interval evaluated by the NES-based ARAIM. Figure 8 shows the global availability of V-ARAIM in the nominal LPV-200 situation with \(\beta=100\). According to Figure 8, the availability of the ARAIM under the traditional method is very close to the actual availability. This indicates that the impact of satellite geometry variation on the integrity performance of the ARAIM is extremely low at a short exposure interval. Furthermore, we summarize the global availability results of the ARAIM under different time correlation strengths of positioning error in Table 2. It can be seen that under weak correlation (\(\beta=10\)), the ARAIM's average availability loss is the lowest. When \(\beta\) increases to 100, the average availability loss increases from 0.24% to 0.82%. This is because the weak geometry could continue to affect multiple epochs as the correlation strength of positioning error increases. However, this does not imply that the average availability of the ARAIM will consistently decrease with the increase in \(\beta\). When \(\beta\) is equal to 1000, the average availability increases by 0.12% compared to \(\beta=100\). This is because when the correlation is strong, the integrity performance of the ARAIM mainly depends on the first epoch in the exposure interval, and there may be only one opportunity for an HMI event to occur in this interval. According to the above analysis, under a short exposure interval, the loss in availability caused by the geometry constant assumption is low and does not change significantly with the \(\beta\) value. As a result, traditional methods do not result in overly optimistic integrity risk evaluation results under a short exposure interval. Figure 9 shows the global availability of V-ARAIM in the LPV-200 under a one-satellite outage situation.