# Impact Analysis of Satellite Geometry Variation on ARAIM Integrity Risk over Exposure Interval
## 4 Experiment and Analysis
### Tightness Analysis of Integrity Risk Evaluate Results
\begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Value** \\ \hline \(P_{\text{EA,REQ}}\) & V-ARAIM: \(3.9\times 10^{-6}/150\) sH-ARAIM: \(5.0\times 10^{-7}/\text{h}\) \\ \(R_{\text{sat}}\) & \(10^{-5}/\text{h}\) for both GPS and Galileo \\ \(R_{\text{const}}\) & \(10^{-8}/\text{h}\) (GPS): \(1\times 10^{-4}/\text{h}\) (Galileo) \\ MFD (mean fault duration) & 1 h for both GPS and Galileo \\ NES & \(t_{\text{exp}}/t_{\text{s}}\) for both integrity and continuity \\ \(t_{\text{exp}}\) & 150 [s] (LPV-200); 3600 [s] (RNP 0.1) \\ \(t_{\text{a}}\) & 6 [s] (LPV-200); 10 [s] (RNP 0.1) \\ \(t_{\text{s}}\) & 2 [s] \\ \(P_{\text{NM}}\) & \(6\times 10^{-8}\) \\ Alarm limit & VAL: 35 [m]; HAL: 185 [m] \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._the empirical cumulative distribution functions (ECDFs) based on the actual integrity risk and reference were very close. This means that the proposed method effectively reflects the integrity risk reference. However, in cases of strong error correlation, the difference between the actual integrity risk results and reference increased. This is attributed to our assumption that \(\text{HMI}_{\text{TTA}/}^{\text{E}}\) is independent of time during the integrity risk evaluation, which leads to conservative evaluation results as the positioning error correlation increases. The more conservative the actual integrity risk, the higher the likelihood of a false decision occurring in the subsequent performance analysis is. The false decision implies that the integrity risk reference is below \(P_{\text{HMI,REQ}}\), but according to the proposed method, we conclude that ARAIM is not available. In order to analyze whether the evaluation results are too conservative, we further analyzed the bounding tightness of the actual integrity risk to the reference. We chose the ratio between the actual integrity risk and the reference as the tightness index. It should be noted that we only considered the reference results below \(10^{-7}/\text{approach}\) for analysis, as results greater than this threshold would not lead to a false decision. As shown in Figure 4, the tightness index of the proposed method is mostly less than 2. This implies that a false decision occurs only when the reference integrity risk is extremely close to the predefined \(P_{\text{HMI,REQ}}\), for instance, falling within the range of \(5\times 10^{-8}/\text{approach}\) to \(1\times 10^{-7}/\text{approach}\). Furthermore, according to the analysis by [20], due to the high sensitivity of integrity risk to geometry variation, it usually either falls significantly below the \(P_{\text{HMI,REQ}}\) or notably exceeds the requirement, and rarely falls near the \(P_{\text{HMI,REQ}}\). The bounding tightness analysis implies that the proposed method has the ability to verify the ARAIM integrity performance in an LPV-200 approach. Figure 4: Histogram of the tightness index of the proposed method under LPV-200 situation. The subfigure (**a,b**) indicates that \(\beta\) is 10 and 1000, respectively. Figure 3: Integrity risk evaluation results of different methods under LPV-200 situation. The subfigure (**a,b**) indicates that \(\beta\) is 10 and 1000, respectively. Figures 5 and 6 illustrate the integrity evaluation results under the RNP 0.1 flight phase. Compared with LPV-200, the tightness index of the proposed method is noticeably increased under RNP 0.1, especially when \(\beta\) = 1000. In this scenario, the bounding tightness of the proposed method significantly deteriorates, and the maximum tightness index reaches nearly 10. This indicates that the evaluation error of the proposed method increases with the lengthening of the exposure interval. Fortunately, the AL during the RNP 0.1 phase is relatively loose, implying that the integrity risk is significantly lower than the \(P_{\text{HMI,REQ}}\). The high tightness index of the proposed method will not cause many false decisions. This conclusion will be further proved in the subsequent global simulation analysis.