# BDS-3 Integrity Risk Modeling and Probability Evaluation
## 4 Result and Discussion  
### Characterization of BDS-3 Signal-In-Space Ranging Errors  
As shown in Table 1, the signal-in-space ranging error (SISRE) is ones of the most important parameters to be characterized for integrity monitoring. The SISRE refers to the ranging error in the user's line of sight, caused by the satellite orbit error and the satellite clock error, usually related to the user's location on earth. For the detailed BDS-3 SISRE calculation, please refer to the reference [23]. The characterization of SISRE depends on the clock and orbit data generated by the Ground Operation Control Center. To investigate the BDS-3 SISRE characteristics, over one and a half years of BDS-3 D1-type navigation data [24], from 1 January 2019 to 31 July 2020, has been collected and the nominal BDS-3 navigation message accuracy were further evaluated. During this period, only navigation ephemerides marked as healthy were assessed in this paper. The long-term orbit errors of the broadcast ephemerides are illustrated in Figure 5. It shows that MEO type of satellites has the smallest orbital errors, followed by IGSO satellites, and GEO type has the largest orbital errors due to their weak geometric strength relative to the ground-based static monitoring stations. Figure 5: Statistical results for BDS-3 orbit errors in the along, cross and radial directions. The boxes in red colors indicate the MEO satellites, those in green colors for the IGSO satellites and blue for the GEO satellites. The box plot is constructed from the 2.5 th, 25 th, 50 th, 75 th and 97.5 th percentiles. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Confidence Levels** & **68\%** & **95\%** & **99\%** & **99.999\%** & **99.99999\%** \\ \hline Posterior anomaly number (0 anomalies) & 0.5 & 1.93 & 3.32 & 9.76 & 14.19 \\ Posterior anomaly number (1 anomalies) & 1.76 & 3.91 & 5.68 & 12.96 & 17.71 \\ Posterior anomaly number (2 anomalies) & 2.94 & 5.54 & 7.55 & 15.43 & 20.44 \\ Posterior anomaly number (3 anomalies) & 4.08 & 7.04 & 9.24 & 17.63 & 22.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: System design values of abnormal events under different confidence. Figure 6 presents the statistical results of the BDS broadcast clock errors. Referring to the precise clock products released by IGS, 95% of clock accuracy in an average range of 1 m can be derived for all BDS-3 satellites. Additionally, we can see that there still exist satellite-dependent clock biases for BDS-3 satellites, which could be partially linked to the lower accuracy of time group delay (TGD) parameters extracted from the BDS downlink navigation message [23]. A monthly statistical analysis of SISRE metrics of SISRE (orbit only), SISRE, SISRE (at the worst user location, WUL) and SISRE (95%) was carried out during the assessment period. As can be seen from Figure 7, the accuracy of SISRE orbit only of MEO and IGSO satellites is better than 0.1 m, but the clock error affects the SISRE accuracy greatly, which is 0.2-0.3 m on average for SISRE. However, in general, SISRE accuracy of MEO satellites is 95% better than 0.5 m and IGSO satellites better than 1 m. The SISRE accuracy of GEO satellites is poorer during the initial evaluation period, but from April 2020 onwards, its SISRE index is significantly improved and stabilized. Figure 6: Statistics of the BDS broadcast clock errors. The boxes in red colors indicate the MEO satellites, those in green colors for the IGSO and blue for the GEO satellites. The box plot is constructed from the 2.5 th, 25 th, 50 th, 75 th and 97.5 th percentiles. Figure 8 provides the SISRE results as a function of cumulative density function. The SISRE is plotted on a per satellite basis aggregating all data available in the analysis period. As can be seen from Figure 7, the MEO and IGSO satellites have the best SISRE performance with 95% up to 1 m, which are much better than the claimed SISRE Accuracy Standard (\(\leq\)2 m, 95%).