## 5 Conclusions  
To investigate the effect of improved integrity parameters on RAIM integrity risk, a conservative integrity risk estimation method based on the worst-case protection concept was developed. The integrity-related parameters were divided into four groups. The worst-case integrity risk was estimated by varying the magnitude of the first group of parameters to acquire the maximum integrity risk. A sensitivity analysis was conducted for the second group of parameters, \(P_{\rm sat}\) and _URA_, while considering the influence of the third and fourth groups of parameters on integrity risk. The acceptable second group of parameters was provided based on the global simulation experiment.  
The simulation results demonstrated that changes in _URA_ significantly affected integrity risk and availability. Conversely, alterations in \(P_{\rm sat}\) had a relatively minor impact on integrity risk and availability, except in areas with disadvantaged satellite geometry. The determination of _URA_ requires closer attention. When IRreq = 4.5 \(\times\) 10\({}^{-8}\), \(P_{\rm sat}\) was 10\({}^{-4}\) and _URA_ was 1.5 m, _URA_ and \(P_{\rm sat}\) both increased by 30%, whereas the global availability coverage decreased by 22.14 and 0.98%, respectively. With the higher requirement of \(P_{\rm fa}\) and VAL, the restriction on _URA_ became more stringent. Moreover, when the single-satellite fault mode was allocated half of the vertical integrity risk requirement of LPV-200, _URA_ values had to be better than 0.88 and 1.14 m, respectively, when \(P_{\rm sat}\) was 10\({}^{-4}\) and 10\({}^{-5}\) so that more than 99.5% of global regions could meet the allocated integrity risk requirement. Currently, GPS, BDS and Galileo have the potential to support RAIM to satisfy the requirement for LPV-200.  
Conceptualization, L.W., L.L. and R.L.; methodology, L.W. and L.L.; validation, R.L., M.L. and L.C.; formal analysis, M.L. and L.C.; investigation, L.L. and R.L.; resources, L.W. and L.L.; writing--original draft preparation, L.W.; writing--review and editing, L.W. and L.L.; visualization, L.W., R.L. and M.L.; supervision, M.L. and L.C.; project administration, L.L.; funding acquisition, L.L. All authors have read and agreed to the published version of the manuscript.  
This research was jointly funded by the National Key Research and Development Program (No. 2021 YFB3901300), the National Natural Science Foundation of China (Nos. 61773132, 61633008, 61803115, 62003109), the 145 High-tech Ship Innovation Project sponsored by the Chinese Ministry of Industry and Information Technology, the Heilongjiang Province Research Science Fund for Excellent Young Scholars (No. YQ2020F009), and the Fundamental Research Funds for Central Universities (Nos. 3072019 CF0401, 3072020 CFT0403).  
The simulation software supporting this research can be found at the hyperlinks as: [[https://gps.stanford.edu/resources/software-tools/maast](https://gps.stanford.edu/resources/software-tools/maast)]([https://gps.stanford.edu/resources/software-tools/maast](https://gps.stanford.edu/resources/software-tools/maast)), accessed on 4 June 2023.  
The authors declare no conflict of interest.