# Integrity Monitoring of GNSS Constellations with Only LEO-PNT Satellites +
## 4 Conclusions  
This paper explores the different options for providing GNSS integrity services when using only an LEO mega-constellation as infrastructure. This study has focused on an automotive user whose integrity FTA has been reused from the Ithaca project. The integrity monitor has been contextualized in this FTA and dimensioned in terms of MDB, Pmd, and Pfa.  
The barrier required for the integrity monitor has been identified and formulated in three different manners, considering a basic WLSQ approach with a priori information. The impact of the a priori formulation on the responsiveness of the barrier (and therefore the TTA) has been initially addressed using a simple example. The error budget for the GNSS on board the LEO mega-constellation has also been analyzed.  
Based on the results obtained with the simulations run by the SVS, it can be concluded that the targeted sigma monitor of 19 cm, resulting from the MDB, Pfa, and Pmd analyses, is achievable, especially when considering the mega-constellations that are projected, which encourages us to continue improving the concept of integrity by utilizing LEO satellites.  
**Author Contributions:** Conceptualization, C.C.C.; methodology, C.C.C. and L.G.I.; software, L.G.I.; validation, C.C.C. and L.G.I.; formal analysis, C.C.C. and L.G.I.; investigation, C.C.C. and L.G.I.; writing--original draft preparation, C.C.C. and L.G.I; writing--review and editing, C.C.C. and L.G.I; supervision, C.C.C. and A.J.M.; project administration, C.C.C. and A.J.M. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The datasets presented in this article are not readily available because the data are part of an ongoing study.  
**Conflicts of Interest:** The authors declare no conflicts of interest. The authors are employed by GMV.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \begin{tabular}{c} **LEO** \\ **Barrier** \\ \end{tabular} & \begin{tabular}{c} **LERE Value** \\ **[cm]** \\ \end{tabular} & \begin{tabular}{c} _w/p_ \\ **Ratio** \\ \end{tabular} & \begin{tabular}{c} **Number of Satellites Used to** \\ **Meet Requirements (0.19 m)** \\ **at 67/95/99.7 Percentile** \\ \end{tabular} & \begin{tabular}{c} **Sigma Monitor Values [m]** \\ **Achieved at** \\ 67/95/99.7 Percentile** \\ \end{tabular} & \
\begin{tabular}{c} **Time \% with** \\ **Achieved at** \\ 67/95/99.7 Percentile** \\ \end{tabular} \\ \hline \hline \multirow{8}{*}{
\begin{tabular}{c} **23 cm** \\ \end{tabular} } & \multirow{4}{*}{4} & 67.0\% & 2 & 67.0\% & 0.21 & 38.264 \\  & & 95.0\% & 2 & 95.0\% & 0.47 & 38.264 \\  & & 99.7\% & 2 & 99.7\% & - & 38.264 \\ \cline{2-7}  & \multirow{4}{*}{16} & 67.0\% & 2 & 67.0\% & 0.23 & 38.264 \\  & & 95.0\% & 2 & 95.0\% & 0.93 & 38.264 \\  & & 99.7\% & 2 & 99.7\% & - & 38.264 \\ \cline{2-7}  & \multirow{4}{*}{100} & 67.0\% & 3 & 67.0\% & 0.25 & 48.553 \\  & & 95.0\% & 4 & 95.0\% & 2.33 & 75.563 \\  & & 99.7\% & 4 & 99.7\% & - & 75.563 \\ \cline{2-7}  & \multirow{4}{*}{50 cm} & 67.0\% & - & 67.0\% & 0.46 & - \\  & & 95.0\% & - & 95.0\% & 1.03 & - \\  & & 99.7\% & - & 99.7\% & - & - \\ \cline{2-7}  & \multirow{4}{*}{16} & 67.0\% & - & 67.0\% & 0.5 & - \\  & & 95.0\% & - & 95.0\% & 2.06 & - \\  & & 99.7\% & - & 99.7\% & - & - \\ \cline{2-7}  & \multirow{4}{*}{100} & 67.0\% & - & 67.0\% & 0.55 & - \\  & & 99.7\% & - & 99.7\% & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 8: Summary of results from a priori strategy for IoD simulations.