## 5 Evaluation for Lunar NHRO Orbiters for NAV/COM Applications
The obtained results are compared with the a posteriori synchronization method based on GPS satellites proposed in [38] in which, after an independent orbit determination, the GPS satellites are used for Time Transfer to the Moon orbiting spacecraft. To mitigate the simplified clock model errors, the time span for estimating the clock parameters was chosen to be equal to 3 h.  
In addition, in this case, the results are encouraging and always better than the ones obtained in [38]. Figures 9 and 10 report the histograms of the RMS error for 500 Monte Carlo runs with and without RR measurements, compared with the method proposed in [38]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Inter-spacecraft Range error (std) & 1 m \\ Inter-spacecraft Range-Rate error (std) & 0.06 mm/s \\ Measurements Interval & 15–30–60 min \\ Time Span for OD & 1–15.5–2 T (= 6.59 days) \\ Time Span for Sync & 3 h \\ Reference Orbit Position error (std) & 100 m \\ Reference Orbit Velocities error (std) & 1 mm/s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters used for the performance evaluation. Figure 7: Histograms for the rms orbit error with 500 Monte Carlo runs, using range and range-rate measures, (**top**) Earth-based OD, (**bottom**) Autonomous OD. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{6}{c}{**Earth ODT Position-DRMS Error in Meters (90 th Percentile)**} \\ \hline  & \multicolumn{2}{c}{**NORR**} & \multicolumn{2}{c}{**RR**} \\ \hline
**int/\(T_{s}\)** & **15 min.** & **30 min.** & **60 min.** & **15 min.** & **30 min.** & **60 min.** \\ \hline
6.59 days (1 T) & 1.97 & 2.86 & 3.96 & 0.74 & 1.01 & 1.44 \\
9.89 days (1.5 T) & 1.05 & 1.49 & 2.15 & 0.32 & 0.46 & 0.66 \\
13.2 days (2 T) & 0.67 & 0.94 & 1.32 & 0.23 & 0.33 & 0.45 \\ \hline \multicolumn{6}{c}{**Autonomous ODT Position-DRMS Error in Meters (90 th Percentile)**} \\ \hline  & \multicolumn{2}{c}{**NORR**} & \multicolumn{2}{c}{**RR**} \\ \hline
**int/\(T_{s}\)** & **15 min.** & **30 min.** & **60 min.** & **15 min.** & **30 min.** & **60 min.** \\ \hline
6.59 days (1 T) & 5.74 & 8.14 & 11.80 & 3.77 & 5.71 & 7.78 \\
9.89 days (1.5 T) & 0.96 & 1.29 & 1.81 & 0.49 & 0.67 & 1.00 \\
13.2 days (2 T) & 0.32 & 0.46 & 0.62 & 0.21 & 0.30 & 0.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: 90 th percentile of the DRMS position error (in meters) for different time spans and measurement rates int and measurement time span, \(T_{s}\). Figure 8: Histograms for the rms orbit error with 500 Monte Carlo runs, using only range measures, (**top**) Earth-based OD, (**bottom**) Autonomous OD. Figure 9: _Cont._  
Figure 10: Histograms for the rms timing error with 500 Monte Carlo runs, using only range measures, **(top)** GNSS timing, **(bottom)** Autonomous timing. Figure 9: Histograms for the RMS timing error with 500 Monte Carlo runs, using range and range-rate measures, **(top)** GNSS timing, **(bottom)** Autonomous timing. In Table 4, more results for the different measurement rates are reported. As before, the 90 th percentile of the RMS error obtained for each run on 500 runs is reported for both cases and using the GNSS satellite or the, here proposed, autonomous solution. These results show that, without the need for an additional payload for deep-space reception of the GPS signal, it is possible to obtain high synchronization performance for the constellation of NHRO satellites with an RMS error of the order of one nanosecond on a time span of three hours.