## 6 Conclusions  
The results reported in the previous section open the way for various considerations. First of all, it was demonstrated that the proposed method could be successfully implemented and used in NHRO orbits, leading to precise orbit determination and timing with performances comparable to or better than those obtained by exploiting Earth-based measurement stations. In particular, concerning the case without the use of the range-rate measurements, the results for the autonomous orbit determination are similar to the Earth-based ones for a measurement time span of 9.89 days (1.5 T) and obtain better than the Earth-based if the time span is increased, bounding the 90 th percentile of the DRMS errors between 0.32 m and 0.62 m.  
On the other hand, in the case of the range and range rate measurements, the results for the autonomous orbit determination are similar to the Earth-based ones starting from a measurement time span of 9.89 days (1.5 T). They remain comparable also for longer time spans, bounding the 90 th percentile of the DRMS errors between 0.21 m and 0.43 m.  
Last but not least, in many cases, the 90 th percentile of the DRMS error of the proposed method is lower than one meter, obtaining ultra-precise orbit parameters for the spacecraft. This consideration is also true in the case of the very simple configuration that does not use the range-rate measurements, allowing for a simplified HW in the anchors. In addition, in this last case, for Time Spans longer than 1.5 T, the performances reach the meter or sub-meter levels. Concerning the synchronization performance, the proposed method always gives better results than the one proposed in [38] by the same authors. One of the reasons is that, in the proposed method, the timing accuracy does not depend on the spacecraft position accuracy and on the GNSS satellite's position accuracy, moreover, the propagation errors are lower (the range measurement from the GNSS satellite used for time synchronization in [18] depends, for example, also on the ionosphere delay). Coming to the application, the Lunar orbiting constellation in NHRO, it is possible to assume that the constellation can be used for navigation purposes due to its high OD&T performance also with no or minimal contact with the Earth, assuring an autonomous navigation service to other spacecraft and rovers. This is an important result because, as mentioned before, in the future, the number of missions to be controlled from the Earth will grow, leading to a possible capacity limit of the terrestrial Deep Space Network. Having \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{6}{c}{**Earth Based GNSS Timing RMS Error in ns (90 th Percentile)**} \\ \hline \multicolumn{6}{c}{**NORR**} & \multicolumn{6}{c}{**RR**} \\ \hline
**int/\(T_{s}\)** & **15 min.** & **30 min.** & **60 min.** & **15 min.** & **30 min.** & **60 min.** \\ \hline
3 h & 2.67 & 2.63 & 2.67 & 2.51 & 2.53 & 2.55 \\ \hline \multicolumn{6}{c}{**Autonomous Timing RMS Error in ns (90 th Percentile)**} \\ \hline \multicolumn{6}{c}{**NORR**} & \multicolumn{6}{c}{**RR**} \\ \hline
**int/\(T_{s}\)** & **15 min.** & **30 min.** & **60 min.** & **15 min.** & **30 min.** & **60 min.** \\ \hline
3 h & 0.88 & 1.27 & 1.76 & 0.93 & 1.22 & 1.60 \\ \hline \end{tabular}
\end{table} 
Table 4: 90 th percentile of the RMS error for the Satellite Time Bias (in nanoseconds) for different measurement rates int and measurement time span, \(T_{s}\), of 3 h.  
the possibility to provide an autonomous and independent navigation service on the Moon by exploiting a small constellation of spacecraft will overcome this limit. Moreover, these autonomous properties can be much more useful for future missions to other planets, such as those for Mars exploration and colonization, just because, as the spacecraft gets further away, it becomes more difficult to perform the OD&T from Earth. Last but not least is some consideration about the limit of the proposed approach.