## 7 Conclusions and Future Work  
This work addressed the potential of performing orbit determination using intersatellite ranging as a primary observable, without the intervention of an extended network of ground sensor stations collecting navigation data. The orbits of a GNSS MEO constellation of 24 satellites were estimated over observation intervals spanning 1, 2, or 3 h orbit arcs, aided by ground-to-satellite ranges obtained from three or four ground stations. Errors and biases were injected into the range observations to emulate realistic measurement data sets. It was shown that dm- to m-level orbit determination accuracy is attainable with a limited ground network extension. When focusing on GNSS applications, the radial orbital error component has the largest weight in defining GNSS navigation performance. To this aim, we also inspected the orbit-only signal-in-space range error SiSRE\({}_{\text{orb}}\) in all the simulated scenarios, showing that SiSRE\({}_{\text{orb}}\) below a decimeter can be reached when orbital arcs of sufficient length are processed, between two and three hours. However, this method cannot be further improved by extending the observed orbital arcs, since the Galileo broadcast F/NAV orbit parametrization introduces larger fitting errors.  
The proposed orbit determination scheme could be used as a back-up procedure to estimate the orbits of GNSS satellites, guaranteeing a continuous navigation message generation in case of ground segment failures, as long as sparse GSR measurement can still be provided. However, we also noted a rapidly deteriorating accuracy of the predicted (extrapolated) orbit based on the estimated F/NAV parameters, which limits the validity interval of the ephemeris.  
As a next step, the proposed method will be extended to process real-time observations with a Kalman filter to guarantee fast updates of the estimated orbital parameters. Additionally, in order to further improve orbit determination performance with the proposed method, it will be assessed whether low-dynamic biases affecting ISR and GSR  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Orbital arc** & \(\sigma_{\text{csn}}\) & \(\sigma_{\text{ssn}}\) & \(\mathbf{b}_{ij}\) & **Radial RMSE** & **Along-tr. RMSE** & **Cross-tr. RMSE** & **SiSRE\({}_{\text{orb}}\)** \\
**Length** & **(mm)** & **(mm)** & **(cm)** & **(cm)** & **(cm)** & **(cm)** & **(cm)** & **(cm)** \\ \hline
1 h & 50 & 1 & None & 39.76 & 293.31 & 321.88 & 68.02 \\ \hline
2 h & 50 & 1 & None & 4.44 & 20.83 & 27.25 & 6.18 \\ \hline
3 h & 50 & 1 & None & 5.46 & 24.55 & 29.50 & 7.27 \\ \hline
1 h & 50 & 1 & [1, 10] & 49.29 & 334.88 & 457.35 & 87.17 \\ \hline
2 h & 50 & 1 & [1, 10] & 12.18 & 54.38 & 54.12 & 15.46 \\ \hline
3 h & 50 & 1 & [1, 10] & 9.78 & 54.47 & 61.64 & 14.24 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Average OD RMSE for a MEO constellation linked to a global network of four ground stations. ISR and GSR measurements are affected by noise and biases.  
Figure 4: Average absolute post fit error and extrapolation error for the 24 MEO satellites obtained in the scenario with a global network of four ground stations, with ISR and GSR observations affected by noise and biases. The orbit parameters are estimated over a 2 h long arc. (**a**) Post fit error. (**b**) Extrapolation error.  
measurements can be co-estimated, mitigating the impact of systematic biases with an identifiable signature.  
Conceptualization, A.T. and G.G.; methodology, A.T. and G.G.; software, A.T., G.M., M.D. and K.H.N.; validation, A.T.; writing, A.T., G.G., G.M. and M.D.; supervision, G.G. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.