## 3 Results
### ISL Range Bias Estimation against Weighting Approach and Ground Station Sets
#### 3.2.3 Comparison of Ground Station Sets with GNSS Only  
To complete our analysis in terms of ground station sets, we analyze the possible improvements of applying weighting methods compared with the GNSS-only solution based on the choice of station set. This represents a continuation of the research in Kur and Kalarus [12] on the possible impact of restricting the number of stations on orbit determination. Here, we focus on the comparison between global and regional station sets with GNSS-only solutions. Results presented in the previous sections show that bias estimation accuracy is not remarkably associated with the number of ground stations as the difference in the worst case is usually less than 20% of initial bias. Thus, in this section we used 9 simulation scenarios presented in Table 7 with a bias value of 0.5 cm (only when ISLs are used in orbit determination). These scenarios have the same simulation properties except station sets for possibility of direct comparison of how weighting approach affects the results of clock estimation and signal-in-space range error (SISRE). The orbit accuracy of navigation satellites can be represented by SISRE to obtain a coarse assessment of expected positioning accuracy [68]. SISRE is the statistical measure for the impact of orbit and clock errors on the pseudorange [69; 70]. The orbit-only contribution to the SISRE is represented as a weighted average of orbit radial, along-track, and cross-track RMS errors [29; 36; 69]. The weights are satellite-to-user line-of-sight dependent. The largest weight is associated with the radial component of the satellite position [69]. In SISRE(orb) the position components (R--radial, S--along-track, and W--cross-track) are used:  
\[\text{SISRE}_{\text{(orb)}}=\sqrt{w_{R}^{2}\times R^{2}+w_{S,W}^{2}\times(5^{2} +W^{2})}, \tag{16}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Förstner**} & \multicolumn{3}{c}{**Nominal**} \\ \cline{2-7}  & **RMS** & **MIN** & **MAX [cm]** & **RMS** & **MIN** & **[cm]** & **MAX [cm]** \\  & **[cm]** & **[cm]** & **MAX [cm]** & **[cm]** & **[cm]** & **MAX [cm]** \\ \hline \multicolumn{7}{c}{ISL range bias = 0.5 cm} \\ SDOW & 0.11 & \(-\)0.27 & 0.26 & 0.11 & \(-\)0.26 & 0.24 \\ SOW & 0.15 & \(-\)0.59 & 0.37 & 0.12 & \(-\)0.43 & 0.29 \\ IPC & 0.18 & \(-\)0.62 & 0.56 & 0.26 & \(-\)0.92 & 0.85 \\ IPO & 0.18 & \(-\)0.68 & 0.63 & 0.27 & \(-\)0.94 & 0.91 \\ \multicolumn{7}{c}{ISL range bias = 1.0 cm} \\ SDOW & 0.10 & \(-\)0.23 & 0.31 & 0.11 & \(-\)0.25 & 0.26 \\ SOW & 0.15 & \(-\)0.47 & 0.36 & 0.13 & \(-\)0.40 & 0.33 \\ IPC & 0.19 & \(-\)0.58 & 0.57 & 0.27 & \(-\)0.90 & 0.89 \\ IPC & 0.31 & \(-\)0.65 & 0.70 & 0.35 & \(-\)0.90 & 0.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Statistics of differences between simulated and estimated values of biases with reference to weighting and connectivity schemes. Presented values are computed for all simulation scenarios with estimated ISL range bias (regardless the ground station set). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scenario** & **Scenario Name** &
\begin{tabular}{c} **ISL Range Bias** \\ **Value [cm]** \\ \end{tabular} & **Weighting** \\
**Number** & **Station Set** \\ \hline (3.1) & 44G-0.5-F & 0.5 & Forstner & 44 (global) \\ (3.2) & 44G-0.5-N & 0.5 & Nominal & 44 (global) \\ (3.3) & 44G-GNSS & - & GNSS-only & 44 (global) \\ (3.4) & 16G-0.5-F & 0.5 & Forstner & 16 (global) \\ (3.5) & 16G-0.5-N & 0.5 & Nominal & 16 (global) \\ (3.6) & 16G-GNSS & - & GNSS-only & 16 (global) \\ (3.7) & 16E-0.5-F & 0.5 & Forstner & 16 (Europe) \\ (3.8) & 16E-0.5-N & 0.5 & Nominal & 16 (Europe) \\ (3.9) & 16E-GNSS & - & GNSS-only & 16 (Europe) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary of simulation scenarios used analysis of number of ground station on clock estimation and signal-in-space range error (SISRE). where \(w_{R}\), \(w_{S}\), and \(w_{R}\) are weights for radial, along-track, and cross-track components, respectively.