## 3 Results
### Comparison of the VCE Approaches
The choice of connectivity scheme can determine the method performance, i.e., results for sequential schemes are more homogen \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**44G-0.5-F**} & \multicolumn{2}{c}{**44G-0.5-H**} & \multicolumn{2}{c}{**16G-0.5-F**} & \multicolumn{2}{c}{**16G-0.5-H**} \\ \cline{2-9}  & **GNSS** & **ISL** & **GNSS** & **ISL** & **GNSS** & **ISL** & **GNSS** & **ISL** \\ \hline Sequential dual & & & & & & & & \\ one-way & 2.89 & 0.86 & 2.90 & 0.85 & 3.29 & 0.90 & 3.29 & 0.91 \\ (SDOW) & & & & & & & & \\ (SOW) & 2.87 & 0.37 & 2.87 & 0.38 & 2.85 & 0.23 & 2.87 & 0.25 \\ Intra-plane closed & & & & & & & & \\ (IPC) & & & & & & & & \\ Intra-plane open & & & & & & & & \\ (IPO) & 2.86 & 0.55 & 2.86 & 0.56 & 2.69 & 0.26 & 2.69 & 0.26 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Value of VCE weighting coefficients \(\frac{1}{\mathcal{S}^{2}}\) obtained for normal equations for GNSS and ISL. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scenario** & **Scenario Name** & \
\begin{tabular}{c} **ISL Range Bias** \\ **Value [cm]** \\ \end{tabular} &
\begin{tabular}{c} **Weighting** \\ **Method** \\ \end{tabular} & **Station Set** \\ \hline (1.1) & 44G-0.5-F & 0.5 & Forstner & 44 (global) \\ (1.2) & 44G-0.5-H & 0.5 & Helmert & 44 (global) \\ (1.3) & 44G-0.5-N & 0.5 & Nominal & 44 (global) \\ (1.4) & 16G-0.5-F & 0.5 & Forstner & 16 (global) \\ (1.5) & 16G-0.5-H & 0.5 & Helmert & 16 (global) \\ (1.6) & 16G-0.5-N & 0.5 & Nominal & 16 (global) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the simulation scenarios used for comparison of the VCE approaches. approach across different scenarios than for intra-plane schemes. For sequential schemes, the choice of VCE approach is not important when 44 ground stations are used (Figure 3d). For the combination of 16 stations and intra-plane schemes, there are modest differences between weighting methods, in favor of the Helmert. For sequential dual one-way scheme, the Forstner approach would be the best choice of VCE method as the orbit errors with 16 stations located globally are slightly lower than for the Helmert approach. For most scenarios, using the Helmert approach gives no more than about 20% improvement in orbit accuracy compared with the Forstner approach, especially when the ISL connectivity scheme is not dynamic (e.g., in intra-plane schemes). Improvement is more noticeable for Forstner or Helmert in relation to Nominal weighting. The difference between extreme values of RMS orbit errors obtained from repeated simulations can reach 20-30% of mean values. It is also worth mentioning that in tested cases the Helmert and Forstner approaches are sensitive to the number of GNSS observations. When 16 stations were used, the standard deviations of solutions are larger than with use of 44 ground stations, but still smaller than for Nominal weighting in respective settings. Figure 3: Comparison of the Helmert and Forstner approaches with Nominal and their impact on orbit estimation mean RMS errors for (**a**) radial, (**b**) along-track, (**c**) cross-track components, and (**d**) the total 3D RMS value. The simulation scenario names are given in Table 3.  
There is a very slight improvement in clock estimation errors for [PERSON] and Forstner approaches for satellite clocks when using 44 ground stations (Figure 4) compared to Nominal (it is less than 0.01 ns for all connectivity schemes). There is also no notable difference between Nominal and Forstner and between Nominal and Helmert for use with measurements for 16 stations. The results presented in Figure 4 suggest no direct impact of the weighting method on clock estimation results in our simulation methodology. Considering orbit and clock estimation outcomes, the impact of choice of VCE approach between Helmert and Forstner also seems to be negligible. For further analysis, we decided to use the Forstner approach, as it is the simpler solution with comparative results to Helmert approach.