## 3 Results  
### Comparison of the VCE Approaches  
Numerous versions of the VCE are available, depending on the problem requiring relative weighting. This section aims to compare the VCE approaches described in Section 2.4: Helmert which might be considered as a strict solution, and Forstner, a simplified version of Helmert approach. The idea of relative weighting of ISL and GNSS in a Galileo-like needs to be examined in the case of complexity of joining two various techniques for orbit determination. A strict solution would be more precise in assigning weighting coefficients but might be more computationally expensive. We simulated six scenarios to conduct a comparison of the following approaches: Forstner, Helmert, and Nominal with 44 and 16 ground stations with global distribution (Table 3). The scenario names given in Table 3, also used in the figures, were created based on the following scheme: [number of stations and their placement]-[ISL range bias value in cm]-[VCE approach], where \(G\) is global, \(E\) is Europe, \(F\) is Forstner, \(H\) is Helmert, and \(N\) is Nominal. \begin{table}
\begin{tabular}{c c c} \hline \hline
**GNSS** & & **ISL (24 Satellites)** \\ \hline
44 stations (global) & 1,181,375 & Sequential dual one-way (SDOW) & 62,066 \\
16 stations (global) & 434,327 & Sequential one-way (SOW) & 31,033 \\
16 stations (Europe) & 431,180 & Intra-plane closed (IPC) & 69,120 \\  & & Intra-plane open (IPO) & 60,480 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Number of GNSS and ISL measurements for 1 day. The weighting coefficients \(\frac{1}{\mathcal{S}^{2}}\) obtained for selected simulation scenarios are presented in Table 4. The differences between Helmert and Forstner approaches are mostly negligible for the same number of ground stations. A comparison of the connectivity schemes for the weighting coefficients indicates that sequential schemes are less sensitive to a limited number of stations as the changes in the coefficient are relatively smaller than those in intra-plane schemes. However, the intra-plane schemes have higher values of the coefficients with 44 stations and the weighting coefficient values decrease for 16 stations. In our simulations, GNSS observations have a considerable effect on the solution. Intra-plane schemes due to lack of links between the orbital planes are more dependent on the number of GNSS measurements what relates to the number of ground stations. Comparison of two connection types reveals that dual one-way is considered as a better solution due to higher values of weighting coefficient. Sequential one-way has lower values of coefficients than sequential dual one-way probably because of taking part in satellite clock estimation. Sequential schemes seem to be more dependent on the connection type than on the VCE approach. Intra-plane schemes are characterized by constant pairs and one-way connection type, and they have higher or similar values of weighting coefficients than sequential one-way. Considering just weighting coefficients, it might suggest that intra-plane schemes are more reliable than sequential one-way, i.e., static schemes using the same connection type as sequential schemes might better contribute to orbit and clock estimation. The results of the orbit determination are presented in Figure 3. The values of weighting coefficients might not have a substantial impact on errors of estimated parameters. The radial component in Figure 3a is the least sensitive on choice of different simulation settings as the results are very similar for all simulation scenarios (range of RMS is from 0.3 cm to 0.6 cm). The impact of various simulation settings is more visible in errors for the along-track and cross-track components. While considering the impact of VCE approach, usually the Helmert method is best, followed by Forstner and Nominal, but the differences between them are very small, i.e., less than 0.2 cm for sequential schemes and up to 0.4 cm for intra-plane schemes.