## 3 Results
### ISL Range Bias Estimation against Weighting Approach and Ground Station Sets
#### 3.2.3 Comparison of Ground Station Sets with GNSS Only
In SISRE, the differences between the radial orbit error and error of clock estimation (denoted as \(\Delta cdt\)) are applied to the modelled pseudorange instead of radial values together with along-track and cross-track components:  
\[\text{SISRE}=\sqrt{\left[rms(w_{R}\times\Delta r_{R}-\Delta cdt)\right]^{2}+w_{ S,W}^{2}\times(S^{2}+W^{2})}. \tag{17}\]  
The radial orbit error and error of clock estimation values might be correlated because of the orbit and clock estimation process. The value of SISRE allows an assessment of the average ranging error. Constellation- and orbit-specific weight factors were delivered in [PERSON] et al. [69]. For the Galileo constellation, \(w_{R}\) and \(w_{S,W}^{2}\) are equal to 0.98 and 1/61, respectively. We use the scenario names formed according to the rules in previous subsections, i.e., {number of stations and their placement}-{ISL range bias value in cm}-{VCE approach}, where \(G\) is global, \(E\) is Europe, \(F\) is Forstner, and \(N\) is Nominal. Here we would like to shortly sum up the results of orbit estimation presented in previous sections in terms of the number of ground stations. Auxiliary orbit estimation results for scenarios described in Table 7 are shown in Figure 10. Radial component is the least sensitive on the ground station sets when ISLs are included. Even for GNSS-only scenario the difference between 44 and 16 stations located uniformly around the Earth is not remarkable (Figure 10(a)). The main reason for this is dynamic orbit determination where force models are used in estimation. Along-track and cross-track components are more fragile for the chosen ground stations, i.e., errors are rising when the number of stations is lower, but still visibly associated with the applied connectivity scheme. The total RMS error pictured in Figure 10(d) shows how much ISL might lower the estimation errors for 16 stations (both global and regional station sets) compared with the GNSS-only solutions. Focusing just on GNSS + ISL solutions, the error increases about 50% between 44 and 16 with global placement, and about 3 times between 16 global and 16 regional stations in Europe. Comparison of the weighting methods indicates that for 44 and 16 globally located stations Nominal weighting is slightly worse than the Forstner approach. This dependance is less clear for the regional station set, and the accuracy is more connected to the choice of connectivity scheme in this case. Figure 8 shows the clock errors for each simulation scenario distinguished by connectivity scheme. Considering global station placement, the results are comparable between Forstner and Nominal weighting, as well as between number of stations. Station and clock estimation errors are at the level of 0.02 ns with ISL included, which is about 50% better than in GNSS-only solution. However, the impact of weighting is clearly apparent for the scenario of 16 regional stations located in Europe except for when the sequential dual one-way scheme is used. The error for satellite clocks is lower when the Nominal weighting is used instead of Forstner. It might suggest that correlation between GNSS and ISL techniques in regional station set cannot be neglected when using VCE. The impact of weighting approach on station clocks is negligible in all simulation scenarios. In general, in our simulation and estimation methodology, clocks are not highly sensitive to the various weighting methods or connectivity schemes, but they are strongly associated with ground station placement, even with ISL support. Figure 9 depicts values of SISRE(orb) and SISRE for adopted ground station sets and confirms that using ISL together with GNSS observations, even with a limited number of uniformly distributed ground stations, helps to improve position accuracy compared with the GNSS-only solution. In GNSS + ISL case, for the same ISL range bias value and with globally located stations mean SISRE(orb) is equal to 0.5 cm while mean SISRE to about 1.0 cm, regardless the connectivity schemes.