## 3 Results
### ISL Range Bias Estimation against Weighting Approach and Ground Station Sets  
#### 3.2.1 Orbit Estimation Errors  
It is expected that the ISL technique will be charged with systematic errors derived from hardware devices, i.e., antennas, electronics, and the measurement system, which we will describe as \"ISL range biases\". Here, we do not investigate the origins of these biases in detail. We instead show the impact of ISL range bias values and their estimation for different ground station sets from the perspective of the choice of weighting approach. The simulations were conducted for an ISL range bias equal to 0 cm (no bias is simulated and estimated) and when ISL range bias is equal to 0.5 cm and 1.0 cm to check the general impact of the ISL range biases on satellite positions. A detailed description of the simulation scenarios used for orbit estimation errors analysis is given in Table 5. Simulations assuming ISL range bias equal to 0.5 cm are used to evaluate the impact of ground station set in a next subsection. These scenario names are created as follows: {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. In Figure 5 we demonstrate orbit errors in each component for the different ground station sets according to scenarios described in Table 5. As shown in Section 3.1, for globally distributed stations and confirmed here, the relation between the Forstner and Nominal weighting is preserved regardless of the bias presence, i.e., Forstner outperforms Nominal. In each component, the same relation is shown between ISL range bias value and weighting method, i.e., using Forstner approach in most cases helps to reduce the error, especially in the along-track component (Figure 5b). The visible impact of bias is apparent in errors for the cross-track component (Figure 5c) for globally distributed stations and for intra-plane schemes. The error bars are slightly larger by about 10% of the mean orbit errors in along-track component (Figure 5b) and cross-track (Figure 5c) when ISL range bias is estimated. However, estimation errors in cross-track component affect the 3D errors the most. The lowest 3D errors at the level of 0.8-0.9 cm are obtained for sequential schemes with 44 ground stations. The situation changes for the 16 stations positioned in Europe. In Figure 5d, with total 3D values of orbit errors for ground stations in Europe, the weighting method affects the estimation results differently for each of the connectivity schemes. For intra-plane closed scheme Forstner approach helps to reduce errors, while for intra-plane open scheme Nominal weighting has lower 3D errors than Forstner approach. However, Forstner approach helps to lower total errors in sequential dual one-way. On the contrary, for sequential one-way the choice of VCE approach is not impactful. Looking at total orbit error (Figure 5d), 16 stations (positioned either globally or regionally) cannot ensure repeatability of solutions obtained from a series of simulations for each connectivity scheme as computed errors are \(\pm\)25% of the mean orbit error obtained for each simulation scenario.