## 3 Results
### ISL Range Bias Estimation against Weighting Approach and Ground Station Sets
#### 3.2.2 ISL Range Bias Estimation  
Figure 6 shows the effect of the weighting method and connectivity scheme when the value of the simulated ISL range biases is 1.0 cm. Estimation errors of ISL range bias estimation equal to 0.5 cm are shown in Figure A1 in Appendix A. For simulated ISL range bias values and for each ground station set we can distinguish the impact of the satellite placement on the orbital plane, especially for intra-plane schemes when 16 stations are used. However, increasing the number of ground stations to 44 for orbit determination does not considerably improve the bias estimation, i.e., the choice of connectivity schemes has a higher impact on the results than station set. Connectivity schemes with invariable  
Figure 5: Comparison of weighting method with reference to ground station set and bias value used in simulations to analyze the impact on mean RMS errors in the orbit estimation 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 5. Because of the higher errors, results for the simulation scenarios with 16 stations in Europe are shown on a separate plot with a different range on the vertical axis. geometry such as intra-plane schemes might not be beneficial or additionally burdened with systemic errors. It is seen in Figure 6b,c where ISL range bias estimation for intra-plane open is affected by systematic error which degrades the mean solution by about 0.4 cm compared to simulated 1 cm bias. Due to geometrical properties of intra-plane open (i.e., missing link), erroneous ISL range bias estimation for one satellite might more affect other satellites on the same orbital plane than it is in case of sequential schemes. Initial values of calibration constants or fixing the ISL range bias value for chosen satellites might improve the ISL range bias estimation in this case, but it needs further testing. We would like to address these questions for next research involving more deeply wide range of possible methods to handle range biases in parameter estimation, including calibration. In terms of the influence of the weighting method and considering all simulation scenarios, the results with the smallest difference among the scenarios are obtained for the sequential dual one-way scheme. The most variable bias results occur for the intra-plane open (\(\pm\)20% of base value) and sequential one-way schemes. Statistical measures presented in Table 6 are computed with distinction to the weighting method and connectivity schemes, but regardless of the ground station set. It means that these values show general possibilities of ISL range bias estimation in applied pro  
Figure 6: Mean estimated ISL range biases of each satellite (simulated value of 1.0 cm) for different ground station sets: (**a**) 44 stations (global), (**b**) 16 stations (global), and (**c**) 16 stations (Europe) under different weighting methods. Please note the scale on the vertical axis. cessing, including presence of systemic errors visible in Figure 6b,c. The RMS is similar for sequential dual one-way and sequential one-way schemes for both types of weighting. For intra-plane schemes the RMS values are higher Nominal than in Forstner weighting. The range of ISL range bias differences is also wider for Nominal weighting. The choice of sequential scheme and ground station set is more crucial for accurate ISL range biases estimation. The distribution of differences between simulated and estimated biases with reference to the ground station sets and weighting approach is shown in Figure 7. The differences are computed for ISL range biases equal to 0.5 cm and 1.0 cm. Forstner method performs better in ranges from \(-\)0.2 cm to 0.2 cm for the global station distribution than Nominal weighting (the number of differences in this range is higher in Forstner than Nominal) and the extreme differences are also smaller with the Forstner than in Nominal weighting.