## 4 Experiments and Analysis
### Impact on the Orbital Accuracy
It can be seen from Figure 8 that, in terms of the orbital accuracy, for almost all satellites and all directions, the orbit accuracy is highest in Experiment 4, followed by Experiment 3, then Experiment 2, and lowest in Experiment 1. For different directions, on the one hand, the orbit accuracy in the radial is the highest for all experiments, followed by the cross, and the ones in along are the lowest. On the other hand, in the radial direction, the difference in orbit accuracy among the four experiments is small. While, in the cross and along directions, the orbit accuracy of experiments 1 and 3 is close, the orbit accuracy of experiments 2 and 4 is also close, but there is a large discrepancy between these two sets. Overall, from the 3D RMS, it can be seen that the orbital accuracy of experiments 1 and 3 is close to 100 cm, with the latter being better than the former, while experiments 2 and 4 have better than 50 cm, with the latter better than the former similarly. That is to say, using the precise ephemeris as the a priori constraint can significantly improve the accuracy of the orbit determination. In addition, for the ISL-only-based autonomous orbit determination, introducing SLR observations can also enhance the accuracy of the orbit, and there are no complex parameters like ambiguities in GNSS to deal with. Thus, this is a very meaningful conclusion for some geoscience research, such as inversion of geocenter motion with post-processing [39; 40; 41]. Finally, noting the significant differences in accuracy among different types of satellites, we compiled the orbital accuracy of different types of satellites, as well as the improvement situation between different experiments. The averaged RMS for the MEO and IGSO satellites are displayed in Figure 9. In each subgraph, the horizontal axis represents the orbital directions, e.g., along, cross, radial, and 3D, and the vertical axis denotes the RMS values. As before, different colored bars correspond to different experiments. The left subgraph is for the MEO satellites, while the right one is for the IGSO satellites. Figure 9: Average orbital accuracy for MEO and IGSO satellites. We can see from Figure 9 that the MEO satellite has better accuracy than the IGSO satellite in all directions, which is consistent with the previous Figures 7 and 8. Meanwhile, for the sake of intuition, we display the detailed orbital accuracy values in Table 5. Additionally, we also notice that, for the MEO satellite, the orbital accuracy in the radial direction is significantly better than that in the along and cross directions, while for the IGSO satellite, similar phenomena are observed in Experiments 1 and 3, whereas in Experiments 2 and 4, the orbital accuracy in all three directions is relatively close. This may be related to the dynamics model of IGSO satellites and the number of ISL/SLR observations. Moreover, the improvement proportions of the orbital accuracy between typical experiments were also calculated, as shown in Table 6. In other words, to evaluate the influence of the a priori values and the observations adopted on the orbital accuracy, we calculated the improvement proportion for four typical combinations: Experiments 1 and 2 (namely Exp1-Exp2), Experiments 3 and 4 (namely Exp3-Exp4), as well as Experiments 1 and 3 (namely Exp1-Exp3) and Experiments 2 and 4 (namely Exp2-Exp4). As shown in Table 6, the improvement ratios of the first two sets (Exp1-Exp2, Exp3-Exp4) indicate that the orbital accuracy can be improved by approximately 75% when using precise ephemeris compared to using broadcast ephemeris as the a priori orbit. The results of the last two sets show that when SLR observations are incorporated into the ISL for combined orbit determination, the orbital accuracy can be enhanced by between 13% and 26%, with the MEO satellites showing a higher improvement ratio than the IGSO satellites. It should be noted that this conclusion is drawn under the condition of ignoring the influence of hardware delay errors in SLR observations.