# Earth Rotation Parameters Estimation Using GPS and SLR Measurements to Multiple LEO Satellites
## 4 ERP Estimation Based on the Combination of Multiple LEO Satellites
### Impact of LEO Number on the ERP Estimation  
In order to investigate the impact of LEO number on the ERP estimation, three combination solutions with 3-, 5- and 7-LEO satellites have been performed. The design of these schemes is on the basis of maximizing the diversity of orbit type, which is beneficial for eliminating the LEO-related orbit signals in ERP estimation. The 3-LEO scheme includes GRACE-C, Swarm-A, and Sentinel-3A. The 5-LEO scheme indicates the solution generated using GRACE-C, GRACE-D, Swarm-A, Swarm-B, and Sentinel-3A satellites. The 7-LEO  
Figure 6: (**a**) Percentage of observations to LAGEOS satellites from core stations and non-core stations; (**b**) number of core stations and non-core stations in 3-day solutions. scheme is with all the LEO satellites mentioned in Section 2, which maximizes the number of LEO observations and further strengthens the observation geometry. The results from the 3-LEO, 5-LEO and 7-LEO solutions are illustrated in Figure 7. Figure 7 shows that the scatter distributions of the 7-LEO solution are much denser near the zero line than those of the 3-LEO and 5-LEO solutions. The ERP RMSs of the 3-LEO solution are the largest, and the best result occurs in the 7-LEO solution with the RMSs of 0.7530 ms, 0.4486 ms and 0.0223 ms for X pole, Y pole and LOD, respectively. It indicates that more LEO satellites included in the estimation lead to a smaller ERP RMS. This improvement can be attributed to the significant increase in SLR observations, and the enhanced observation geometry with more LEO satellites. Moreover, the 7-LEO solution performs better than the LAGEOS solution (see Table 7) for ERP estimation, which indicates that for the ERP estimation under the short arc condition, the multiple-LEO solution can reach a similar or even better accuracy compared with the LAGEOS solution. Figure 8 gives the spectral analysis for the 3-LEO, 5-LEO and 7-LEO solutions. It can be clearly observed that the 119-day period for Sentinel-3A, mentioned in Section 3.3, is eliminated in the 3-LEO solution, which suggests that the ERP estimation with multiple LEO satellites can mitigate the orbit-related signal of single LEO in ERP solutions. Moreover, the amplitude of the 5-LEO solution is smaller than that of the 3-LEO solution for X pole, Y pole, and LOD. This indicates that the inclusion of Swarm-B and GRACE-D improves the orbit diversification, which can further improve the ERP solution. Additionally, the 7-LEO solution obtains the smallest amplitude within the period less than 120 days. Figure 7: Time series of pole coordinates and the length-of-day differences with respect to finals2000A.data series for the 3-LEO, 5-LEO and 7-LEO solutions. Values in the top right corner indicate the mean and RMS of differences for these three schemes. Figure 9 shows the differences in all the stations' coordinates w.r.t SLRF2014 for the 3-LEO, 5-LEO, and 7-LEO solutions. The corresponding statistics are severally listed in Table 9. With more LEO satellites included in, more observations can be used for estimating station coordinates. For core station solutions, a notable improvement can be seen in the north component. Compared with the 3-LEO solution, the 7-LEO solution improves by 32% in the north component. For the non-core stations, we can find that the combination of more LEO satellites can lead to an obvious improvement in all three components for non-core stations. The best results for non-core stations are in the 7-LEO solution, with IQRs of 19.6 mm, 13.6 mm, and 25.6 mm in the east, north, and up component, respectively. This is because more LEO satellites bring more observations and strengthen the observation geometry, which is especially vital for the estimation of these non-core stations with less observations. In addition, there are some stations, such as SVEL and BEIL, whose coordinates are unavailable in the 3-LEO solution, due to the lack of observations. However, we can get a relatively reliable coordinate solution for such stations in the 5-LEO and 7-LEO solutions.