# Earth Rotation Parameters Estimation Using GPS and SLR Measurements to Multiple LEO Satellites
## 4 ERP Estimation Based on the Combination of Multiple LEO Satellites
### Combination of LEO Satellite and LAGEOS  
The routine ERP product from ILRS is majorly based on LAGEOS. Hence, the investigation of the contribution of LEO satellites and LAGEOS combination to ERP estimation is especially meaningful. Figure 10 shows the ERP differences w.r.t the finals2000A.data series of the LAGEOS solution, the 7-LEO solution, and the combined solutions. The combined solution characterized by more concentrated blue dots reflects that the stability of the ERP solution is notably improved. In contrast to the LAGEOS solution, the combined solution shows RMS reductions of 0.644 ms, 0.629 ms and 0.028 ms for X pole, Y pole and LOD, respectively, since the involvement of seven LEO satellites offers a large number of observations. Besides, from the spectrum in Figure 11, it can be seen that the correlations between the LOD and LAGEOS satellite orbital parameters are weakened when LEO satellites are included. The 118-day period signal in LOD, which is related to the 112.5-day eclipsing period of LAGEOS-2, is visibly mitigated in the combination solution. When compared with the 7-LEO solution, the combination of LAGEOS and seven LEO satellites also attains a superior result, with a distinct decrease in the RMS of ERP. Figure 10: Time series of pole coordinates and the length-of-day differences with respect to finals2000A.data series for the LAGEOS solution, 7-LEO solution and combined solution. Values in the top right corner indicate the mean and RMS of differences for these three schemes. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Station**} & \multirow{2}{*}{**Solution**} & \multicolumn{2}{c}{**E (mm)**} & \multicolumn{2}{c}{**N (mm)**} & \multicolumn{2}{c}{**U (mm)**} \\ \cline{3-8}  & & **Median** & **IQR** & **Median** & **IQR** & **Median** & **IQR** \\ \hline \multirow{3}{*}{**Core**} & 3 LEO & 1.9 & 14.8 & 2.5 & 15.6 & \(-\)1.7 & 9.8 \\ \cline{2-8}  & 5 LEO & 1.3 & 17.7 & \(-\)0.8 & 11.4 & \(-\)0.2 & 12.0 \\ \cline{2-8}  & 7 LEO & \(-\)3.4 & 15.0 & 0.4 & 10.6 & 2.8 & 11.3 \\ \hline \multirow{3}{*}{**Non-core**} & 3 LEO & \(-\)1.5 & 22.7 & 1.3 & 18.7 & 14.3 & 30.5 \\ \cline{2-8}  & 5 LEO & 1.5 & 23.4 & \(-\)0.6 & 15.2 & 12.1 & 24.3 \\ \cline{2-8}  & 7 LEO & \(-\)1.1 & 19.6 & 0.2 & 13.6 & 12.9 & 25.6 \\ \hline \end{tabular}
\end{table} 
Table 9: Differences in estimated SLR station coordinates w.r.t. SLRF2014 for the 3-LEO, 5-LEO and 7-LEO solutions with core stations and non-core stations decomposed into the east, north, and up components (in mm). Figure 12 depicts the differences in all the estimated SLR station coordinates w.r.t. SLRF2014, and the statistical data are presented in Table 10. For all the stations, the combination of seven LEO satellites and LAGEOS satellites can obtain a superior coordinate result, with an IQR below 10 mm in the east and north components, which improves notably when compared with the LAGEOS solution and 7-LEO solution. It is visible that the estimated coordinates of the core stations are further improved when the LEO data are included. The results for the core station with the combination of LEO satellites and LAGEOS can reach the accuracy level below 10 mm in all three components. The combination solution is improved by 7 mm, 3 mm, and 3 mm compared to the 7-LEO solution. Figure 11: Spectral analysis for the LAGEOS solution, the 7-LEO solution and the combined solution. Figure 12: Differences in all estimated SLR station coordinates w.r.t. SLRF2014 for the LAGEOS solution, the 7-LEO solution and the combined solution. Additionally, the LEO observations can serve as a supplement in the case where the high-quality LAGEOS data are missing. Figure 13 gives the time series of 7110 station coordinates. It can be observed that the coordinate solution of the station is unavailable from DOY 10 to DOY 20, and from DOY 40 to DOY 50 in the LAGEOS solution, due to the lack of observations. When the LEO data are used, the station coordinates' time series can be more continues, with denser red dots.