# Earth Rotation Parameters Estimation Using GPS and SLR Measurements to Multiple LEO Satellites
## 5 Discussion  
This paper is devoted to discussing the contribution of LEO satellites to ERP estimation. The SLR observations to seven LEO satellites from three different missions, including Sentinel-3, Swarm, and GRACE-FO, are processed in this study. With the proposed single-receiver phase ambiguity resolution method in [39], the ambiguity-fixed orbit is used for decreasing the impact of possible orbit error in the ambiguity-float orbit for ERP estimation. We find that the single-LEO ERP solution cannot reach the comparable accuracy level of the LAGEOS solution, even if the ambiguity-fixed orbit is used. The same phenomenon also occurs in [9]. This may be due to the limited observations for single-LEO satellites, or the  
Figure 16: Average RMS of Sentinel-3A orbit difference with respect to the CNES product for the two-step solution and one-step solution. Values in the top right corner indicate the mean of RMS for the whole processing period.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \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{2}{*}{**All**} & **Two-step** & 3.9 & 9.7 & \(-\)0.9 & 7.8 & 0.1 & 13.5 \\ \cline{2-8}  & **One-step** & 0.3 & 15.9 & \(-\)0.8 & 14.4 & 1.0 & 20.1 \\ \hline \multirow{2}{*}{**Core**} & **Two-step** & 4.5 & 8.1 & \(-\)1.2 & 7.0 & \(-\)3.0 & 8.7 \\ \cline{2-8}  & **One-step** & 0.8 & 12.6 & \(-\)1.9 & 12.7 & \(-\)1.6 & 11.6 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Differences in estimated SLR station coordinates w.r.t. SLRF2014 using two-step method and one-step method classified into all SLR stations and core stations (in mm).  
LEO satellite orbit-related errors conveyed into the ERP solution. The station coordinate derived from the single-LEO solutions can reach the similar accuracy of a few centimeters with that in [20]. For the estimated core station coordinates, the solution based on some LEO satellites, such as GRACE-C and GRACE-D, is comparable to that based on LAGEOS satellites. This phenomenon confirms the potential of LEO satellites in geodetic parameter estimation to some extent.  
Rather than just focus on the single-LEO satellite, the combination of multiple-LEO satellites for ERP estimation is highlighted in our study. By increasing the LEO number in the processing, a notable improvement can be observed in the ERP solution. With seven LEO satellites included, a better ERP result than that based on LAGEOS in [46] is obtained. Moreover, the combination of multiple LEO satellites is especially of benefit for weakening the LEO orbit-related signal in single-LEO solutions. Furthermore, the combination of seven LEO satellites and LAGEOS satellites can reach the best result, with the smallest RMS for ERP. Such combination offers a large number of observations and maximizes the diversity of the orbit type, which is especially beneficial for estimating ERP and obtaining more reliable estimated station coordinates. Our result indicates that this method exhibits a great potential to be a strong supplement, even an alternative to the current SLR-based reference frame realization only based on LAGEOS and Etalon satellites.