# Earth Rotation Parameters Estimation Using GPS and SLR Measurements to Multiple LEO Satellites
## 3 ERP Estimation Based on the Single LEO Satellite
### Impact of Using Ambiguity-Fixed Orbit on the ERP Estimation  
Considering the relationship between the quality of the estimated ERP and LEO orbit accuracy, the contribution of ambiguity-fixed orbit to the ERP estimation is investigated \begin{table}
\begin{tabular}{c c c c c c} \hline
**Satellite** & **Orbit Type** & **Along (mm)** & **Cross (mm)** & **Radial (mm)** & **Product Source** & **Solution Type** \\ \hline \multirow{3}{*}{GRACE-C} & Ambiguity-float & 12.4 & 9.9 & 8.0 & National & \\ \cline{2-6}  & Ambiguity-fixed & 7.3 & 8.6 & 6.6 & Aeronautics and Space & Ambiguity-fixed \\ \hline \multirow{3}{*}{GRACE-D} & Ambiguity-float & 13.4 & 10.5 & 7.4 & Administration & orbit \\ \cline{2-6}  & Ambiguity-fixed & 8.2 & 9.2 & 5.9 & (NASA) JPL [39] & \\ \hline \multirow{3}{*}{Swarm-A} & Ambiguity-float & 15.3 & 14.3 & 7.1 & \\ \cline{2-6}  & Ambiguity-fixed & 11.5 & 13.3 & 6.0 & \\ \hline \multirow{3}{*}{Swarm-B} & Ambiguity-float & 16.2 & 14.7 & 7.4 & \\ \cline{2-6}  & Ambiguity-fixed & 12.6 & 13.4 & 6.0 & \\ \hline \multirow{3}{*}{Swarm-C} & Ambiguity-float & 15.9 & 14.7 & 7.3 & \\ \cline{2-6}  & Ambiguity-fixed & 12.0 & 13.8 & 6.0 & \\ \hline \multirow{3}{*}{Sentinel-3A} & Ambiguity-float & 13.7 & 8.8 & 9.6 & \\ \cline{2-6}  & Ambiguity-fixed & 10.9 & 9.3 & 8.7 & \\ \hline \multirow{3}{*}{Sentinel-3B} & Ambiguity-float & 15.2 & 9.3 & 10.3 & \\ \cline{2-6}  & Ambiguity-fixed & 12.1 & 9.6 & 9.1 & \\ \hline \end{tabular}
\end{table} 
Table 4: Average RMS of orbit difference with respect to the external orbit products of seven LEO satellites (GRACE-C/D, Swarm-A/B/C, Sentinel-3A/B). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{3}{*}{**Satellite**} & \multicolumn{4}{c}{**SLR Residuals (mm)**} \\ \cline{2-5}  & \multicolumn{2}{c}{**Ambiguity-Float**} & \multicolumn{2}{c}{**Ambiguity-Fixed**} \\ \cline{2-5}  & **Mean** & **STD** & **Mean** & **STD** \\ \hline GRACE-C & 2.2 & 14.6 & 1.3 & 11.8 \\ \hline GRACE-D & 3.0 & 15.9 & 3.2 & 12.8 \\ \hline Swarm-A & \(-\)0.4 & 20.9 & 0.5 & 19.5 \\ \hline Swarm-B & 1.0 & 21.7 & 1.2 & 20.5 \\ \hline Swarm-C & 1.0 & 21.5 & 1.0 & 20.1 \\ \hline Sentinel-3A & 1.2 & 18.0 & 1.5 & 16.9 \\ \hline Sentinel-3B & 2.6 & 20.4 & 2.2 & 19.1 \\ \hline \end{tabular}
\end{table} 
Table 5: Mean bias and STD of SLR residuals for the ambiguity-float solutions and ambiguity-fixed solutions. based on the two-step method in this subsection. Taking GRACE-D as an example, Figure 2 typically presents the pole coordinate and LOD differences between the finals2000A.data series and the ERP solutions, based on different orbits. It can be observed that the orbit improvement derived from the ambiguity fixing contributes an evident improvement to the ERP estimation. Compared with the ambiguity-float orbit solution, the ambiguity-fixed orbit solution exhibits a smaller variation, which indicates a better consistency with respect to the finals2000A.data products. With the application of the ambiguity-fixed orbit, the RMS values of X pole and Y pole differences are reduced by 12 uas and 22 uas, respectively, but slight accuracy degradation is observed in LOD. The benefit of ambiguity fixing is also visible in the coordinates of SLR stations. Table 6 presents the station coordinate differences between SLRF2014 and the different GRACE-D solutions. On average, the interquartile range (IQR) of SLR station coordinates in the east, north and up components are reduced by 18%, 14%, and 13%, respectively, when introducing the ambiguity-fixed orbit. Particularly, the better accuracy is achieved by the core stations, due to the large amount of SLR data they collected. Meanwhile, we can find that the application of the ambiguity-fixed orbit yields a smaller median of core station coordinate differences with respect to the SLRF2014. From the above results, we can conclude that the ERP estimation based on the ambiguity-fixed LEO orbit can obtain a better result. Therefore, all LEO-involved ERP solutions hereafter are performed based on the ambiguity-fixed orbit.