# Earth Rotation Parameters Estimation Using GPS and SLR Measurements to Multiple LEO Satellites
## 3 ERP Estimation Based on the Single LEO Satellite
### Orbit Validation  
The capacity of generating high-quality orbit for LEO satellites is a vital prerequisite for the recovery of ERP. Hence, before the ERP estimation, we firstly assess the accuracy of the following two types of LEO orbit solutions that we generated: ambiguity-float solutions and ambiguity-fixed solutions.  
Table 4 lists the average root-mean-square (RMS) value of orbit differences, with respect to the external product in the along-track, cross-track and radial components for the ambiguity-float solutions and ambiguity-fixed solutions. Thanks to the additional geometric constraint offered by the ambiguity fixing, the ambiguity-fixed solution shows a smaller RMS value compared to the ambiguity-float solution, and the most distinct improvement is observed in the along-track component. Meanwhile, we can find that GRACE-FO satellites achieve the largest improvement compared to the other missions, and the improvement with respect to the ambiguity-float orbit in the along-track, cross-track and radial components can reach 40%, 13% and 18%, respectively. This can be easily understood by the fact that the GRACE-FO product delivery by JPL is an ambiguity-fixed solution. In the case of Swarm, the benefits of ambiguity fixing are not as evident as they are in the GRACE-FO mission, since the reference orbits are produced with carrier phase ambiguities treated as float values. However, a better consistency to the reference orbits is still visible for the ambiguity-fixed solutions. When referred to Sentinel-3, the consistency with the orbit product is improved for the along-track and radial components in the ambiguity-fixed solution when compared to the ambiguity-float solution. Since the orbit product of Sentinel-3 is based on GPS and Doppler Orbitography by radiopositioning integrated on  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **LAGEOS-1/2** & **LEO** \\ \hline SLR station coordinate & One set for three-day arc & One set for three-day arc \\ \hline Range bias & Estimated for selected sites & Estimated for all sites \\ \hline Earth rotation parameters & PWL daily & PWL daily \\ \hline Satellite orbits & & \\ \hline Satellite initial state & Position and velocity at initial epoch & — \\ \hline Atmospheric drag & One constant scale parameter & — \\  & the whole arc & — \\ \hline  & One constant and two & \\ Empirical accelerations & periodic accelerations in the & — \\  & cross-track and along-track directions & — \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameter estimated related with SLR observations for LAGEOS and LEO satellites in two-step method.  
satellite (DORIS) observations, this result indicates that the ambiguity fixing processing can weaken the inconsistency between the LEO orbit based on different techniques.  
Table 5 summarizes the mean bias and standard deviation (STD) of SLR residuals for seven LEO satellites. Here, the SLR validation is performed based on a subset of 12 high-quality core stations (Graz, Greenbelt, Haleakala, Hartebeesthoek, Herstmonceux, Matera, Mt Stromlo, Potsdam, Wettzell (two stations), Yarragadee, and Zimmerwald) [10]. The SLR residuals over \(\pm\)0.2 m are regarded as outliers and are excluded from the result statistics. As shown in Table 5, an evident reduction of 1-3 mm in STD of SLR residuals of ambiguity-fixed solutions indicates the better orbit accuracy enabled by the ambiguity-fixing processing. These improved orbits will naturally facilitate the estimation of geodetic parameters, such as ERP.