# Earth Rotation Parameters Estimation Using GPS and SLR Measurements to Multiple LEO Satellites
## 2 Data Set and Processing Strategy  
In order to evaluate the performance of LEO satellites for ERP determination, one-year onboard SLR and GPS data in 2019, from seven LEO satellites, including Sentinel-3A, Sentinel-3B, Swarm-A, Swarm-B, Swarm-C, GRACE-C, and GRACE-D, are used in this study. Table 1 gives the orbit information of these satellites, and the types of LRR and GPS receivers they carried. Two types of LRR, with different basic designs, are carried by the satellites we selected. The LRR with seven-prism, made by the Institute of Precision Instruments Engineering (IPIE), is mounted on the Sentinel-3 satellites, while the gravity recovery and climate experiment follow-on (GRACE-FO) and Swarm are equipped with a four-prism LRR, manufactured by the GeoForschungsZentrum (GFZ). The Swarm and Sentinel-3 onboard GPS receivers are developed by RUAG Space, and have eight channels that are available for dual-frequency tracking of GPS satellites. While GRACE-FO is equipped with the Jet Propulsion Laboratory (JPL) TriG receiver, which can observe the GPS signal at L1/L2 and track up to 16 GPS satellites. In addition to the LEO observations, we also process SLR observations of LAGEOS-1/-2 satellites, to obtain a LAGEOS-based solution for a reference. In this study, we adopt two methods to estimate the ERP from the SLR and GPS observations of LEO satellites, namely, the two-step method and one-step method. Figure 1 gives the flowchart of these two methods. In the two-step method, the orbits of the LEO satellites are firstly estimated, using the onboard GPS observations. Here, we choose to independently perform POD for the seven LEO satellites, rather than directly using the external precise orbit products; this is because the external LEO orbit products are \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Satellite** & **Perigee Altitude/km** & **Inclination/deg** & **LRR** & **GPS Receiver** \\ \hline
**Sentinel-3A** & 814 & 98.65 & 7-prism & RUAG \\ \hline
**Sentinel-3B** & 814 & 98.65 & 7-prism & RUAG \\ \hline
**Swarm-A** & 462 & 87.35 & 4-prism & RUAG \\ \hline
**Swarm-B** & 511 & 87.35 & 4-prism & RUAG \\ \hline
**Swarm-C** & 462 & 87.35 & 4-prism & RUAG \\ \hline
**GRACE-C** & 500 & 89.00 & 4-prism & TriG \\ \hline
**GRACE-D** & 500 & 89.00 & 4-prism & TriG \\ \hline
**LAGEOS-1** & 5860 & 109.90 & 426 corner cubes & — \\ \hline
**LAGEOS-2** & 5620 & 52.67 & 426 corner cubes & — \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview of LEO mission used in this study. generated based on different processing strategies, software platforms and GPS products, and these inconsistencies may introduce additional errors to the final ERP solutions. After the LEO POD processing, we estimate ERP from SLR observations with the LEO orbit fixed. In the one-step method, the GPS and SLR observations are jointly processed to simultaneously estimate the LEO orbit and ERP in a common least-squares adjustment. The pseudorange, carrier phase observations, and SLR observations are weighted according to the ratio of about 1:15,000:15,000. It should be noted that, in the two-step method, the orbits are only determined based on GPS observations, while in the one-step method, the orbits are calculated using GPS and SLR observations simultaneously. In order to avoid the possible accuracy degradation of the estimated LEO orbit in an orbit arc with a longer length (such as 7 days), in this study we select a 3-day arc length with 2-day overlaps between two adjacent consecutive orbit arcs. In the LEO POD processing, we use undifferenced ionosphere-free GPS observations with 30-s sampling, and the cutoff elevation angle is set to 1\({}^{\circ}\). The GPS phase center offset (PCO) and phase center variation (PCV) are corrected with igs14.atx [22]. For the LEO satellite antennas, the PCO corrections from ground calibration are employed, while the PCV values are computed using the in-flight calibrated model estimated by the residual method [23; 24].