# Earth Rotation Parameters Estimation Using GPS and SLR Measurements to Multiple LEO Satellites
## 3 ERP Estimation Based on the Single LEO Satellite
### ERP Estimation with Different LEO Satellites  
Figure 3 typically presents the number of SLR observations (normal points, NPs) of each 3-day solution for GRACE-D, Sentinel-3A, Swarm-A, Swarm-B, and LAGEOS satellites. An evident difference between LEO and LAGEOS satellites can be noted. In general, the average number of SLR observations used for a 3-day solution is 213, 204, 129, 437, and 317 for GRACE-D, Sentinel-3A, Swarm-A, Swarm-B and LAGEOS, respectively. The largest number of SLR observations is achieved by Swarm-B, which is even over three times more than that of Swarm-A. The observation number of most LEO cannot reach a similar level to that of LAGEOS, because there are two LAGEOS satellites and LAGEOS are calibration satellites for SLR stations, hence most stations track them. In addition, we can see that the core stations contribute to almost 70% of the SLR observations for LEO and LAGEOS satellites. Table 7 presents the statistical data of ERP based on SLR observations to seven LEO satellite ambiguity-fixed orbits, respectively. The LAGEOS-based solution is also listed here to provide a reference. In the case of a single-LEO solution, the estimated ERP become more sensitive to the number of SLR observations, since only one LEO satellite is used. We can find that the quality of ERP exhibits a strong dependence on the observation numbers. Among the LEO-based solutions, the Swarm-B solution exhibits the best consistency with the IERS product, thanks to its obviously largest number of available observations, and the RMS value for X pole, Y pole and LOD is 1.9286 ms, 1.6634 ms and 0.0673 ms, respectively. It should be noted that, though the nearly comparable amount of SLR observations is achieved for GRACE-FO and Sentinel-3 satellites, the Sentinel-3 solution shows an evidently worse ERP result than that of GRACE-FO solutions. The main reason for this phenomenon is that the specific sun-synchronous orbit of Sentinel-3, with the orbital inclination of 98.6\({}^{\circ}\), results in a low sensitivity for polar motion [41]. On the other hand, the relatively lower orbit accuracy of Sentinel-3 also accounts for their degraded ERP result (see Table 5). It can be seen that the accuracy of single-LEO solutions is not comparable to that of the LAGEOS solution, even for the Swarm-B solution. The superior performance of the LAGEOS solution is resulted from their simple satellite structure, the uncomplicated force model, and enough observations. Figure 3: Number of observations in 3-day solution for GRACE-D, Sentinel-3A, Swarm-A, Swarm-B, and LAGEOS (LAGEOS-1 + LAGEOS-2) collected by all stations (left) and core stations (right). Figure 4 typically gives the spectral analysis results for four single-LEO solutions and the LAGEOS solution. It can be seen that the LEO solutions apparently have more noisy signals with the period up to 50 days than the LAGEOS solution. No evident semiannual signal is visible in all the solutions. However, a distinct signal, with a 119-day period in the pole coordinates, can be observed in the Sentinel-3A solution. This signal may be related with the perigee revolution of 122 days for the Sentinel-3 satellite. Figure 5 gives the differences of the estimated station coordinates w.r.t SLRF2014 for the different satellite solutions, and summarized data are shown in Table 8. For all the LEO solutions, the positioning of all the SLR stations obtains the accuracy at the level of 20 mm-30 mm. While for the core stations, the accuracy level can reach about 10 mm-20 mm. Although there is the largest number of available observations for Swarm-B, the Swarm-B solution is inferior, with an IQR of 29 mm, 23 mm and 24 mm in three components for all the stations, which is probably due to the relatively poor precision of the Swarm-B orbits (see Table 5). Among these LEO satellite solutions, the GRACE-C and GRACE-D solutions can obtain better results than other solutions, with an IQR of about 15-20 mm in the E, N, U components for all the stations, thanks to their high-accuracy ambiguity-fixed orbit.