## 3 Results
### POD of GOCE Satellite Based on the RD_STP Method
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Items** & **Bernese GPS Software** & **RD\_STP POD** \\  & **KIN and RD POD [11]** & **RD\_STP POD** \\ \hline \multirow{6}{*}{GPS measurement model} & Undiferenced & Undiferenced \\  & ionosphere-free phase & ionosphere-free phase \\  & jgs05.atx & jgs05.atx \\  & GOCE PCOs + PCVs & GOCE PCOs + PCVs \\  & CODE final GPS ephemerides and 5 s clocks & CODE final GPS ephemerides and 5 s clocks \\  & Elevation cut-off 0\({}^{\circ}\) & Elevation cut-off 0\({}^{\circ}\) \\  & 10 s/1 s (RD/KIN) sampling & 1 s sampling \\ \hline \multirow{6}{*}{Gravitational forces} & EIGEN-5S (120 \(\times\) 120) [44] & \multirow{6}{*}{EGM2008(90 \(\times\) 90) [41]} \\  & Solid Earth, pole and ocean tides & & \\ \cline{1-1}  & luni-solar-planetary gravity & & \\ \cline{1-1}  & N/A for KIN PSO & & \\ \hline Non-gravitational forces & Empirical constant & N/A \\ \cline{1-1}  & N/A for KIN PSO & & \\ \hline Estimation & Batch least squares & Batch least squares \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of dynamical and measurement models that are employed for the orbit determination of GOCE. Figure 7: (**a–c**) Differences between the RD_STP, KIN, and RD (the reference orbit) POD solutions: R (**a**), T (**b**), and N (**c**), at day of year (DOY) 330, 2009.  
of EGM2008 and EIGEN5S is set to 90, and the root of the noise variance of the accelerations computed from these two models is set to \(10^{-5}\) ms\({}^{-2}\). According to Figure 9, the differences are less than 0.5 mm for the R, T, and N directions, illustrating that the RD_STP POD solutions are not so sensitive to the a priori gravity field model, and the assumption of the stochastic model for the STP pseudo-observation is reasonable. This outcome is consistent with the conclusion given in Section 3.1.3. Moreover, the differences in the radial direction are larger than the ones in the other directions, which is reasonable because the acceleration differences between EGM2008 and EIGEN5S in the radial direction are biggest. Figure 8: Daily mean and RMS of the differences between the RD_STP and the RD (the reference orbit) POD solutions for DOY 318 to 332 of 2009. Figure 9: Differences of the RD_STP solutions based on the EGM2008 and EIGEN5S models up to 90 d/o, at DOY 330 of 2009. To analyze the influences of the relative weights of the STPs, we estimated several RD_STP solutions corresponding to the different stochastic models at DOY 319 of 2009, the radial differences (compared with the RD solutions) of the KIN solutions, and the RD_STP solutions are shown in Figure 10. As with the previous experiment, the EGM2008 model up to degree and order 90 is also used as the a priori dynamic model. The blue solid line in Figure 10 represents the differences of the kinematic solutions (named KINw) estimated by our own software. Further, the red solid line, green solid line, and black solid line represent the differences of the RD_STP solutions with the stochastic models \(\sigma_{\Delta M_{TL}}~{}=~{}10^{-2}\Delta t^{2}(\text{m})\) (named RD_STP_E2), \(\sigma_{\Delta\Delta M_{TL}}~{}=~{}10^{-4}\Delta t^{2}(\text{m})\) (RD_STP_E4), and \(\sigma_{\Delta M_{TL}}~{}=~{}10^{-5}\Delta t^{2}(\text{m})\) (RD_STP_E5), respectively. According to Figure 10, when the noise of the accelerations computed from EGM 2008 is set to be larger, which means a smaller weight for the STP pseudo-observations, the KINw and the RD_STP solutions are very close to each other (see the blue solid line and red solid line in Figure 10). Therefore, the RD_STP solutions will be exactly the same as the kinematic solutions when the weight of the STP pseudo-observations is small enough. Moreover, the larger weight (smaller \(\sigma_{\Delta\Delta M_{TL}}\)) of the statistical model produces a smoother solution, especially in nearly polar and equatorial regions (see the green and black solid line in Figure 10). This is consistent with the findings of [PERSON] et al. (2012), who showed that there are systematic errors in GOCE orbits in those regions.