## 3 Results
### Accuracy Analysis of Residual Accelerations  
Using the carrier phase/orbit differentiation method, we derived four acceleration sets with gross error elimination applied from the datasets described in the previous section. To analyze the accuracy of the derived accelerations, residual accelerations were obtained by subtracting the prior accelerations derived from the DGM-1S model from the differentiated accelerations. Statistics of the residual accelerations derived by the four different methods are listed in Table 4. According to the root mean square (RMS) in Table 4, the accelerations obtained by the carrier phase differentiation method had a slightly higher precision than the others in the three directions. In consideration of the 3D-RMS in the Table 4, the accuracy of the results obtained by the carrier phase differentiation method were 20%, 6%, and 12% higher than those obtained by the ESA-orbit differentiation, the Graz-orbit differentiation, and the SGG-orbit differentiation, respectively. Our results derived by the two different methods were close to each other. The main reason for this is that the same carrier phase data and similar processing strategies were adopted for the carrier phase differentiation method and the orbit differentiation method. Furthermore, the RMS of the residuals revealed that  
We also plotted the square root of the power spectral density (PSD) of 1 day residual accelerations derived by four different methods, which are shown in Figure 2. As seen in the Figure 2, the PSD curves of the residual accelerations of the four cases were similar, especially for the carrier phase and SGG-orbit differentiated accelerations, which showed that the errors increased with an increase in the frequency when \(f<0.015\) Hz. This character is consistent with the inherent property of the numerical differentiation, i.e., the time series signal will be multiplied by \(\omega^{2}\) in the frequency domain after applying numerical differentiation, where \(\omega\) is the frequency. In addition, the errors of the radial component were about twice that of the other two components. Simultaneously, the magnitudes of the square-root PSDs derived from the different methods were slightly different. For all three components, the magnitude in the case of the carrier phase method was slightly lower than those in the case of the SGG-orbit method in the high frequency part (\(\sim\)\(f>0.003\) Hz). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **Component** & **Min** & **Max** & **Mean** & **RMS** & **3D-RMS** \\ \hline \multirow{3}{*}{ESA-orbit} & Along-track & \(-3.921\times 10^{-5}\) & \(3.921\times 10^{-5}\) & \(-2.706\times 10^{-9}\) & \(1.231\times 10^{-5}\) & \multirow{3}{*}{\(1.557\times 10^{-5}\)} \\  & Cross-track & \(-3.699\times 10^{-5}\) & \(3.699\times 10^{-5}\) & \(7.520\times 10^{-10}\) & \(9.675\times 10^{-6}\) & \(1.557\times 10^{-5}\) \\  & Radial & \(-8.975\times 10^{-5}\) & \(8.975\times 10^{-5}\) & \(2.410\times 10^{-9}\) & \(2.408\times 10^{-5}\) & \\ \hline \multirow{3}{*}{Graz-orbit} & Along-track & \(-3.664\times 10^{-5}\) & \(3.664\times 10^{-5}\) & \(2.471\times 10^{-9}\) & \(1.221\times 10^{-5}\) & \multirow{3}{*}{\(1.319\times 10^{-5}\)} \\  & Cross-track & \(-3.634\times 10^{-5}\) & \(3.634\times 10^{-5}\) & \(-3.226\times 10^{-9}\) & \(1.211\times 10^{-6}\) & \(1.319\times 10^{-5}\) \\  & Radial & \(-7.023\times 10^{-5}\) & \(7.023\times 10^{-5}\) & \(8.513\times 10^{-9}\) & \(2.341\times 10^{-5}\) & \\ \hline \multirow{3}{*}{SGG-orbit} & Along-track & \(-3.692\times 10^{-5}\) & \(3.692\times 10^{-5}\) & \(4.038\times 10^{-9}\) & \(1.123\times 10^{-5}\) & \multirow{3}{*}{\(1.422\times 10^{-5}\)} \\  & Cross-track & \(-3.669\times 10^{-5}\) & \(3.669\times 10^{-5}\) & \(4.498\times 10^{-9}\) & \(1.223\times 10^{-5}\) & \(1.422\times 10^{-5}\) \\ \cline{1-1}  & Radial & \(-6.664\times 10^{-5}\) & \(6.664\times 10^{-5}\) & \(6.468\times 10^{-9}\) & \(2.221\times 10^{-5}\) & \\ \hline \hline \end{tabular}
\end{table}