## 4 POD with Ambiguity Resolution
### Results
#### 4.2.2 Single Satellite Orbit Validation  
JPL's precise orbit of GRACE-FO satellites is also included in the level 1B product. The orbit is calculated with single receiver ambiguity resolution [32; 44] and can be used to assess the orbits generated in this investigation. The effect of PCV correction on POD is first evaluated. Figure 7 presents the along-track orbit differences between SD AR solution and JPL's orbit. The upper panel is for GRCC satellite and lower part is for GRCD satellite. The red dots are daily RMSs of differences of the orbit determined with PCV corrections while blue dots are RMSs without PCV corrections. Using created PCV maps, the RMS of the GRCC satellite decreases from 7.2 to 6.0 mm, and from 6.4 to 5.9 mm for the GRCD satellite. The detailed results for three components of SD AR and DD AR orbits can be found in Table 3. The average improvements in along-track, cross-track, and radial direction are 12.2%, 1.6%, and 1.0% for SD AR solution, and are 10.3%, 1.5%, and 3.5% for DD AR solution. The improvement of along-track orbit accuracy is the most significant, which validates the necessity of PCV calibration, especially for PBD. Figure 6: Fixing rates of (**a**) SD WL and NL ambiguities of GRCC and GRCD satellites and (**b**) DD WL and NL ambiguities. RMSs on DOY 100, 141, and 159 of GRCC satellite, and RMSs on DOY 204 and 290 of GRCD satellite are larger than other days. It has been found that sometimes, in these days, fewer GPS satellites are available, which leads to a decrease in orbit accuracy. Orbit accuracy with different AR methods is also evaluated. Figure 8 presents the RMSs of along-track orbit differences of FA, DD AR, and SD AR solutions with JPL's orbit. For GRCC satellite, the along-track RMS of the FA solution is 8.8 mm, the RMS is improved to 8.3 mm with DD AR and further achieves 6.0 mm by using the SD AR method. Results of three orbit components of the two satellites are listed in Table 4. Compared with the FA solution, the DD AR orbit has an average improvement of 6.3% while the SD AR result has an improvement of 18.3%. Similar to PCV correction, the along-track orbit accuracy has the most significant improvement, which is more than 30%. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Solution** & **Satellite** & **Orbit** & **No PCV/mm** & **With PCV/mm** & **Improvement** \\ \hline \multirow{4}{*}{SD AR Solution} & \multirow{2}{*}{GRCC} & Along-track & 7.2 & 6.0 & 16.7\% \\ \cline{3-6}  & & Cross-track & 6.2 & 6.2 & 0 \\ \cline{3-6}  & & Radial & 5.2 & 5.1 & 1.9\% \\ \cline{3-6}  & & Along-track & 6.4 & 5.9 & 7.8\% \\ \cline{3-6}  & & Cross-track & 6.3 & 6.1 & 3.2\% \\ \cline{3-6}  & & Radial & 5.1 & 5.1 & 0 \\ \hline \multirow{4}{*}{DD AR Solution} & \multirow{2}{*}{GRCC} & Along-track & 9.5 & 8.3 & 12.6\% \\ \cline{3-6}  & & Cross-track & 6.5 & 6.4 & 1.5\% \\ \cline{3-6}  & & Radial & 5.8 & 5.6 & 3.4\% \\ \cline{3-6}  & & Along-track & 8.8 & 8.1 & 8.0\% \\ \cline{3-6}  & & Cross-track & 6.4 & 6.3 & 1.6\% \\ \cline{3-6}  & & Radial & 5.7 & 5.5 & 3.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Orbit improvements with application of PCV maps for SD AR and DD AR solutions. Figure 7: Daily RMSs of along-track orbit differences between JPL’s orbit and SD AR solution with (red dots) and without (blue dots) PCV corrections. The upper panel is for the GRCC satellite and lower panel is for the GRCD satellite. GRACE-FO satellites are equipped with SLR retroreflectors. The independent SLR data can be used as external validation. SLR normal points from nine laser stations (Yarragadee, Greenbelt, Haleakala, Zimmerwald, Mount Stromlo, Wettzell, Graz, Herstmonceux, and Potsdam) are used for orbit evaluation. Residuals larger than 10 cm are rejected and an elevation cutoff of 10\({}^{\circ}\) is applied. Figure 9 shows the RMSs of SLR residuals. Red, green, and blue dots are RMSs of FA, DD AR, and SD AR orbits. The RMSs of the GRCC satellite are 11.5, 10.2, and 9.6 mm, which confirms the positive impact of AR on the orbit quality.