# Phase Center Corrections for BDS IGSO and MEO Satellites in IGb14 and IGSR3 Frame
## 4 Results and Validation
### Estimated Phase Center Offsets  
For the estimation of the PCOs values of BDS satellites, the above estimated satellite-block-specific PCVs and scale of reference frame were fixed. Additionally, the PCOs corrections with respect to the values in jigs14_2101.atx were obtained. To obtain stable results from these daily solutions, we carried out quality control and further analysis of the time series of PCOs estimates. The satellite-specific PCO estimates including their formal standard deviations, as well as the number of daily solutions, are listed in Table 5. The delta symbol \(\Delta\) is used to indicate that the parameters are given relative to the CSNO released metadata values for F14 solutions, whereas \(\delta\) represents the differences of the FR3 solution with respect to F14 estimates. Here, only the offsets of Z-PCO between FR3 and F14 for each satellite are listed, as the discrepancy for the horizontal estimates was within 1.0 mm, due to no impacts of scale on the estimation of horizontal PCOs. The standard deviations illustrate that the precision of the horizontal offset estimates was approximately 10 times better than that of the Z-offsets on average. The standard deviations of IGSO satellites were about two times larger than that of MEO satellites in each component due to relatively poor observation conditions. Moreover, relatively larger standard deviations occurred in the cases of fewer data available, e.g., for C35-C37 satellites. Although more than 300 days of data were \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c} \hline
**Nadir** (’) & **0** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** \\ \hline
**BDS-21** & \(-\)0.79 & 0.41 & \(-\)1.14 & \(-\)0.46 & 0.47 & 0.92 & 0.77 & 0.49 & 1.34 & \(-\)1.97 & & & & \\ \hline
**BDS-2M** & \(-\)3.65 & \(-\)3.18 & \(-\)2.70 & \(-\)1.05 & 0.40 & 2.09 & 3.03 & 3.62 & 3.43 & 2.50 & 0.91 & \(-\)0.53 & \(-\)1.10 & \(-\)3.58 \\ \hline
**BDS-3M-CAST** & 1.73 & 1.71 & 1.22 & 0.33 & \(-\)0.47 & \(-\)0.79 & \(-\)1.23 & \(-\)1.45 & \(-\)1.51 & \(-\)1.29 & \(-\)1.14 & \(-\)0.47 & 1.25 & 1.91 \\ \hline
**BDS-3M-CAST** & 2.50 & 2.53 & 1.74 & 0.52 & \(-\)0.60 & \(-\)1.22 & \(-\)1.88 & \(-\)2.14 & \(-\)2.14 & \(-\)1.85 & \(-\)1.52 & \(-\)0.50 & 1.75 & 2.65 \\ \hline \end{tabular}
\end{table} 
Table 4: Estimated satellite-block-specific PCVs for BDS IGSO and MEO satellites (unit: mm). Figure 5: The satellite-specific and satellite-block-specific PCV values for BDS-2 IGSO, BDS-2 MEO, BDS-3 CAST MEO, and BDS-3 SECM MEO. processed for them, about one of third were excluded due to poor quality because of fewer stations available before DOY 200, 2019. Several meters' discrepancy was observed between the estimated F14 and the CSNO-released Z-PCO for the BDS-2 IGSO and MEO satellites, and it was already noticed by [PERSON] et al. (2011) and [PERSON] et al. (2012). However, it is still unclear for the root. On the other hand, the agreement between the estimated F14 and the CSNO released Z-PCO for BDS-3 MEO satellites was good. However, we clearly notice that most of the estimated Z-PCO was larger than the corresponding metadata values. If we compute the average of the Z-PCO estimates of 19 BDS-3 MEO satellites, we obtain a mean value of +98.8 mm. A common bias of this size would impact the station heights and the scale of the terrestrial reference frame. For the FR3 solution, we clearly observed an averaged shift for the Z-PCO up to about \(-414.9\) mm, and \(-174.1\) cm for the IGSO and MEO satellites, respectively, which is equivalent to a scale increase of +1.27 ppb, quite closed to the scale differences  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**PRN**} & \multirow{2}{*}{**Days**} & \multicolumn{3}{c}{**F14 w.r.t CNO**} & \multicolumn{2}{c}{**FR3 w.r.t F14**} \\ \cline{3-6}  & & \(\Delta\mathbf{x}\) & \(\Delta\mathbf{y}\) & \(\Delta\mathbf{z}\) & \(\delta\mathbf{z  
(+1.24 ppb) when IGb14 was transformed to IGSR3.