# Phase Center Corrections for BDS IGSO and MEO Satellites in IGb14 and IGSR3 Frame
## 3 Data Processing  
The Position and Navigation Data Analyst (PANDA) software [23] was modified for estimating raw PCVs and PCOs of BDS satellite antennas. The B1I and B3I signals are selected based on two facts: (1) both BDS-2 and BDS-3 satellites broadcast the two signals, (2) much more receivers can support tracking them. We estimated one-day solutions by using undifferenced IF combinations of dual-frequency code and phase measurements collected by more than 130 ground tracking stations equipped with the antennas in Table 2 and belonging to MGEX and iGMAS from DOY 1 to 365, 2019. The distribution of these stations in Figure 3 shows that they have been able to provide good ground tracking conditions for BDS. Moreover, it also shows the feasibility of PCC estimation based on the receiver antenna PCCs. As PCVs are independent from the reference frame used, hence only one solution was estimated for PCVs. Additionally, two PCO solutions for BDS IGSO and MEO satellites were determined by fixing the scale to that of IGb14 and IGSR3 frame, denoted as the F14 as well as FR3 solution hereafter. As aforementioned, as no more than 30 stations were available with the ability to track satellites with PRN exceeding C38 during the selected period, those satellites were not included for analysis in this study. \begin{table}
\begin{tabular}{c c c c} \hline
\begin{tabular}{c} NONE \\ SCIS \\ \end{tabular} & B1I/B2b/B3I/B1c/B2a/B2a+B2b & COPIED \\ \hline \end{tabular}
\end{table} 
Table 2: Antenna/radome combinations with phase center corrections (PCC) available for BDS B1I and B3I signals in jigsR3_2077.atx. The GPS/BDS integrated approach was used to estimate the raw PCVs and PCOs of BDS IGSO and MEO satellites. In this procedure, we used a 24-h arc length, a 5 min sampling rate, a 7\({}^{\circ}\) cutoff elevation, and an elevation-dependent weighting. The raw PCV or PCO parameters were estimated with the station coordinates, receiver clocks, inter-system biases, tropospheric zenith total delays, satellite orbits, as well as satellite clocks and earth rotation parameters. To get a reasonable solution for PCOs and PCVs, it is well accepted that these parameters should be estimated by fixing the scale and the receiver antenna PCOs and PCVs. For the PCCs of ground receiver antennas in BDS signal frequencies, the ground calibration models in jgsR3_2077.atx were used, and that of GPS L1 and L2 were used in case of no corrections for BDS signals. Although the discrepancy of PCCs for receiver antennas of GPS signals in ICS legacy jgs14_2101.atx as well as jgsR3_2077.atx is marginal, the GPS PCCs for ground receiver antennas in jgs14_2101.atx as well as jgsR3_2077.atx were used for the F14 and FR3 solutions to keep the consistency. Correspondingly, the PCC correction models for GPS transmitter antennas were also fixed to the absolute values in jgs14_2101.atx as well as jgsR3_2077.atx for F14 and FR3 solutions, respectively. It is worth noting that the PCVs as well as horizontal PCOs are the same for GPS transmitter antennas in jgsR3_2077.atx. and jgs14_2101.atx. However, the discrepancy of Z-PCO reaches +160.0 mm, equivalent to a \(-\)1.24 ppb scale shift when IGSR3 was transformed to IGb14. For BDS IGSO and MEO satellites, the correction models of transmitter antennas were estimated in data processing. The initial values of nadir-dependent PCVs were set as 0, whereas the IGS recommended PCO values in jgs14_2101.atx were used as the initial ones. These values were derived based on the CSNO-released BDS PCOs. Considering the correlations between Z-PCO and satellite clock offset as well as the correlations between horizontal PCO and orbital parameters, it was necessary to introduce appropriate constraints to reduce their impact on data processing. It should be mentioned that the signal transmitter located in the Y-axis. Hence, strong constraint was usually used, and it was even fixed to the initial value [11].