# Phase Center Corrections for BDS IGSO and MEO Satellites in IGb14 and IGSR3 Frame
## 4 Results and Validation  
### Distribution of Observations  
Before analyzing the actual results of the estimation of PCVs and PCOs, it is worth considering the distribution of observations with respect to nadir angle for BDS IGSO and MEO satellites, as shown in Figure 4 for the 1-day solution of DOY 365, 2019 for  
\begin{table}
\begin{tabular}{c c} \hline
**Items** & **Description** \\ \hline Number of stations & About 130 stations from MGEX and iGMAS \\ \hline Time interval & DOY 1 to 365, 2019 \\ \hline Software & PANDA [23] \\ \hline Observation & Zero-difference ionosphere-free combination of phase and code observations of GPS \\  & L1/L2 and BDS B1I/B3I \\ \hline Sampling rate & 300 s \\ \hline Elevation cut-off angle & 7\({}^{\circ}\) \\ \hline Weighting & Elevation-dependent \\ \hline Inter-system-bias & A constant value per day for each station \\ \hline Station Coordinates & Align to IGb14 or IGSR3 frame with no-net-scale and no-net-rotation constraint \\ \hline \multirow{3}{*}{Troposphere} & GPT2w used as the empirical meta data; Saastamoinen model with VMF mapping function [24; 25; 26] \\  & Hourly estimation as piece-wise constant \\ \hline \multirow{2}{*}{Ionosphere} & The first-order effect eliminated by the ionosphere-free linear combination; the higher-order \\  & effects are ignored \\ \hline Receiver Clock & Epoch estimation as white noise \\ \hline \multirow{4}{*}{Orbits} & 24-h orbital arcs \\  & 6 initial position and velocities parameters \\ \cline{1-1}  & BDS-3 MEO: 5-parameter Extended CODE Orbit Model (ECOM1) [27] + A prior \\ \cline{1-1}  & box-wing model [28] \\ \cline{1-1}  & Other: ECOM1+Constant acceleration in along-tracking direction \\ \hline \multirow{4}{*}{Satellites PCOs} & GPS: igsR3\_207.txt used for FR3 solution, and igs14\_2101.txt used for F14 solution. \\ \cline{1-1}  & BDS: The PCO values in igs14\_2101.txt used as the initial and estimated as daily constant with \\ \cline{1-1}  & 10, 0.1, 10 m constraint for X-PCO, Y-PCO and Z-PCO. \\ \hline \multirow{4}{*}{Satellites PCVs} & GPS: igsR3\_207.txt used for FR3 solution, and igs14\_2101.txt used for F14 solution. \\ \cline{1-1}  & BDS: the initial values of nadir-depended set as zero for PCVs estimation, and fixed as the \\ \cline{1-1}  & estimated satellite-block-specific values for BDS PCO estimation. \\ \hline \multirow{2}{*}{Receiver PCOs and PCVs} & GPS: igsR3\_207.txt used for FR3 solution, and igs14\_2101.txt used for F14 solution. \\ \cline{1-1}  & BDS: igsR3\_2077.txt; and GPS L1 and L2 used in case of no corrections for BDS signals. \\ \hline \end{tabular}
\end{table}
Table 3: Strategy used for PCO and PCV estimation of BDS IGSO and MEO satellites.  
IGSO C06 and MEO C19 satellites. The reason for selecting these two satellites is that the distribution characteristics of observations from other IGSO or MEO satellites show an obvious consistency with these two satellites. As the IGSO orbital altitude is quite greater than that of MEO satellites, the maximum nadir angle (8.7\({}^{\circ}\)) is lower compared to MEO (13.02\({}^{\circ}\)). The distribution of observations shows an increasing trend with the increase of the nadir angle, and it drops down dramatically above 8.5\({}^{\circ}\) and 13\({}^{\circ}\), as more and more receivers do not track the low elevation data of IGSO and MEO satellites. For estimating raw PCVs, a linear piecewise function model with the maximum nadir angle up to 9\({}^{\circ}\) and 13\({}^{\circ}\) was built up for IGSO and MEO satellites. As low nadir angles are poorly covered by observations, their estimation of raw PCVs was relatively poorer than others.