## 4 Precise Orbit Determination (POD)
### POD Strategy
[28], orbit precision declines dramatically during ON periods, and therefore a constant force in along-track is introduced to compensate for the ECOM output. The orbit precision during ON period is improved to the same level as that during YS period, but it is still low during transitions between attitude control modes. In this study, the five parameters in ECOM together with an additional acceleration bias were used for the combined POD of BeiDou-2 and BeiDou-3e satellites. It should be noted that YS mode alone, as in the case of GPS satellites, was used for BeiDou-3e satellites according to information provided by Operational Control Center (OCC). To further improve the precision of POD, integer ambiguity resolution (AR) can be crucial. The method of ambiguity fixing used in this study was proposed by [PERSON] et al. [31]. The ambiguities of the undifferenced ionosphere-free combination were divided into wide-lane (WL) and narrow-lane (NL) ambiguities. WL and NL ambiguities are linear combinations of phase ambiguities and can be expressed as:  
\[\left\{ \begin{array}{l}N_{WL}=N_{i}-N_{j}\\ N_{NL}=N_{i}+N_{j}\end{array} \right. \tag{2}\]  
where \(N\) represents carrier phase ambiguity, and the subscripts \(i\) and \(j\) are used to denote different number of frequencies. The geometry-free WL phase ambiguity was initially constrained to integer values through the Hatch-Melbourne-Wubbena (HMW) combination [32; 33; 34], and then an attempt  
Figure 4: BeiDou-2 satellite attitude control modes: yaw-steering (YS) (**a**) and orbit-normal (ON) (**b**). In YS mode, the satellite rotates around the z axis, and the x axis remains yawing all the time, while during the ON period, the x axis stops yawing and is consistent with the velocity throughout. was made to fix the geometry-based NL phase ambiguity. In addition, in our experiments the GEO ambiguities were not fixed due to their poor geometry. When implementing AR during a POD process, the pseudorange measurement quality can have significant impacts on the resolution success rate of the geometry-free WL phase ambiguities [35]. The code bias correction model supplied by [PERSON] [PERSON] was adopted to eliminate pseudorange errors in the BeiDou-2 IGSOs and MEOs signals [6]. With respect to the BeiDou-3e signal performance, there was no obvious code bias and corrections were not needed. Table 3 summarizes the observational models and force models used in the POD processing. Specifically, the station coordinates were calculated as constants and the ZTDs were estimated as piece-wise constants every 120 min, whereas the clock offsets of the satellites and stations were estimated on an epoch basis and constrained by a random walk model. Owing to the different frequencies and signal modulation methods used by GPS and BeiDou, there is a bias in receiver clock offsets between these two systems relative to the reference time. This bias is stable and can be estimated as inter-system bias [36]. In addition, as the tracking stations used in our analysis were regional stations, the Earth rotation parameters were not estimated but were fixed in accordance with the international reference time series for the Earth orientation parameters, referred as \"IERS C04\" (Combined 04), which was provided by the Earth Orientation Center of the International Earth Rotation Service. For the BeiDou-2 satellites, only the initial PCO values were supplied by the IGS-MGEX without phase center variation (PCV) parameters. Hence, we used the PCO and PCV values calculated by Wuhan University to correct data for the IGSOs and MEOs [7]. Unfortunately, no precise PCO parameters for C13 are available. There is only the initial value of 60, 0, and 110 cm in satellite-fixed coordinates for C13. For BeiDou-3e satellites, PCO values are provided by OCC with no PCV information, as listed in Table 4.