# Precise Orbit Determination of FY-3C with Calibration of Orbit Biases in BeiDou GEO Satellites
## 2 BeiDou Orbit Error Analysis and Mitigation
### Mitigation of BeiDou GEO Orbit Errors
The impact factors for the along-track and cross-track change within the range of \(-\)0.18 to 0.18. The sensitivities of FY3C-C04 range errors on C04 radial biases change from 1 to 0.985 when FY-3C flies from the center to the border of the service region. The discrepancies in the range observation models caused by GEO orbit radial biases will stay almost constants since the changes of impact factors are extremely inconspicuous even though the ranges errors are very sensitive to GEO orbit radial biases. The distribution pattern of impact factors for any other GEO orbit biases is almost exactly the same as that of C04 while centering in the corresponding sub-satellite point projection on the equator. Figure 2: Zenith and azimuth series variation of vectors from FY-3C positioning antenna to the transmitter antenna of BeiDou GEO in the GEO orbital reference frame during 14 July 2017. In the case of FY-3C POD the GEO radial biases can be ignored since the majority of the invariant parts of the orbit radial errors and satellite clock offsets can be absorbed by the float phase ambiguity parameters. This is thanks to the small zenith angle of the line-of-sight which changes within 0\({}^{\circ}\) to 10\({}^{\circ}\), while biases in along-track and cross-track should be modeled accurately since the azimuth angle in the satellite orbital frame changes widely within 0\({}^{\circ}\) to 360\({}^{\circ}\). In view of this and the existing large DBDs that cannot be neglected in GEO orbits, the GEO orbit errors are modeled as daily systematic constant biases in the FY3C POD process. In order to validate the performance of mitigating BeiDou GEO orbit errors using the proposed method, we made a very rough and effective experiment adopting a batch least square estimation by adjusting the receiver clock offsets and phase ambiguities while fixing the GPS-based FY-3C precise orbit in one whole day period. At the same time the weight of the observations from GEO had been set to one percent of those from IGSO and MEO. This can avoid the distortion that comes from the presence of the common parameters such as receiver clock offsets, which are contributed by observations from all BeiDou satellite types. The derived observation residuals can evaluate the performance of simulating errors in BeiDou GEO orbits as constants in along-track and cross track. Figure 4 shows the time-varying phase residual series of five GEO satellites without and with orbit biases modeled as constants in the sample period of 14 July 2017. Figure 4 indicates that the phase residuals show apparent regular relationships with time, and the residuals range within \(-\)0.6 to 0.6 m without calibration of the GEO orbit biases while those decrease to \(-\)6 to 6 cm when calibrating the GEO orbit biases. The results indicate the efficiency of estimating the systematic biases existed in GEO orbit products together with the adjustment process while fixing the LEO reference orbit. Phase residuals with a magnitude greater than 1 cm are likely to be caused by limiting the weight of the phase observations from GEO to one percent with respect to those from IGSO and MEO. An assessment of more detailed phase observation residuals is carried out in Section 3.4 for FY-3C POD where all the phase observations have the same weight for different BeiDou satellite types. Figure 3: Magnitudes of distance errors along with the sight from FY-3C to C04 caused by unit orbit biases in the observable region for C04 during July 2017 looking down on the Earth from the perspective of C04. The left, center, and right are impact factors of C04 orbit biases in along-track, cross-track, and radial components, respectively.