# BeiDou Geostationary Satellite Code Bias Modeling Using Fengyun-3C Onboard Measurements
## 2 Fengyun-3C Onboard Data Quality Analysis
### BDS Code Multipath  
MP effects are caused by non-line-of-sight signal propagation between navigation satellites and the GNOS positioning antenna due to the Fengyun-3C's assembly parts reflection. In this section, we determine and calculate the MP effects using a linear combination of single-frequency code and dual-frequency carrier-phase observations, namely the MP combination, which can be expressed as [11; 12; 13]:  
\[ \begin{array}{ll}MP_{i}&=C_{i}-\frac{f_{i}^{2}+f_{i}^{2}}{f_{i}^{2}-f_{j}^{2 }}\lambda_{i}\varphi_{i}+\frac{2f_{i}^{2}}{f_{i}^{2}-f_{j}^{2}}\lambda_{j} \varphi_{j}\\ &+\frac{f_{i}^{2}+f_{j}^{2}}{f_{i}^{2}-f_{j}^{2}}\lambda_{i}N_{i}-\frac{2f_{i} ^{2}}{f_{i}^{2}-f_{j}^{2}}\lambda_{j}N_{j}-D_{c}\end{array}  \tag{1}\]  
where \(C\) is the code observables in meters and \(\varphi\) is the carrier-phase observables in cycles; \(f\), \(\lambda\), and \(N\) are frequency, wavelength, and integer ambiguity respectively; the subscripts \(i\) and \(j\) (\(i\
eq j\)) are used to denote different frequencies; and \(D_{C}\) is the constant parts of hardware-induced delays. In theory, this linear combination can eliminate ionospheric and tropospheric delays and all geometric contributions including, for example, clock errors, orbit errors, and the geometry ranges between navigation satellites and receiver, and mainly reflects MP effects and code tracking noise [8; 11]. Figure 1: Numbers of BDS and GPS satellites tracked by the onboard GNOS receiver per epoch in DOY 062. Figure 2: Percentage histogram of the observed GPS and BDS satellites for the 26-day data set. However, the MP combination contains the constant parts of hardware-induced delays and carrier-phase ambiguities. Because these are usually considered as invariant values for each continuous ambiguity block, the practical way to separate them from MP variations is to subtract the mean value of raw MP variations for each block with clean observables and no cycle slips. As a consequence, the MP combination provides only the relative quantity, and the real biases cannot be obtained. For BDS signals, the obtained MP variations can reveal systematic code-carrier divergences, and can be used for code bias modeling. To calculate the MP magnitude of the onboard data set, the daily RMSs of BDS and GPS MP effects were computed for the data above the elevation angle 0\({}^{\circ}\). Figure 3 shows the daily MP1 and MP2 RMSs, and indicates that the variations were very stable. The averaged MP1 and MP2 RMSs are 0.731 m and 0.662 m for BDS, and 0.380 m and 0.724 m for GPS. Compared with GPS MP1, GPS MP2 appears much larger. This is because the SNR of the P2/L2 signals is general poorer than that of C1/L1, with maximum values in our data set being 36.1 and 51.6 dB-Hz respectively. Disclosing additional biases in the MP variations of BDS satellites, Figure 4 shows an example of the B1 and B2 frequency MP time series of 3 complete BDS satellite passes whose maximum elevation angles were close to 90\({}^{\circ}\). The blue dots represent the MP values, and the dark green lines denote the elevation time series. Due to the rapid movement of the Fengyun-3C satellite, the ascending and descending phases of BDS satellites were very rapid and the time interval of a complete satellite pass was only approximately 40 min, which is much smaller than that of ground stations. As illustrated in Figure 4, obvious elevation-dependent biases can be seen, particularly for C11. But it is strange that the MP values do not vary strictly with the elevation values, which is often the case with ground-based BDS MEO data. For C05, there is obviously a periodic signal with unstable wavelength in the time series. The wavelength gradually varies to reach a maximum during the low-elevation range. However, the cause of this phenomenon is still not clear, and we do not discuss it in this paper. With regard to the onboard data set we used, note that there seems to be an elevation-angle limit for the signals of the ascending navigation satellites.