## 3 Satellite-Borne GPS Data Quality Analysis
### Multipath Error  
During the propagation of satellite signals, external factors in the surrounding environment can lead to the phenomenon known as multipath effect. This effect occurs when reflected signals become superimposed on the direct satellite signals received by the receiver. In our analysis, we investigated the multipath errors present in the HY-2B/2C/2D satellite-borne GPS data during our experiment. Figure 5 provides a visual representation of the temporal variations in multipath errors in the L1 and L2 bands. Notably, the time-frames when significant errors in MP1 (multipath error in L1) and MP2 (multipath error in L2) occur are nearly identical.  
Based on the linear combination of pseudo-range and carrier phase data, the multipath errors in L1 and L2 bands can be calculated by ignoring the effect of measurement noise [26]:  
\[\begin{array}{l}MP1=M_{1}-(1+\frac{2}{\alpha-1})\varphi_{1}+(\frac{2}{\alpha- 1})\varphi_{2}\\ MP2=M_{2}-\frac{2}{(\alpha-1)}\varphi_{1}+(\frac{2\alpha}{\alpha-1}-1)\varphi_{ 2}\end{array} \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **C1C** & **C1P** & **C2P** & **L1C** & **L2P** \\ \hline HY-2B missing amount & 3592 & 114,359 & 217,844 & 14,652 & 228,309 \\ HY-2B missing percent & 0.09\% & 2.85\% & 5.42\% & 0.36\% & 5.69\% \\ HY-2C missing amount & 2818 & 123,452 & 226,025 & 9955 & 233,007 \\ HY-2C missing percent & 0.07\% & 3.15\% & 5.76\% & 0.25\% & 5.94\% \\ HY-2D missing amount & 2146 & 117,773 & 204,863 & 8807 & 211,108 \\ HY-2D missing percent & 0.06\% & 3.14\% & 5.47\% & 0.24\% & 5.63\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Statistics of missing observational data.  
Figure 5: Multipath error (**(a)** HY-2B satellite MP1, **(b)** HY-2B satellite MP2, (c) HY-2C satellite MP1, **(d)** HY-2C satellite MP2, **(e)** HY-2D satellite MP1, **(f)** HY-2D satellite MP2).  
where _MP_1 and _MP_2 represent the multipath errors of two frequencies; \(M\)1 and \(M\)2 are the pseudorange observations of the two frequencies; _\(\varphi_{1}\)_ and _\(\varphi_{2}\)_ are the carrier phase observations of the two frequencies; and _\(\alpha=f_{1}/f_{2}\)_, where _\(f_{1}\)_ and _\(f_{2}\)_ are the frequencies of the two bands.  
To better illustrate the multipath effect, data from the first one and a half hours before the first day of each satellite experimental period were selected for multipath error analysis, and the results are shown in Figure 5. From the observations made in Figure 5, it is evident that the MP1 values are slightly higher than the MP2 values. The multipath errors for most satellites display minimal fluctuations and only exhibit significant changes during the early and late stages of GPS satellite signal reception. Notably, lower elevation angles have a more pronounced impact on MP1, leading to more substantial fluctuations in MP1 compared to MP2 during the initial and final phases of signal reception. However, in the middle of signal reception, both MP1 and MP2 values become smaller and more stable, primarily due to the higher elevation angle.  
Table 3 summarizes the quality indicators of HY-2B/2C/2D satellite-borne GPS data, including multipath error, average elevation angle, and satellite visibility. The root mean square (RMS) average values for multipath errors in the L1 band for HY-2B/2C/2D satellites are 0.36 m, 0.38 m, and 0.34 m, respectively. In the L2 band, the RMS average values for multipath errors are 0.24 m, 0.27 m, and 0.22 m, respectively. Given that the surface environment of the satellites remains largely consistent, there are no significant variations in the average elevation angle, multipath error, and satellite visibility. This uniformity in the quality of satellite-borne GPS data across HY-2B/2C/2D satellites highlights that the \"HY2_Receiver\" operates effectively and reliably.