# Validating Precise Orbit Determination from Satellite-Borne GPS Data of Haiyang-2D
## 3 Results and Discussion  
### Quality Analysis of Satellite-Borne GPS Data  
The satellite signals received by the GPS receiver consist of the direct signal and a superimposed signal of reflection; the latter can affect the quality of the observations. The impact on the pseudo-range can reach tens of meters, while the impact on the carrier phase is small, at only a few centimeters. Multipath errors are closely related to antenna characteristics, receiver environments, incidence angle, etc. It is difficult to establish a uniform and accurate model, so the multipath effect is considered one of the most important factors affecting the quality of data [29; 30]. Based on the linear combination of pseudo-range observations and carrier-phase observations, multipath errors of \(L_{1}\) and \(L_{2}\) frequency can be calculated [31]:  
\[MP1=M_{1}-(1+\frac{2}{\alpha-1})n_{1}\lambda_{1}+(\frac{2}{\alpha-1})n_{2} \lambda_{2}-(1+\frac{2}{\alpha-1})\varphi_{1}+(\frac{2}{\alpha-1})\varphi_{2} \tag{14}\]  
\[MP2=M_{2}-(\frac{2\alpha}{\alpha-1})n_{1}\lambda_{1}+(\frac{2\alpha}{\alpha-1 }-1)n_{2}\lambda_{2}-(\frac{2\alpha}{\alpha-1})\varphi_{1}+(\frac{2\alpha}{ \alpha-1}-1)\varphi_{2} \tag{15}\]  
where \(M_{i}\) is the multipath effect of pseudo-range on both frequencies; \(\alpha=\frac{f_{1}^{2}}{f_{2}^{2}}\); \(n_{i}\) and \(\lambda_{i}\) denote the integer ambiguity of carrier-phase \(L_{i}\) and wavelength of the carrier-phase \(L_{i}\); \(\varphi_{i}\) denotes the multipath noise of \(L_{i}\) band. The carrier-phase multipath as well as the elevation angle of G03 as observed from HY-2D were calculated and are shown in Figure 1. Figure 1a,c illustrate statistical assessments of MP1 and MP2 and elevation angles, while Figure 1b,d illustrate the exceptional cases of MP1 and MP2 during the period when the GPS satellite was just locked by the satellite-borne GPS receiver at the beginning of the observations. It can be seen from (a) that MP1 converged rapidly when the satellite elevation angle was greater than 60\({}^{\circ}\). When elevation angles were less than 60\({}^{\circ}\), MP1 fluctuated more; the fluctuations were between \(-2\) and \(2\) m. During the period in Figure 1b, the satellite elevation angles were all less than 45\({}^{\circ}\), so MP1 fluctuated greatly throughout the period and no convergence occurred. The phenomenon indicated in (b) was a rare occurrence. At the beginning when the receiver locked GPS and started to collect observations, MP2 maintained a large negative value, and after a short period, it returned to normal. Figure 1c reflects that the change of elevation angle did not have a drastic effect on MP2; when the elevation angle was greater than 40\({}^{\circ}\), MP2 always fluctuated within a small range of about \(-0.2\) to \(0.2\) m and within \(-0.5\) to \(0.5\) m overall. During the period in Figure 1d, the satellite elevation angles were all less than 30\({}^{\circ}\), so the MP2 fluctuated more, and the overall fluctuation ranged between \(-2\) and \(2\) m.  
The number of satellites observed can reflect the quality of the data and thus the stability of the receiver. Through the quality analysis of HY-2D satellite-borne GPS data for 7 days from DOY 262 to 268, six or more satellites could be observed 78.7% of the time, and fewer than four satellites were observed only 0.15% of the time. O/slps represents the ratio of the actual number of epochs observed over a period to the number of cycle slips epochs; the more cycle slips occurring, the smaller the O/slps will be. Data completeness represents the ratio of the actual number of epochs observed by the GPS receiver to the theoretical number of epochs in a period, while in the actual process of data acquisition various factors may lead to missing data. The data utilization rate is the ratio of the actual number of epochs observed by four or more satellites with dual-frequency observations to the theoretical number of epochs observed.