# First In-Orbit Validation of Interferometric GNSS-R Altimetry: Mission Overview and Initial Results
## 2 Mission Overview
### iGNSS-R Sea Surface Height Retrieval  
#### 2.4.1 Geometry Model for iGNSS-R SSH Calculation  
The geometry model for iGNSS-R SSH calculation is illustrated in Figure 7.  
Figure 6: Simulated minimum iGNSS-R resolution cells for BDS, GPS, and Galileo systems. (**a**) BDS, B1, (**b**) BDS B2, (**c**) GPS L1, (**d**) GPS L5, (**e**) GAL E1, (**f**) GAL E5.  
In Figure 7, T denotes a GNSS satellite, R represents a GNSS-R receiver, S indicates the sea surface specular point where the signal emitted by GNSS satellite T is reflected by the sea surface and received by iGNSS-R altimeter R, O\({}_{1}\) is the theoretical sea surface specular point on the reference ellipsoid surface, O\({}_{0}\) is the projection point of specular point S onto the reference ellipsoid surface, and \(\alpha\) represents the incidence angle. The distance between O\({}_{0}\) and S is the height of the GNSS-R specular point relative to the reference ellipsoid surface, which is the instantaneous SSH (\(SSH_{ori}\)) measurable by GNSS-R. Points R\({}_{1}\) and R\({}_{2}\) represent the mirror images of receiver R relative to the ellipsoid surface and sea level, respectively. According to the mirror image principle, the distance between R\({}_{1}\) and R\({}_{2}\) equals twice the \(SSH_{ori}\).  
The formula for calculating the GNSS-R \(SSH_{ori}\) is as follows [44]:  
\[\begin{array}{ll}SSH_{ori}=\frac{\Delta\rho_{g}}{2 cos\alpha}&=\frac{\left( \rho_{gg}^{\alpha}-\rho_{gg}^{\alpha}\right)-c\Delta\tau}{2 cos\alpha}\\ &+\frac{\rho_{turb}+\left(\rho_{lum}^{\alpha}-\rho_{lum}^{d}\right)+\rho_{ transg}^{d}+\rho_{instr}^{d}+\rho_{real}^{d}}{2 cos\alpha}\end{array} \tag{1}\]  
where \(\Delta\rho_{g}\) is the geometric distance difference of TR\({}_{1}\) and TR\({}_{2}\) in the geometry model; \(\rho_{gg}^{\alpha}\) represents the sum of the distance from the GNSS satellite to O1 and the geometric distance from O1 to the iGNSS-R altimeter R; \(\rho_{gg}^{do}\) is the geometric distance between the iGNSS-R altimeter R and the GNSS satellite T; \(c\) is the speed of light; \(\Delta\tau\) is the measured propagation delay difference between the GNSS sea surface reflected signal and the direct signal, and is measured utilizing the leading edge of the iGNSS-R DM in this study; \(\rho_{\text{trop}}^{\text{r}}\) accounts for the tropospheric delay of the GNSS reflection path, including dry and wet tropospheric delays; \(\rho_{ion}^{r}\) and \(\rho_{ion}^{d}\) represent the ionospheric delays along GNSS reflection path and direct path, respectively; \(\rho_{rough}^{r}\) accounts for the electromagnetic deviation caused by sea surface roughness; \(\rho_{instr}^{rd}\) is the receiver hardware delay; and \(\varepsilon^{d}\) is the ranging error caused by the measurement error of \(\Delta\tau\).  
Figure 7: Geometry model for iGNSS-R SSH calculation.  
Similarly to the radar altimeter, after obtaining the instantaneous sea surface height \(SSH_{ori}\), it is necessary to apply geophysical corrections to it to compare measurements at different times or compare measurements to the mean sea surface, removing the influence of factors such as ocean tides, polar tides, solid Earth tides, and dynamic atmospheric correction (DAC) in order to obtain the final SSH.