## 2 Proposed Method
### Selection of the Available Reflected Signals  
We propose a three-step method for selection of the available GNSS reflected signals. (1) The potentially available GNSS satellites are selected for each LEO satellite; (2) the locations of the specular reflection points between the LEO and GNSS satellites are computed; (3) the specular reflection points that lie below the minimum antenna gain are removed. In the processing of both ground-based and airborne GNSS-R measurements, we can simply select the available satellites based on the cutoff elevation because the direct signals can be deemed to be parallel with the reflected signals. However, the reflected points are very far away from the receivers in the spaceborne case, so that the views of the two signals are no longer in parallel. Here, we present a new method for selection of the available GNSS satellites. Figure 4 shows the geometrical relationships among the antenna face direction (\(\alpha\)), the elevation beamwidth (\(\beta\)), the minimum elevation angle (\(\epsilon_{min}\)), the maximum elevation angle (\(\epsilon_{max}\)), the geocentric angle between the LEO and the specular reflected point (\(\Phi\)), and the geocentric angle between the GNSS satellite and the LEO (\(\theta\)). In Figure 4, point O represents the center of the Earth; point P is the specular reflection point; point B is the location of the receiver antenna; \(R\) is the Earth's mean radius; \(h\) is the orbit height of the GNSS-R LEO observatory, and \(H\) is the GNSS satellite's orbit altitude. The red arcs indicate the profiles of the reflecting ground coverage. When the specular points are located at the edges of these red arcs, there are minimum and maximum elevations. These minimum and maximum elevations can be derived using the following equations. Figure 4: Geometrical relationships among the angles in the GNSS-R system. Here, in order to show the angles clearly, only two GNSS satellites and one GNSS-R LEO satellite are given in this figure. \[\frac{R+h}{sin(90^{\circ}+\varepsilon)}=\frac{R}{sin\Big{(}\alpha\pm\frac{\beta}{2} \Big{)}}\]  
\[\varepsilon_{min}=sin^{-1}\Big{[}\frac{R+h}{R}sin\Big{(}\alpha+\frac{\beta}{2} \Big{)}\Big{]}-90\]  
\[\varepsilon_{max}=sin^{-1}\Big{[}\frac{R+h}{R}\sin\Big{(}\alpha-\frac{\beta}{2} \Big{)}\Big{]}-90^{\circ} \tag{2}\]  
The minimum elevations are 40.31\({}^{\circ}\) and 31.18\({}^{\circ}\) at L1 and L2, respectively, while the maximum elevations are 78.13\({}^{\circ}\) and 86.23\({}^{\circ}\) at L1 and L2, respectively. After the minimum elevation with respect to the specular points is obtained, based on the sine theorem within the triangle that is formed by the LEO, the Earth's center and the specular point, Equation (3) can be given as follows. \[\frac{R+h}{sin(90^{\circ}+\varepsilon)}=\frac{R}{sin(180^{\circ}-90^{\circ}- \varepsilon-\Phi)} \tag{3}\]  
\(\Phi\) can then be calculated using Equation (3). Subsequently, \(\theta\) can be derived based on Equation (4). \[\theta=\Phi+\cos^{-1}\bigg{(}\frac{R\cos\varepsilon}{R+H}\bigg{)}-\varepsilon \tag{4}\]  
In Equation (4), because the minimum and maximum angles of \(\Phi\) have already been determined, the value of \(\theta\) is dependent on \(H\) and \(\varepsilon\). Therefore, \(\theta\) will change with the altitudes of the different GNSS satellites, which range from 19,100 km to 35,900 km. Table 3 lists the values of \(H\) and \(\theta\) for the different types of GNSS satellites. We can then select the available GNSS satellites based on their geocentric angles at different epochs. After the appropriate GNSS satellites have been selected, the locations of the reflections can then be determined using the method that was proposed by [PERSON] and [PERSON] (2017). The equations of computing the latitude and longitude of a specific specular reflected point according to the geometry shown in Figure 4 are provided in this subsection. The locations of specular reflected points can be computed using Equations (5) and (6).