## 4 Discussion  
The improvements of the positioning accuracy of the specular reflection point are in accordance with the tens of meters magnitude of geoid undulation [1]. According to the corrections of the GFRRSCM and the NPRRSCM, the positioning error caused by the reflection reference surface elevation difference is about twice that caused by the normal-radial difference, indicating that the elevation difference of the reflection reference surface is the main error source of the specular reflection point positioning. In the space coordinate directions, the positioning accuracy improvement in the \(Z\) direction is the most by the GFRRSCM but the least by the NPRRSCM. As the combination result, the GF-NPRRSCM also has the highest accuracy improvement in the \(Z\) direction consistent with the GFRRSCM; this is because the positioning correction to the elevation difference is larger than that to the normal-radial difference. The accuracy improvement in the \(X\) and \(Y\) directions are always close by both the GFRRSCM and the NPRRSCM. In order to study the along-track variation of the reflection geometry determined by the specular reflection points by different methods, the results of the 5 th track from 21:00 31 March to 3:00 1 April 2018 (UTC) are taken as an example. Figure 6 shows the angles of incidence and emergence, and the differences between them determined by the specular reflection point by the GFRRSCM and TDS-1. The angles of incidence and emergence by the two methods reduce first, and then increase. As the angles approach the minimum, the decreasing speed of the angles gradually reduces, while after reaching the minimum, the increasing speed of the angles gradually increases to a stable level  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Spatial Distance (m)**} & \multicolumn{3}{c}{**X (m)**} & \multicolumn{3}{c}{**Y (m)**} & \multicolumn{3}{c}{**Z (m)**} \\ \cline{2-13}  & **Min** & **Max** & **Mean** & **Min** & **Max** & **Mean** & **Min** & **Max** & **Mean** & **Min** & **Max** & **Mean** \\ \hline \multirow{3}{*}{**the NPRRSCM to**} & 5.173 & 5.610 & 1.305 & 7.291 & 4.344 & 6.843 & 1.506 & 4.802 & 6.794 & 3.133 & 4.035 & 5.832 \\  & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) \\  & \(10^{5}\) & \(10^{1}\) & \(10^{1}\) & \(10^{6}\) & \(10^{1}\) & \(10^{9}\) & \(10^{5}\) & \(10^{1}\) & \(10^{9}\) & \(10^{5}\) & \(10^{1}\) & \(10^{9}\) \\ \hline \multirow{3}{*}{**the GF-NPRRSCM**} & 3.958 & 1.045 & 2.866 & 3.051 & 8.175 & 1.373 & 2.884 & 7.657 & 1.322 & 3.583 & 8.452 & 1.608 \\  & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) \\  & \(10^{2}\) & \(10^{2}\) & \(10^{1}\) & \(10^{5}\) & \(10^{1}\) & \(10^{1}\) & \(10^{8}\) & \(10^{1}\) & \(10^{1}\)subsequently. This change of the angles reflects the change in the angle between the position vectors of the TDS-1 satellite and the GPS satellites. The angles of emergence by TDS-1 differ greatly from the angles of incidence, and their difference increases with the angle increases, indicating that the larger the angle of incidence or emergence, the larger the error of the reflection geometric relationship and the lower the accuracy of the specular reflection point positioning by TDS-1. When the angle of incidence exceeds \(20^{\circ}\), the angle difference of TDS-1 is about \(1^{\circ}\). When the angle of incidence exceeds \(45^{\circ}\), the angle difference exceeds \(10^{\circ}\). If the TDS-1 specular reflection point position data is used, the corresponding angle of incidence or emergence should be screened to select more accurate specular reflection point positions considering the related distance error. Compared with TDS-1, the angles of incidence and emergence by the GFRSCM are very close, and their difference does not change significantly as the angle changes along the track.