## 3 Results
### The Normal Projection Reflection Reference Surface Correction Method
#### 3.1.2 The Specular Reflection Point Positioning Accuracy  
In order to quantify and compare the differences in the positioning accuracy of the three methods, the arithmetic mean of modes of the spatial distances (Euclidean distance) and the coordinates difference in the geodetic and the space coordinates systems with the corresponding standard deviations between the specular reflection points positions by the three methods were calculated based on April 2018 TDS-1 data, see Table 2. Based on the results in Section 3.1.1, the positioning accuracy of the S-C Wu method and the GFRRSCM is relatively close and both higher than that of TDS-1. Therefore, the positioning improvement by the S-C Wu method to TDS-1 can be regarded as that by the GFRRSCM to TDS-1, it also quite shows the positioning error caused by the elevation difference between the TDS-1 reflection reference surface and the sea surface, see the second row of Table 2. In the space coordinate system, the S-C Wu method improves the positioning accuracy by more than 40 km based on that by TDS-1. The accuracy in the \(Z\) direction is improved the most, exceeding 27 km, and the accuracy in the \(X\) and \(Y\) directions is improved by more than 17 km. In the geodetic coordinate system, the comprehensive positioning accuracy is improved by about 0.4\({}^{\circ}\), the accuracy of longitude and latitude is improved by the same magnitude, while longitude is improved more.  
The improvement of the positioning accuracy by the [PERSON] method to TDS-1 can be regarded as that by the GFRRSCM to TDS-1 considering the huge relative difference of positioning accuracy. Compared with the [PERSON] method, the GFRRSCM corrects the reflection reference surface from the WGS-84 ellipsoid to geoid. The difference in the specular reflection point position between the two methods shows the improvement by reducing the elevation difference between the reflection reference surface and the sea surface, it also quite shows the positioning error caused by the elevation difference between the WGS-84 ellipsoid and the sea surface, see the fourth row of Table 2. In the space coordinate system, the positioning accuracy is improved by 25.15 m. The improvement in the \(X\)  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & **Spatial** & **X (m)** & **Y (m)** & **Z (m)** & **B (\({}^{\circ}\))** & **L (\({}^{\circ}\))** \\ \hline \multirow{2}{*}{**the S-C Wu method vs TDS-1**} & **mean** & \(4.147\times 10^{4}\) & \(1.761\times 10^{4}\) & \(1.756\times 10^{4}\) & \(2.764\times 10^{4}\) & \(3.488\times 10^{-1}\) & \(4.839\times 10^{-1}\) \\  & **standard deviation** & \(2.027\times 10^{4}\) & \(9.304\times 10^{3}\) & \(9.388\times 10^{3}\) & \(1.372\times 10^{4}\) & \(1.745\times 10^{4}\) & \(1.635\times 10^{4}\) \\ \hline \multirow{2}{*}{**the GFRRSCM vs the [PERSON] method**} & **mean** & \(2.515\times 10^{3}\) & \(1.085\times 10^{3}\) & \(1.170\times 10^{3}\) & \(1.459\times 10^{3}\) & \(2.817\times 10^{4}\) & \(1.733\times 10^{4}\) \\  & **standard deviation** & \(7.821\times 10^{3}\) & \(4.352\times 10^{3}\) & \(4.695\times 10^{3}\) & \(6.267\times 10^{3}\) & \(2.078\times 10^{3}\) & \(7.448\times 10^{4}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The spatial distances and the coordinates difference modes with the corresponding standard deviations between the specular reflection points positions by the three methods.  
\(Y\), and \(Z\) directions in Table 2 are the elevation correction \(\sigma_{X}\), \(\sigma_{Y}\), and \(\sigma_{Z}\) in Equation (2), respectively. The accuracy in the \(Z\) direction is improved the most, by about 15 m, and in the \(X\) and \(Y\) directions the accuracy is improved by about 11 m. In the geodetic coordinate system, the comprehensive positioning accuracy is improved by about \(2\times 10^{-4\circ}\), the accuracy of latitude and longitude is improved by the same magnitude, while latitude is improved more.