## 3 Results  
### The Normal Projection Reflection Reference Surface Correction Method  
#### 3.1.1 The Angle of Incidence and Emergence  
In order to compare the accuracy of the specular reflection point position methods, the angle of incidence and emergence were calculated according to the positions of the transmitter, the receiver, and the specular reflection points contained in the TDS-1 dataset and those calculated by the S-C Wu method and the GFRRSCM. Taking the results of the 95 tracks from 21:00 31 March to 3:00 1 April 2018 (UTC) as an example, the specular reflection point positions in the geodetic coordinate system and the corresponding angles of incidence and emergence are shown in Figure 4. The TDS-1 orbited the earth for about four circles in six hours, and there was a maximum of four sub-tracks on earth's surface at the same time in each circle, resulting from the four channels of the SGR-ReSl. The angle of incidence by TDS-1 varies the most, the variation on the same track can be up to about 50\({}^{\circ}\), which is significantly higher than the other methods. With a significant difference from the angle of incidence, TDS-1 has smaller variation in the angle of emergence. Since the GFRRSCM and the S-C Wu method approach the actual position of the specular reflection point on the reflection reference surface based on iterative method, the maximum difference between the angle of incidence and emergence is less than the high-accuracy iteration cutoff threshold. There is no distinguishable difference between the angle of incidence and emergence by both the S-C Wu method and the GFRRSCM. In addition, there was no significant difference between the tracks by the S-C Wu method and those by the GFRRSCM, which means that the positioning results of the two methods are very close in the geodetic coordinate system, while the tracks by TDS-1 are different from the other two methods. Figure 5 is the difference between the angles of emergence and incidence by the three methods in Figure 4. The TDS-1 has the largest angle difference, and the maximum reaches 150\({}^{\circ}\), indicating that the specular reflection point positioning error is large. Since the same high-accuracy correction iteration cutoff threshold \(10^{-5}\) rad is set, the angle difference by the S-C Wu method and that by the GFRRSCM are both small. No significant difference between the results of the two methods is observed, indicating that their reflection geometric relationships are more accurate than TDS-1's, and the specular reflection points have higher positioning accuracy. Furthermore, it has been observed in the results of all the three methods that the angle difference on the same track is not changing continuously, there are continuous jumps along the tracks. The magnitude of the jumps are degrees in the TDS-1 results, and \(10^{-4}\) degrees in the results of both the S-C Wu method and the GFRRSCM, discussions in detail are in Section 4. Figure 3: Geometry of the normal reflection reference surface correction: (**a**) the correction in the incidence plane, and (**b**) the correction in the plane perpendicular to the incidence plane. In order to quantitatively analyze and compare the accuracy of the reflection geometric relationship determined by the specular reflection point positions of the three methods, the angle of incidence, emergence, and the difference between them are calculated based on the TDS-1 data of April 2018, as shown in Table 1. Because of the same iteration cut-off threshold set, the GDRRSCM and the S-C Wu method have very close angle difference, which are much smaller than that of TDS-1, indicating that the reflection geometric relationship and the corresponding specular reflection point position by the two methods are close and both of them are more accurate than those in the TDS-1 data.