# Research on Shore-Based River Flow Velocity Inversion Model Using GNSS-R Raw Data
## 4 River Flow Velocity Inversion Result and Analysis  
### River Flow Velocity Inversion Results  
The inversion river flow velocity results per 2 min were calculated according to the shore-based carrier phase river flow velocity inversion method in Section 2. Figure 13 shows the GPS L1 inversion results. The blue solid circle represents the real river flow velocity \(v_{real}\) per 5 min; green points are split up into squares (results of PRN 4) and triangles (results of PRN 9). Inversion results are shown in 2-min intervals. Figure 14 shows the BDS B11 inversion results. The blue solid circle represents the real river flow velocity \(v_{real}\) per 5 min; orange points are split up into squares (results of GEO 2) and triangles (results of IGSO 10). Inversion results are shown in 2-min intervals.  
Four satellites' (GPS PRN 4, GPS PRN 9, BDS GEO 2 and BDS IGSO 10) results and the accuracy verification results are listed in detail in Table 2.  
The Spearman correlation coefficient is used to measure relevance in this paper. The correlation coefficient \(R\) is as follows:  
\[R=\frac{\sum_{i}\left(xi-\overline{x}\right)\left(yi-\overline{y}\right)}{ \sqrt{\sum_{i}\left(xi-\overline{x}\right)^{2}\sum_{i}\left(yi-\overline{y} \right)^{2}}} \tag{13}\]  
In the formula, \(x_{i}\) and \(y_{i}\) are correlated variables, \(\overline{x}\) and \(\overline{y}\) are the average values of the variables, and \(R\) ranges from \(-1\) to \(1\). Generally, \(R>0.7\) demonstrates a strong  
Figure 12: Photograph of the Yangtze River surface.  
Figure 13: GPS L1 inversion results. In the figure, “\(\copyright\)” represents the 1 st period of GPS PRN4 inversion, and “\(\copyright\)”represents the second stage of GPS PRN4 inversion.  
correlation between variable, while \(0.7>R>0.4\) indicates there is a moderate correlation between variables.  
By analyzing the results in Figure 13, Figure 14, and Table 2, GPS PRN 4 (1 st period) inversion MAE reaches up to 0.028 m/s and root mean square error RMSE reaches 0.036 m/s. By contrast, GPS PRN 4 (2 nd period) inversion MAE and RMSE are 0.080 and 0.090, respectively. The BDS IGSO 10 inversion MAE and RMSE are 0.061 m/s and 0.073 m/s, respectively. Compared with BDS IGSO 10 inversion results, the MAE and RMSE of BDS GEO 2 are improved by 0.013 m/s and 0.01 m/s, respectively, showing more accurate inversion results. \(R\) of PRN 4 (1 st period), GEO 2, and IGSO 10 are higher than 0.7, showing strong correlation, which proves the effectiveness of inversion. Among these, a large gap existed between the inversion results of PRN 4 (1 st period) and PRN 4 (2 nd period). This may be due to the influence of obstacles or relatively fewer \"close points\", as the current meter cannot accurately characterize the river velocity of specular points. The precision of PRN 9 is also lower than other inversion results, which may be due to the specular points of GPS PRN 9 being farther away from the current meter: the fixed current meter cannot represent the velocity at the specular points well, which affects the evaluation of results and the effectiveness of inversion.