3.3.3. Mean Fusion Retrieval Results of Multi-GNSS System

After the mean fusion of multi-frequency in the four GNSS systems, the retrieval results of highly similar trends are obtained. To further improve the accuracy, the mean fusion of the snow depth retrieval results of the multi-GNSS system is carried out, and the final GNSS system retrieval results are obtained, as shown in Figure 13.

**Figure 12.** Mean fusion of multi-frequency retrieval results in the four GNSS systems.

**Figure 13.** Mean fusion retrieval results of multi-GNSS system.

Figure 13 shows that the mean fusion results between the multi-GNSS system are in good agreement with the PBO snow depth results, and that the trend is basically the same.

#### **4. Discussion**

*4.1. Accuracy Analysis between Multi-GNSS and Multi-Frequency GNSS-IR Snow Depth Retrieval Results and PBO Snow Depth*

The above retrieval results are further analyzed, and the retrieval results of different frequency signals in multi-GNSS system are compared; the correlation coefficient (R) and root mean square error (RMSE) are shown in Figure 14.

**Figure 14.** Correlation and RMSE between multi-GNSS and multi-frequency GNSS-IR snow depth retrieval results and PBO snow depth: (**a**) GPS S1C; (**b**) GPS S2L; (**c**) GPS S5Q; (**d**) GLONASS S1C; (**e**) GLONASS S2C; (**f**) Galileo S1C; (**g**) Galileo S5Q; (**h**) Galileo S6C; (**i**) Galileo S7Q; (**j**) Galileo S8Q; (**k**) BDS S2I; (**l**) BDS S6I; (**m**) BDS S7I.

Figure 14 shows the correlation of multi-GNSS and multi-frequency GNSS-IR snow depth retrieval results compared with the PBO snow depth. Table 3 shows the specific R and RMSE.


**Table 3.** R and RMSE between multi-GNSS and multi-frequency GNSS-IR snow depth retrieval results and PBO snow depth.

Figure 14 and Table 3 show that the snow depth results of the GNSS-IR retrieval at different frequencies of the four GNSS systems have a strong correlation with the PBO snow depth. The R of the GPS S2L and S5Q results were 0.99 and 0.98, respectively, which are highly correlated, whereas the R of the S1C was 0.90, which is relatively low. The R of GLONASS S1C and S2C were 0.83 and 0.97, respectively. The correlation of S2C was strong and that of S1C was weak. The R of Galileo S5Q, S6C, S7Q, and S8Q results was approximately 0.95, and that of S1C was 0.88, which is rather weak. The R of BDS S6I and S7I results was 0.95 and 0.93, showing a strong correlation, and that of S2I was 0.86, which was rather weak. At the same time, the RMSE of the results of different frequencies of the four GNSS systems and PBO data were basically in the range of 5 cm to 10 cm, and the error was small. The above data show that the feasibility of retrieving the snow depth using multi-GNSS and multi-frequency GNSS-IR is high. At the same time, for GPS S1C, GLONASS S1C, Galileo S1C, and BDS S2I, the results in the four GNSS systems are rather weak. From the above results, in addition to GPS and GLONASS signals, the Galileo and BDS signals also have a good ability in snow depth retrieval.

#### *4.2. Accuracy Analysis of Multi-Frequency Mean Fusion Results in the GNSS Systems*

Mean fusion retrieval is carried out for multi-frequency retrieval results under the four GNSS systems; the accuracy between the retrieval results and PBO snow depth are further analyzed, as shown in Figure 15.

Figure 15 shows that the retrieval results of the four GNSS systems are obtained by averaging the snow depth results of the GNSS-IR retrieval at multi-frequency. The R between the GPS, GLONASS, Galileo, BDS, and PBO results was 0.99, 0.94, 0.97, and 0.95, respectively, showing strong correlations. At the same time, the RMSE of the four GNSS systems have been reduced to a certain extent, to basically in the range of 4 cm to 7 cm, indicating that the mean fusion of different frequency retrieval results in the four GNSS systems has a good effect on the improvement of retrieval accuracy, which can eliminate the weak correlation of GPS S1C, GLONASS S1C, Galileo S1C, and BDS S2I.

Compared with the snow depth of the different frequency signal in the multi-GNSS system retrieval results, the GNSS multi-frequency mean fusion method can effectively improve the retrieval accuracy. The specific improvement accuracy is shown in Table 4.

**Figure 15.** Mean fusion accuracy analysis of multi-frequency retrieval results in the four GNSS systems: (**a**) GPS multi-frequency fusion; (**b**) GLONASS multi-frequency fusion; (**c**) Galileo multifrequency fusion; (**d**) BDS multi-frequency fusion.

**Table 4.** Comparison of different frequency signal in the multi-GNSS system retrieval results; multifrequency mean fusion accuracy increases in R and decreases in the RMSE.


As can be seen from Table 4, the R of the GNSS multi-frequency mean fusion increases by 11.7%, which is higher than a single frequency in multi-GNSS system retrieval results, and the GLONASS S2C results decrease by 3.2%, but most of the results' correlations are improved. At the same time, the RMSE decreases by 55.6%, and though the retrieval accuracy of Galileo S7Q and BDS S6I is not improved, the other accuracy has been greatly

improved. This shows that the mean fusion of the GNSS multi-frequency retrieval results can effectively improve the accuracy of the snow depth retrieval.

#### *4.3. Accuracy Analysis of Mean Fusion Retrieval between Multi-GNSS System*

The accuracy of multi-frequency fusion retrieval results has been improved to a certain extent. Furthermore, the fusion accuracy of the retrieval results of the four GNSS systems is analyzed, as shown in Figure 16.

**Figure 16.** Comparison of the mean fusion results of multi-GNSS system with PBO snow depth.

Figure 16 shows that the R between the mean fusion results of the multi-GNSS system and PBO snow depth was 0.99, showing a strong correlation. At the same time, the RMSE was 3 cm, and the error was also significantly reduced, indicating the effectiveness of this method.

In order to further improve the combined retrieval accuracy of the GNSS system, the GNSS multi-frequency fusion results are further mean fused. The fusion results are compared with the four GNSS systems, and the results are shown in Table 5.


BDS 4.0% 40%

**Table 5.** Comparison of multi-frequency mean fusion; multi-GNSS system fusion accuracy increases in R and decreases in the RMSE.

It can be seen from Table 5 that the accuracy of the results after multi-GNSS system fusion is further improved. Compared with the results of GNSS multi-frequency fusion, the R of the four GNSS systems are improved, except for GPS. GLONASS has the highest increase of 5.1%. In terms of RMSE, GLONASS increased by 57.1%. The GPS is not improved on R, but it is improved by 25% on RMSE. It can be seen from the above results that the further fusion of the multi-frequency retrieval results of the four GNSS systems can effectively improve the retrieval accuracy. Therefore, the multi-GNSS system combined snow depth retrieval method has strong reliability.
