## 5 Results and Discussion  
### Separation of the Modulation Terms  
According to the previous description of SNR separation, EMD was used to decompose the SNR of each satellite adaptively, and the decomposition results of PRN 14 and 32 are shown in Figure 6. It can be seen that as the decomposition layers increased, the components from IMF1 to the residual tended to smooth, the frequency decreased in order, and the changing trend among the low-frequency components showed a basic consistent feature. The components of PRN 14 and 32 were further analyzed for correlation with SNR, as shown in Table 3. Visibly, the correlation coefficients (\(r\)) from IMF1 to the residual gradually increased, and there were obvious cut-off points, such as IMF6 for PRN14 and IMF7 for PRN32. Further, \(r\) between IMF1-IMF6 for PRN14 and IMF1-IMF5 for PRN32, which tended to be the high-frequency modulation terms, was less than 0.600. In addition, \(r\) between IMF7-residual for PRN14 and IMF6-residual for PRN32, which tended to be the low-frequency trend terms, was greater than 0.600. It follows that the cut-off points for the high- and low-frequency components were not fixed. If one or several layers of IMF were fixed directly as the trend term, this would probably cause large errors. As such, reasonably and flexibly determining the correlation coefficient threshold (\(r_{m}\)) corresponding to \(IMF_{T}\) was extremely important for effectively separating the modulation and the trend terms of SNR. After many experiments and comparative analyses, it was found that when \(r_{m}\) was 0.600, the decomposition effect was better. Accordingly, \(r_{m}\) was set to 0.600 in this paper. To further compare and analyze the effect of the trend items obtained from the combination of different low-frequency components, the components determined by residual, IMF9-residual, IMF8-residual, IMF7-residual, and the IMF discriminant method were used, and the trend items obtained are shown in Figure 7.  
Figure 5: Flowchart for retrieving SM. For the model establishment, the previous 70% of all data from DOY98 to DOY209 were used as the training set, and the following 30% from DOY210 to DOY256 were used as the test set. It can be seen in Figure 7 that the trend terms separated by the IMF discriminant method were consistent with the total trend of SNR. By comparison, the fitting results from other single-layer or multi-layer IMF component combinations showed some bias. Therefore, the IMF discriminant method could effectively determine the cut-off points of the trend term and modulation term. The separation results of the modulation and trend terms for different satellites obtained by combining EMD and the IMF determination method are shown in Table 4. For SNR of different satellites, the number of EMD decomposition layers was basically located in 9-10 layers, and the demarcation points of the trend and modulation term were mainly concentrated in IMF6-IMF8. Therefore, the IMF modulation term components extracted from the SNR of different satellites were not fixed, and the trend term could be accurately separated using the combination of multiple low-frequency IMF components determined by the IMF discrimination method. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**IMF**} & \multicolumn{2}{c}{**_r_**} \\ \cline{2-3}  & **PRN14** & **PRN32** \\ \hline SNR & 1 & 1 \\ IMF1 & 0.064 & 0.015 \\ IMF2 & 0.065 & 0.050 \\ IMF3 & 0.013 & 0.053 \\ IMF4 & 0.174 & 0.051 \\ IMF5 & 0.018 & 0.056 \\ IMF6 & 0.703 & 0.208 \\ IMF7 & 0.989 & 0.925 \\ IMF8 & 0.989 & 0.989 \\ IMF9 & 0.989 & 0.989 \\ residual & 0.905 & 0.988 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Correlation coefficient (_r_) of each IMF with the original SNR. Figure 6: The decomposition results of EMD. In the Figure, the horizontal axis represents the epoch of the satellite, and the vertical axis represents the amplitude of the signal. The intrinsic mode function is represented from IMF1 to the residual, with a gradually decreasing frequency.