## 3 Methodology
### CCSS Method  
For the SNR data of the same satellite, its ascending (S) and descending (J) tracks are considered as independent [24]; so, they were processed independently. The amplitude and phase in Equation (2) can be obtained by LLS fitting the separated modulation term of SNR [62]. Since the phase of a satellite can better characterize SM changes [39], it was used for SM retrieval in this paper. However, the phases of different satellites have different sensitivities to SM, and not all satellite tracks are suitable for SM monitoring [51]. So, the satellite phases needed to be selected. According to previous experiments, it was found that the phases of different satellites that are strongly related to the SM reference values have similar regular variations. Taking 2015 DOY96-256 of P043 as an example, the correlation coefficients were calculated between the phases of each satellite solved during this period and the SM reference values, as shown in Figure 4. It can be seen that satellites with high correlation with the SM reference values, such as PRN07, PRN23, PRN30, etc., also had high correlation with each other. According to this property, and in order to realize satellite selection adaptively, this paper proposes a cross-correlation satellite selection (CCSS) method independent of the SM reference values. The satellites were selected directly according to the degree of cross-correlation between their phase sequences. Therefore, the effective satellites were selected by calculating the cross-correlation coefficients between different satellite phases and then by reasonably setting the threshold range of the cross-correlation coefficient based on the correlation degree (Table 2). \begin{table}
\begin{tabular}{c c c c c c} \hline
**Degree of** & **Very Weak** & **Weak Correlation** & **Medium** & **Strong** & **Very Strong** \\
**Cross-Correlation** & **Correlation** & **Correlation** & **Correlation** & **Correlation** \\ \hline correlation coefficient & 0–0.2 & 0.2–0.4 & 0.4–0.6 & 0.6–0.8 & 0.8–1 \\ \hline \end{tabular}
\end{table} 
Table 2: Cross-correlation threshold range. Figure 4: Correlation coefficient of different satellite phases and SM (2015 DOY96–256). In the figure, the color change from dark green to light yellow indicates a change in correlation from 0 to 1. The darker the color, the lower the correlation, and vice versa. The specific process of CCSS was as follows:  
1. During the experiment, the satellites with relatively complete phase data (more than 95% of the total data) were selected preliminarily. Because for the multisatellite combination retrieval mode, the selected satellite data needed to meet the requirement of continuous and consistent reflection trajectories within the range of satellite perception elevation, the continuous phase could be generated throughout the annual product day observation period. 2. Based on the satellites selected in step 1, the cross-correlation coefficient (\(r_{1}\)) between each satellite phase and other satellite phases was calculated separately. Then, considering the medium correlation as the initial reference condition according to the cross-correlation threshold range in Table 2, the satellites with \(r_{1}\) greater than 0.400 were selected as long as they existed, and the satellites without \(r_{1}\) greater than 0.400 were excluded. \[r(\varphi_{a},\varphi_{b})=\frac{Cov(\varphi_{a},\varphi_{b})}{\sqrt{Var[\varphi _{a}]}\sqrt{Var[\varphi_{b}]}}\] (6) where \(a\) and \(b\) correspond to different (PRN) numbers of GNSS satellites, \(Cov(\varphi_{a},\varphi_{b})\) is the covariance corresponding to \(a\) and \(b\), \(Var[\varphi_{a}]\) represents the variance of \(a\), and \(Var[\varphi_{b}]\) represents the variance of \(b\). 3. The cross-correlation coefficient (\(r_{a}^{i}\)) and its average value (\(\overline{r_{a}^{i}}\)) for each satellite selected in step 2 were calculated.