## 3 DDPR-Dependent Model Based on Optimal Satellite Subset
The RMS values of the three schemes in planar positioning are 4.19 m, 5.70 m, and 5.41 m, respectively, showing a consistent pattern with the Huawei Mate40 smartphone. Therefore, compared to satellite elevation, the integrated C/N0 is more indicative of the quality of GNSS observational values for a smartphone, and a satellite selection scheme based on integrated C/N0 can select satellites of higher quality to ensure better positioning accuracy. According to the above analysis, this paper proposes a DDPR-dependent stochastic model based on the optimal satellite subset with an integrated C/N0. For a visual representation, the algorithm flowchart is provided in Figure 5. The steps to establish the stochastic model are outlined as follows. First, combined with the C/N0 of both the reference station and the smartphone, the observational quality evaluation index, namely the integrated C/N0, was calculated. Based on this, the optimal satellite subset for the pseudorange differential positioning solution was determined. Secondly, utilizing the optimal subset of satellites, coupled with Equation (10) defining C/N0 variance, the C/N0-dependent stochastic model was established, and the approximate terminal position can be derived by pseudorange differential positioning. \[{\sigma_{\text{R/S}}^{i}}^{2}=\hat{a}+\hat{b}\times 10^{-\frac{(C/N0)_{i}}{ \hat{b}0}} \tag{10}\]  
where \(\sigma\) represents the pseudorange noise. C/N0 represents the carrier-to-noise density ratio for each satellite, which can be directly obtained from the smartphone's observation values. Parameters \(\hat{a}\) and \(\hat{b}\) needed to be determined for each piece of equipment at different \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Huawei Mate40**} & \multicolumn{3}{c}{**Huawei P40**} \\ \cline{2-7}
**Selection Scheme** & **N** & **E** & **Horizontal** & **N** & **E** & **Horizontal** \\ \hline Integrated C/N0 & 2.90 & 2.05 & 3.55 & 2.87 & 3.06 & 4.19 \\ Satellite elevation & 3.89 & 4.71 & 6.11 & 2.88 & 4.92 & 5.70 \\ Elevation-C/N0 & 3.71 & 3.29 & 4.96 & 2.88 & 4.58 & 5.41 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: RMS values of positioning results with different satellite selection schemes (unit: meter). Figure 5: Flowchart of DDPR-dependent model based on optimal satellite subset. frequencies and constellations. For further detail on the calibration of parameters \(\hat{a}\) and \(\hat{b}\), refer to the work of [PERSON] et al. (2018, 2019). Finally, the DDPRs for each satellite were estimated. While the residual is influenced by the terminal's approximate position, it can still signify the quality of the DD observations, particularly gross errors like multipath errors and NLOSs. By taking the reciprocal of its absolute value as the weight factor, an observational stochastic model was formulated, expressed as the following:  
\[W=diag(w_{1}\;\;w_{2}\;\cdots\;w_{m}\;) \tag{11}\]  
\[w_{i}\;=\frac{1}{|\text{DDPR}_{i}|} \tag{12}\]  
In essence, this was achieved by diminishing the weight of observations with large pseudorange residuals, thereby mitigating their impact on the positioning results.