## 5 Conclusions  
A stochastic model plays a crucial role in determining the accuracy of a positioning model solution. However, the traditional C/N0-dependent stochastic model often fails to account for the impacts of unmodeled errors such as multipath and atmospheric delays. Leveraging the concept of a DDPR and experimental data, this paper delved into the correlation between DDPR, integrated C/N0, and satellite elevation. Subsequently, we introduced a DDPR-dependent stochastic model based on the optimal satellite subset.  
Figure 11: CDFs of positioning error based on the two models in the occluded environment.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Device**} & \multirow{2}{*}{**Direction**} & \multicolumn{2}{c}{**C/N0-Dependent**} & \multicolumn{2}{c}{**DDPR-Dependent**} & \multirow{2}{*}{**Accuracy**} & \multicolumn{1}{c}{**C/N0-Dependent**} \\  & & **Dependent** & **(m)** & **Improvement** & **(m)** \\ \hline \multirow{3}{*}{Mate40} & N & 6.01 & 4.19 & 30\% & 4.25 \\  & E & 6.67 & 4.50 & 32\% & 4.72 \\  & U & 16.75 & 11.01 & 34\% & 12.34 \\ \hline \multirow{3}{*}{P40} & N & 4.54 & 3.36 & 26\% & 3.68 \\  & E & 7.45 & 4.98 & 33\% & 5.53 \\ \cline{1-1}  & U & 15.66 & 11.90 & 24\% & 14.19 \\ \hline \hline \end{tabular}
\end{table}
Table 3: RMS values of positioning results with different stochastic models in the occluded environment.  
Real-world datasets collected from a Huawei P40 and a Huawei Mate40 were utilized to validate the proposed method. The conclusions of this study are the following:  
* The DDPR effectively reflects the quality of observations. While the correlation between the DDPR and satellite elevation is not significant, it exhibits a strong correlation with the integrated C/N0.
* In occluded environments, a satellite subset boasting superior observational quality can be selected using the integrated C/N0. The positioning accuracy, when relying on this optimal satellite subset, markedly surpasses that derived from the entire constellation.
* In open settings, the merits of a DDPR-dependent stochastic model in pseudorange relative positioning are not markedly superior to the C/N0-dependent stochastic model. The experimental results from both smartphones indicate comparable positioning accuracy between the two models. However, in an occluded setting, the former model proficiently diminishes the weight of inferior-quality observations. This leads to enhanced positioning accuracy for both smartphones. Specifically, the Huawei Mate40 exhibited improvements of 30%, 32%, and 34% in the N, E, and U directions, respectively. The Huawei P40 also showcased enhancements of 26%, 33%, and 24% in the same respective directions.  
A DDPR, when based on an optimal satellite subset, can somewhat capture the effects of significant gross errors, such as multipath ones and NLOSs, in its observations. The resultant stochastic model can mirror the impact of unmodeled errors. This model, with its ease of implementation and low computational demands, shows promise for enhancing GNSS positioning in smartphone navigating in complex urban environments. However, the selection of the optimal satellite subset remains paramount in model construction. Future endeavors will holistically weigh factors such as satellite elevation, C/N0, and satellite spatial distribution to refine satellite selection strategy.  
Methodology, J.D. and A.Z.; software, J.D. and H.W.; formal analysis, J.D. and H.W.; data curation, S.W.; writing--original draft preparation, H.W. and J.D.; writing--review and editing, A.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Natural Science Foundation of Fujian Province, Grant Numbers 2022J011237 and 2020J01262.  
Not applicable.  
Due to restrictions, data are only available upon request.  
The authors declare no conflicts of interest.