## 4 Results and Discussion
### Open Environment  
In the experiment, GPS and BDS satellites were chosen. Figure 7 displays the distributions and counts of the observed satellites in the open environment. It is evident that throughout the experiment, the satellite count in the northern direction was relatively  
Figure 6: Experimental scenarios. (**a**) Reference station. (**b**) Smartphones in an open environment. (**c**) Smartphones in an occluded environment.  
sparse. The combined count of the BDS/GPS satellites per epoch never dropped below 16, and consistently remained between 24 and 27 for the majority of the time.  
The relative positioning performance for Mate40 and Huawei P40 smartphones were derived using code pseudorange observations for each epoch. These were then juxtaposed against known benchmark coordinates. Figure 8 delineates the positioning errors in the N, E, and up (U) directions using both the C/N0-dependent stochastic mode and the DDPR-dependent mode. The positioning errors in the N and E directions for both modes predominantly fall within the [\(-\)5 m, +5 m] range, with marginal differences between them. However, the U direction errors are more pronounced, mainly spanning the [\(-\)10 m, +10 m] range. Observational errors, such as multipath errors, caused anomalies with substantial errors in certain epochs across all three directions. Broadly speaking, the positioning precision with both stochastic modes is comparable. Nevertheless, during specific epochs, like the 3000 to 4000 epoch span for the Huawei Mate40, the presence of satellites with inferior observational quality leads to a noticeable surge in positioning errors. During these instances, the DDPR-dependent stochastic model, which reduced the weight of satellite observations with significant pseudorange residuals, showcased superior positioning accuracy compared to the C/N0-dependent stochastic mode.  
Table 2 presents the RMS values of the positioning results derived from the various stochastic models. The data clearly show that, only for the Huawei P40 in the N direction, the RMS value based on the DDPR-dependent stochastic model is about 0.3 m higher than that of the C/N0-dependent stochastic mode, while in other directions, the former is smaller than that of the latter. In general, there is little difference in the RMS values obtained by the two stochastic models, but the overall positioning performance based on the DDPR-dependent model is slightly better than that of the C/N0-dependent model.  
The final column in Table 1 also enumerates the positioning performance when utilizing the optimal satellite subset with the C/N0-dependent stochastic mode. It is obvious that its positioning accuracy is slightly inferior to that of the full satellite positioning (as indicated in the third column of Table 2). This discrepancy primarily stems from the high-quality signals received from all satellites in an open environment. When juxtaposed against full constellation positioning, the optimal subset satellite positioning employs fewer satellites, resulting in a larger DOP value. Consequently, the corresponding RMS is also relatively higher. In essence, the optimal subset satellite does not offer a pronounced advantage in open environments.  
Figure 7: Distributions and counts of the observed satellites in the open environment.