## 3 DDPR-Dependent Model Based on Optimal Satellite Subset  
The key purpose of this method is to select the satellite with better observation quality from all visible satellites. Two main criteria are generally used to evaluate the quality of observations: the satellite elevation and the C/N0 value. Previous research has demonstrated that single-differenced pseudorange residuals have a stronger correlation with C/N0 values than satellite elevations, particularly for smart devices [4]. When it comes to relative positioning, the basic observation is typically in the form of DD observation. The reference satellite observations included in each DD observation are the same; hence, the quality difference primarily depends on the non-reference satellite observations of the reference station and the smartphone. Given that the C/N0 value can more accurately reflect the quality of satellite observations, an integrated C/N0--which is defined as the sum of the C/N0 of the non-reference satellite corresponding to the reference station and the smartphone--is used as the quality evaluation index of the DD code pseudorange observations. The data of the Huawei P40 smartphone in the ultra-short baseline described in the above section were further analyzed. Two satellites, G07 and C09 in the GPS and BDS systems, respectively, which have a long viewing time and a large range of elevation variation, were selected. Figure 2 illustrates the correlation between the DDPR and the satellite-integrated C/N0 and elevation. A larger DDPR indicates a poorer quality of double-difference observations. From the figure, it is evident that when the DDPR fluctuates within the range of \(-10\) m to \(10\) m, the corresponding integrated C/N0 is primarily concentrated within the range of \(70\) to \(90\) dB-Hz. Particularly, when the DDPR becomes abnormally large, for example, around the 2000 th and 8000 th epochs of satellite G07 and around the 3000 th and 6000 th epochs of satellite C09, the corresponding integrated C/N0 also suddenly changes and is far less than the normal value. Conversely, when comparing the satellite elevation with the DDPR, Figure 2 reveals that the correlation between the DDPR and satellite elevation is not obvious on the whole. Furthermore, low-elevation satellites, compared to high-elevation satellites, have a higher probability of DDPR outliers. The correlation between DDPR and integrated C/N0, as well as the elevation of all satellites, was further analyzed. The DDPRs were sorted in ascending order of the satellite elevation angle and integrated C/N0, respectively, and the mean of absolute values of  
Figure 2: DDPRs against the satellite C/N0 and elevation. (**a**) Satellite G07. (**b**) Satellite C09. each interval of 1 degree and 1 dB-Hz were computed. Figure 3 shows the mean values of absolute DDPRs at different elevation angles and integrated C/N0 values. As can be seen from Figure 3, the mean value of the DDPR fluctuates greatly in the sequence of satellite elevation changes. In general, the DDPR tends to decrease with the increase in satellite elevation, but the whole trend line is not smooth enough and the correlation is not obvious. In Figure 3, the integrated C/N0 values above 80 dB-Hz correspond to mean DDPR values within 3 m, indicating better observational quality. Overall, there is a consistent decrease in the DDPR with increasing integrated C/N0, demonstrating a smooth trend line and strong correlation between the two variables. As analyzed in the previous section, the integrated C/N0 and satellite elevation can to some extent indicate the quality of satellite observations, and the satellite selection according to different quality evaluation indicators will lead to different positioning effects. This study attempts to develop three satellite selection schemes based on quality assessment indicators. Scheme 1 is developed using the integrated C/N0. Scheme 2 utilizes the satellite elevation as its basis. Scheme 3 combines both the satellite C/N0 and satellite elevation for its development.