# Estimating BDS-3 Satellite Differential Code Biases with the Single-Frequency Uncombined PPP Model
## 4 Experimental Results and Analysis
### Satellite DCBs Estimated by SF Data from Multiple Stations  
The preceding section has demonstrated the capability of a single SF receiver to estimate satellite DCBs. Nevertheless, it is crucial to acknowledge that the accuracy of these estimates may vary, primarily due to ionospheric variability. To address this challenge and achieve more robust outcomes, the incorporation of SF data from multiple receivers becomes imperative. In this section, two schemes, namely scheme 1 and scheme 2, are proposed for estimating satellite DCBs using data from multiple receivers. In scheme 1, the satellite DCBs are derived from a total of 25 stations, as depicted in Figure 5. This scheme utilizes observations from all 25 stations to estimate the satellite DCBs. In scheme 2, a subset of stations is selected by excluding eight low-latitude stations. The remaining 17 stations are used to estimate the satellite DCBs. In both scheme 1 and scheme 2, the satellite DCBs are estimated for each individual station. For each satellite, the DCBs obtained from the selected stations are averaged to derive the final value of satellite DCBs. This final satellite DCBs are compared to the CAS DCB products to calculate the absolute offset. As an illustrative example, the absolute offsets for all BDS-3 satellites on DOY 64 and 71, 2023, are provided in Figure 6a,b, respectively. Note that the BDS-3 PRN40 was not included in the WUM precision product on DOY 71, resulting in the absence of the corresponding result for this particular satellite in Figure 6b. On DOY 64, scheme 2 resulted in a reduction in the absolute offsets for 22 out of the 27 BDS satellites compared to scheme 1. The RMS of the absolute offsets for scheme 1 was 0.72 ns, while for scheme 2 it was reduced to 0.45 ns. This reduction in RMS indicates an improvement in the accuracy of the satellite DCB estimates when using scheme 2. Similarly, on DOY 71, excluding the low-latitude stations in scheme 2 led to a reduction in the absolute offsets for 22 out of the 26 BDS-3 satellites. The RMS of the absolute offsets for scheme 1 was 0.76 ns, whereas for scheme 2 it was reduced to 0.41 ns. Once again, scheme 2 resulted in improved estimation accuracy for satellite DCBs. Consistently across both days, scheme 2 yielded absolute offset values for all BDS-3 satellites below 1 ns, indicating closer agreement with the CAS DCB product. This contrast supports the conclusion that excluding low-latitude data leads to improved accuracy in the estimation of satellite DCBs. These experimental results demonstrate that scheme 2 enhances the estimation accuracy of satellite DCBs, as evidenced by the reduced absolute offsets and lower RMS values. Figure 6: The absolute offsets for all BDS-3 satellites in two schemes on DOY 64 and 71, 2023. Figure 7 reveals insights into the performance of scheme 1 and scheme 2 for the estimation of BDS-3 satellite DCBs throughout the experiment's duration. According to the data presented in Figure 7a, when considering scheme 1, the average daily absolute offsets in the satellite DCB estimates remained below 0.7 ns, with a monthly average of 0.57 ns. Interestingly, scheme 2, which excluded data from low-latitude stations, consistently exhibited daily mean absolute offsets below 0.5 ns, resulting in a monthly average of 0.41 ns, except for the experimental result on DOY 88. Further analyzing Figure 7b, it can be observed that in scheme 1, the daily RMS of absolute offsets in March remained below 0.8 ns, with a monthly average of 0.68 ns. On the other hand, scheme 2 consistently displayed daily RMS values below 0.63 ns, leading to a notable monthly average of 0.49 ns. These findings substantiate a notable refinement in the accuracy of DCB estimates, especially when excluding data from low-latitude stations, thereby minimizing the influence of ionospheric variability prevalent in such regions on ionospheric modeling.