The uncombined model using undifferenced triple-frequency observations provides an alternative approach for the precise estimation of differential code biases (DCBs) of GPS satellite and receiver. However, the accuracy of DCB estimation is significantly affected by the satellite clock offset due to their strong correlation. We aim to analyze the impact of the satellite clock offset on the estimation of GPS DCB for different frequency pairs. The relationship between satellite clock offset and DCB estimates is rigorously studied based on the derived full-rank triple-frequency uncombined model. Theoretical analysis indicates that the initial satellite clock bias would affect the size of satellite DCB estimates in a linear way. To test our analysis, precise products released by the international GNSS service (IGS), the Center for Orbit Determination in Europe (CODE) and the German Research Centre for Geosciences (GFZ), are used for data processing and comparison. The channel types 1W, 2W and 5X for both GPS triple-frequency code and phase measurements are chosen for DCB estimation. Results show that the average monthly standard deviation (STD) is 0.06 ns and 0.08 ns for GPS satellite C1W–C2W and C1W–C5X DCB estimates. Different satellite clock products have no significant effect on the STDs. When compared with the DCB computed by CODE and Deutsches Zentrum für Luft-und Raumfahrt (DLR), the mean RMS values of GPS satellite C1W–C2W and C1W–C5X DCB differences are 0.10 ns and 0.42 ns. Different satellite clock products have a significant effect on the RMSs. Through linear regression analysis, we find that 46% and 27% of initial satellite clock biases would be included in the satellite C1W–C2W DCB and C1W–C5X DCB estimates, respectively. In addition, the satellite clock offset has little impact on the receiver DCB estimates though it significantly affects the satellite DCB estimates.
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This work was sponsored by the National Natural Science Foundation of China (Grant Nos. 41804024, 41574027, 41804026) and the State Key Research and Development Program (2017YFB0503401). The authors are grateful to the International GNSS Service (IGS) for providing GPS data and products. We thank the Center for Orbit Determination in Europe (CODE) and German Aerospace Center (DLR) for providing multi-frequency DCB products.
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Fan, L., Shi, C., Wang, C. et al. Impact of satellite clock offset on differential code biases estimation using undifferenced GPS triple-frequency observations. GPS Solut 24, 32 (2020). https://doi.org/10.1007/s10291-019-0946-8
- Differential code bias
- Uncombined model
- Satellite clock offset