Satellite’s differential code bias conversion model between different IGS clock products using uncombined BDS-3 multi-frequency data

Differential code bias (DCB) is widely used to achieve consistency between global navigation satellite system (GNSS) observations at different frequencies. Since a strong correlation exists between satellite DCBs at different frequencies and the satellite clock offset, the DCB products need to be aligned with the corresponding clock products. This paper proposes a satellite’s DCB conversion model between different clock products released by the International GNSS Service (IGS) via the uncombined method. First, a one-step uncombined approach with a simplified ionospheric processing model is proposed for multi-frequency DCB estimation. In the second step, a linear function model is applied to represent the relationship between the initial satellite clock bias and the DCB estimates at different frequencies. To test the proposed model, BeiDou global system (BDS-3) multi-frequency data collected from 60 multi-GNSS experiment stations and precise clock products released by four IGS analysis centers are used to estimate the DCB. The DCB estimates are compared to the DCB products released by the Chinese Academy of Sciences (CAS) and the Deutsches Zentrum für Luft-und Raumfahrt (DLR). The average root-mean-square (RMS) values of the differences between the DCB estimates and the two DCB products are 0.61 ns and 0.52 ns, which are significantly larger than the corresponding monthly standard deviations. This indicates that systematic bias exists between the DCB estimates and the two DCB products. Additionally, systematic biases are also observed in the DCB estimation when different clock products are used, with the maximum value reaching 4 ns. In order to study the propagation of parameter errors between the DCB estimates and the clock products, regression analysis is conducted to determine the linear model coefficients of the DCB conversion model. The results show that the model coefficients for the four frequency pairs C2I-C6I, C2I-C1X, C2I-C5X and C2I-C7Z are 0.394, 0.237, 0.238, and 0.238, respectively. Kinematic precision point positioning is conducted for model verification. During the first 6-h period, the average three-dimensional RMS of the positioning errors is 13.5 cm when the DCB estimates are corrected by the conversion model, which is improved by 32.5%, 14.6%, and 11.3% compared with the usage of the CAS and DLR products and those without model conversion, respectively.