Inter-frequency code bias handling and estimation for multi-frequency BeiDou-3/Galileo uncombined precise point positioning

The development of a global navigation satellite system (GNSS) with multi-frequency signals brings new opportunities for providing high-quality positioning, navigation and timing (PNT) services. Proper inter-frequency code bias (IFB) handling is a prerequisite for multi-frequency uncombined precise point positioning (UC-PPP) to ensure reliable and accurate PNT services. This work focuses on analyzing the mathematical representation of estimated parameters, as well as the relationship between different multi-frequency UC-PPP models, caused by whether to correct the inter-frequency satellite differential code bias (DCB) or the external ionosphere. Multi-GNSS experiment (MGEX) network stations tracking Galileo E1/E5a/E5b/E6/E5ab and BeiDou-3 (BDS-3) B1I/B3I/B1C/B2a signals were used to investigate the positioning performance and parameter estimations of three multi-frequency UC-PPP models. The results show that the loosely constrained ionosphere will make the estimated ionosphere and DCB/IFB parameters unable to effectively separate due to their high linear dependence. The 3D positioning accuracy of UC-PPP using Galileo five-frequency, BDS-3 four-frequency and Galileo/BDS-3 multi-frequency signals in static mode is 1.76, 2.36 and 1.39 cm, while the corresponding accuracy in kinematic mode is 6.40, 7.08 and 4.16 cm, respectively. The consistency of Galileo IFBs with respect to the MGEX DCB files is rather good, and the probability of deviations within 0.3 ns is 96.58%. Compared to Galileo, the agreement of the BDS-3 IFBs with respect to the reference values is worse, with 92.69% of them within 1 ns.