Improvement of BDS-3 inter-frequency clock bias estimation and its application in multi-frequency precise point positioning

•Evaluated the advantages of the reconstructed method for BDS3 IFCB estimation.•Analyzed the characteristics of BDS3 multi-frequency IFCB variations.•Proposed a real-time forecasting service for BDS3 multi-frequency IFCB in PPP. BDS-3 broadcasts five civilian signals, establishing a fundamental basis for multi-frequency real-time precise point positioning (RT PPP). Nevertheless, the existence of inter-frequency clock bias (IFCB) renders the current satellite clock error product unsuitable for multi-frequency PPP processing. Consequently, there is a critical need to conduct a thorough analysis of BDS-3 IFCBs and propose real-time service methods for RT PPP users. In this study, 8-day BDS-3 multi-frequency data obtained from 130 International GNSS Service (IGS) stations are employed to scrutinize the characteristics of BDS-3 IFCBs and validate the proposed real-time service method. The results disclose a noticeable disparity between the constant part of IFCBs computed using the differential code bias (DCB) product and those estimated from observations. The time-varying parts of different IFCBs, estimated using various combinations, are examined using the Fast Fourier Transform (FFT). The outcomes indicate that these IFCBs exhibit identical periods of 12, 6, and 4 h, although their fourth-period terms differ. To model the sequences of IFCBs, a polynomial with a fourth-order harmonic model is utilized, and the coefficients of the fitted model are subsequently transmitted for RT PPP processing. Experimental results show that the predicted accuracies of IFCBs for most satellites exceed 90 %, albeit with a noticeable decline as the prediction time increases. When applied in RT PPP for 20 IGS stations, the method significantly shortens the convergence time in dual-frequency and triple-frequency RT PPP when predicted IFCBs are provided. In the B1C/B2a, B1C/B3I, and B1I/B2a dual-frequency combinations, the average convergence times for RT PPP are reduced by 58 %, 46 %, and 59 %, respectively. In the B1I/B2a/B3I triple-frequency combinations, it is reduced by 48 %.