A unified model of multi-GNSS and multi‑frequency precise point positioning for the joint estimation of ionospheric TEC and time-varying receiver code bias

The short-term variability in receiver code biases (RCBs) has been identified as a prominent source of error leading to the degradation of precise point positioning (PPP) performance and ionospheric total electron content (TEC) estimation accuracy. To minimize the adverse impact of RCB variability, this study extends the modified PPP (MPPP) method from the GPS only dual-frequency (DF) model to multifrequency (MF) and multiconstellation cases. In the MF MPPP method, multi-GNSS (GPS, BDS and Galileo) dual-, triple- or even arbitrary-frequency observations can be jointly processed in a flexible and reliable way by taking the time-varying RCBs of all available signals into account. Benefiting from this, the between-epoch fluctuations experienced by RCBs for all constellations and frequencies can be detected and their adverse impacts on the ionospheric observables and ambiguity parameters are mitigated. Compared to the traditional MF PPP method, the retrieval accuracy of the multi-GNSS-based ionospheric observables using our proposed method can be improved by more than 74% in the presence of significant intraday RCB variations. The variation trends are not always consistent for RCBs in different frequency bands for different satellite systems. The dependence of multi-GNSS and MF RCB variations on the ambient temperature is also verified. The percentages of the stations analyzed with the absolute Pearson correlation coefficient (PCC) values above 0.8 for BDS are higher than those of GPS and Galileo, and the temperature dependence of RCB on the second frequency band is higher than those of the first frequency band for all the three constellations.