Abstract
With the rapid development of multi-GNSS and multi-frequency observations, the code observable‑specific bias (OSB) emerges due to its flexibility and convenience compared to the traditional differential code bias (DCB). To estimate the GNSS multi-frequency code OSBs, the geometry-free model is commonly used, where ionospheric error handling is a key issue. For ionospheric handling, previous studies mostly focus on the ionospheric-float approach based on ionospheric modeling and the ionospheric-fixed approach using an external empirical model. We proposed an improved estimation approach aided by geometry-free and ionospheric-free (GFIF) observations to estimate multi-frequency code OSBs. The proposed approach expands the DCB to multiple code bias (MCB) using the GFIF model, eliminating the first-order ionospheric error. Then, the satellite-plus-receiver MCB observations with high precision and reliability are extracted. Finally, a full-rank estimable functional model after the identification and elimination of rank deficiencies is proposed. The effectiveness of the proposed approach is verified, where the multi-frequency code OSBs of GPS, BDS-3, and Galileo are estimated. Taking the code OSB products provided by the Chinese Academy of Sciences (CAS) as the references, the estimated code OSBs exhibit good consistency, showing an average RMS of 0.115, 0.130, and 0.161 ns for GPS, BDS-3, and Galileo, respectively. The average STD of all code OSBs for GPS, BDS-3, and Galileo is 0.187, 0.296, and 0.331 ns, respectively, which is smaller than that of CAS products for GPS and Galileo. In conclusion, the proposed approach can estimate the reliable GNSS multi-frequency code OSBs with high consistency and stability.