Determation of the ionospheric observable and short-term variations of receiver DCBs using modified carrier‑to‑code leveling method with multi-frequency and multi-GNSS data

When sensing the Earth’s ionosphere using pseudorange observations of global navigation satellite systems (GNSS), the satellite and receiver Differential Code Biases (DCBs) account for one of the main sources of error. For the sake of convenience, Receiver DCBs (DCBs) are commonly assumed as constants over a period of one day in the traditional carrier-to-code leveling (CCL) method. Thus, remarkable intraday variability in the receiver DCBs have been ignored in the commonly-used assumption and may seriously restrict the accuracy of ionospheric observable retrieval. The Modified CCL (MCCL) method can eliminate the adverse impact of the short-term variations of RDCBs on the retrieval of ionospheric TEC. With the rapid development of the GPS, GLONASS, Galileo and BeiDou systems, there is a strong demand of precise ionospheric TEC products for multiple constellations and frequencies. Considering the existed MCCL method can only be used for dual-frequency GNSS data, in this study, we extend the two-frequency MCCL method to the multi-frequency and multi-GNSS case and further carry out a series of investigations. In our proposed method, a newly full-rank multi-frequency (more than triple frequency) model with raw observations are established to synchronously estimate both the slant ionospheric delays and the RCB offset with respect to the reference epoch at each individual frequency. Based on the test results, compared to the traditional CCL-method, the accuracy of the ionospheric TEC retrieved using our proposed method can be improved from 5.12 TECu to 0.95 TECu in the case that significant short-term variations existed in receiver DCBs. In addition, the between-epoch fluctuations experienced by receiver code biases at all frequencies tracked by a single receiver can be detected by our the proposed method, and the dependence of multi-GNSS and multi-frequency RDCB offsets upon ambient temperature further are verified in this study. Compared to Galileo system, the RDCB in BDS show higher correlation with temperature. We also found that the RDCB at different frequencies of the same system show various characteristics.