Fast calibration of between-receiver GPS/Galileo/BDS differential phase bias with millimeter accuracy based on short baseline mode

The differential code and phase biases induced by the receiver hardware (including receiver, antenna, firmware, etc.) of the Global Navigation Satellite System (GNSS) have significant effects on precise timing and ionosphere sensing, thus deserve careful treatment. In this contribution, we propose an approach to fast fix the single-difference ambiguity to finally obtain the unbiased estimates of between-receiver differential phase bias (BR-DPB) and between-receiver differential code-phase bias (BR-DCPB) based on the short baseline mode. The key to this method is that the error sources can be significantly eliminated due to the length of the baseline is very short. At the same time, the empirical constraints and random characteristics of BR-DPB/BR-DCPB were considered, which is conducive to the resolution of single-difference ambiguity. Several sets of GNSS data (GPS L1/L2, Galileo E1/E5b, and BDS B1/B3), recorded by the short baselines in an interval of 30 s and covered a broad range of receiver/antenna types (JAVA, SEPT, LEIC, and TRIM), were used to verify the effectiveness of the proposed method. The numerical tests show that the proposed method is capable of fast fixing the single-difference ambiguity successfully within a few epochs and then providing the unbiased estimates of BR-DPB and BR-DCPB in an epoch-by-epoch manner. Experiments show that the estimated BR-DPB is in millimeter accuracy, which is of great significance for the millimeter-accuracy phase time transfer and ionospheric delay estimation. Furthermore, the calibrated BR-DPB/BR-DCPB can be treated as the known products for long-distance precise timing and ionosphere sensing based on the inter-station single-difference model.