Accounting for BDS-2/BDS-3 inter-system biases in PPP and RTK models

Inter-system Biases (ISBs) between BDS-2 and BDS-3 is of great importance for BDS-2/BDS-3 joint processing, which is meaningful to make full use of BDS observations and improves PNT (positioning, navigation, timing) performance. In this contribution, we derive ISBs models with undifferenced ionospheric-free (IF) combination and double-differenced model, corresponding to the IF-PPP and RTK technologies respectively. To analyze code ISB in PPP, we processed data from 55 multi-GNSS experimental (MGEX) stations including 7 receiver types and conduct a detailed analysis on the effect of frequency, receiver types and precise products from 4 IGS Analysis Centers (ACs). It is concluded that both the overlapping frequency and the non-overlapping frequency of BDS-2/BDS-3 exist code ISB. The code ISB of overlapping frequency is within 10 ns, and that of the non-overlapping frequency can reach 100 ns. Moreover, code ISB is influenced by receiver types as well as satellite geometry. The average ISB of stations with the same manufactures tend to be the same while that of stations from different manufactures are different. Affected by the satellite geometry, the ISB characteristics exhibit periodicity and correlation with the location of stations. By comparing ISB calculated by different precise clock products from the GeoForschungsZentrum (GFZ), European Space Agency (ESA), Center for Orbit Determination in Europe (CODE) and Wuhan University (WHU), the results show that the daily STD of ISB_COD, ISB_WHU,ISB_ESA and ISB_GFZ is about 0.2 ns, which means that ISB can be calibrated by constant estimation when these products are used. As for Differential Inter-system Biases (DISBs) in RTK, it is discovered that the BDS-2/BDS-3 joint differenced system has a Differential Inter-system Code Bias (DISCB) that exceeds 3.4 ns when the rover and base receivers are made by different manufactures and the hardware delay characteristics for BDS-2 and BDS-3 are different. However, the Differential Inter-system Phase Bias (DISPB) doesn't exist and can be neglected in RTK.