Triple-frequency carrier phase precise time and frequency transfer models for BDS-3

The third-generation BeiDou navigation satellite system (BDS-3) began providing global positioning, navigation and timing service on December 27, 2018. We present three triple-frequency carrier phase (CP) precise time and frequency transfer models using the BDS-3 B1I/B3I/B2a signals, named IF-PPP1, IF-PPP2 and UC-PPP models, respectively. The BDS B1I/B3I dual-frequency ionospheric-free (IF) model is also introduced, known as IF-PPP0 model. The corresponding mathematical and stochastic models are developed. Two stations located at time laboratories and connected to a high-precision atomic clock are utilized to assess the performances of the proposed CP precise time and frequency transfer models. In addition, the number of visible satellites, position dilution of precision, time dilution of precision, estimated positioning errors, zenith tropospheric delay and inter-frequency bias for two stations are also analyzed. The results show that BDS CP precise time and frequency transfer can achieve better performances with increasing number of BDS-3 observations. The proposed models all can be applied for precise time and frequency transfer with the BDS-3 triple-frequency signals, with stability and accuracy identical to the BDS IF-PPP0 solution. The stability of 10,000 s for the proposed BDS CP precise time and frequency models is better than 1.5 × 10−14.