Estimation of GNSS satellite bias corrections using non-common frequency model with application to PPP-AR

Corrections of satellite phase biases (SPBs) enable precise point positioning with ambiguity resolution (PPP-AR), which shortens the convergence time and improves positioning precision compared with PPP. Extending PPP-AR from dual-frequency to multi-frequency can further enhance the positioning performance by correcting satellite code biases (SCBs) at the third frequency and above. In formulating a multi-frequency model to estimate satellite bias corrections (SBCs), including SPBs and SCBs, existing studies use only satellite observations collected at common frequencies (CFs). This study proposes a non-CF (NCF) model that utilizes dual- and multi-frequency satellites to estimate SBCs simultaneously. To validate the NCF model, we collect data from an Australian network to estimate the SBCs and apply these corrections to the PPP-AR user positioning. The results show that the NCF model can provide SBCs for more satellites and frequencies than the CF model. After correction of SBCs, the proportion of fractional parts of float PPP ambiguities, which are less than 0.1 cycles, has a significant increase from 20% to 70%, indicating the successful restoration of the integer properties of PPP ambiguities by the SBCs. Moreover, a comparable experiment between the NCF and CF PPP-AR models is conducted. The NCF PPP-AR model demonstrates superior performance over the CF model using triple-frequency satellites in convergence speed and positioning precision, achieving improvements of 41.16% and 39.52%, respectively. Meanwhile, compared to the CF model using dual-frequency satellites, the NCF PPP-AR model shows improvements of 17.16% and 7.46% in these aspects. The positioning performance of the NCF PPP-AR model is evaluated across ten user stations sampled over three days. The results indicate the root mean square positioning errors for the east, north and up components are 0.41, 0.51 and 2.46 cm, respectively. Additionally, the average convergence time for achieving 3D positioning errors within 1 dm is 9.75 min.