Objectives  Precise point positioning (PPP) combines the advantages of standard point position‍ing (SPP) and relative positioning, which can achieve centimeter level positioning. With the development of BeiDou satellite navigation system (BDS), more and more BDS satellites begin to provide global positioning, navigation and timing services, which also promotes the development of multi-frequency and multi-system PPP. For a long time, because of the atmospheric delay and hardware delay of satellite and receiver, the ambiguity of PPP is not an integer. PPP needs a long time to converge, which greatly lim‍its its application.The ambiguity can be restored to integer and the convergence time can be shortened with the help of fractional cycle bias (FCB).

  Methods  In order to improve the effect of precise point positioning-ambiguity resolution (PPP-AR) of BDS as a whole, we estimate the FCBs of GPS and BDS based on the observation data from August 1 to August 31 in 2020 of globally distributed stations. The single difference between satellites is used to eliminate the influence of hardware delay at the receivers, and the single differ‍ence ambiguity vector is solved by the whole network adjustment to obtain the FCB estimation of each satellite.

  Results  The results of the time series of BDS-3 wide lane (WL) and narrow lane (NL) FCBs show that the WL FCBs has long-term stability, the change of BDS-3 WL FCBs in 31 days is less than 0.2 weeks, and the change of GPS WL FCBs is less than 0.1 weeks. The FCBs of BDS-3 NL can keep stable for a period of time, and the change is less than 0.1 weeks. The percentages of GPS WL and NL FCBs residuals within 0.15 weeks are 99.8% and 99.3% respectively, and the percentages of BDS-3 are 99.7% and 98.1% respectively. In order to reflect the improvement effect of FCBs on PPP, static and dynamic PPP-AR tests were carried out at 8 stations around the world. The results show that under the static condition, the average fixed time and convergence time of BDS-3 are 31.5 min and 24.9 min respectively, which is 24.8% shorter than the float PPP. The errors in E, N and U directions are 1.03 cm, 0.60 cm and 1.72 ‍cm respectively, and the fixed rate is 89.8%. Under the dynamic condition, the average fixed time and convergence time of BDS-3 are 33.3 min and 50.7 min respectively, which is 17.4% shorter than the float PPP. The errors in E, N and U directions are 2.57 cm, 2.29 cm and 3.71 cm respectively, and the fixed rate is 83.9%.

  Conclusions  PPP-AR can shorten the convergence time of PPP to a certain extent, but the improvement of positioning accuracy is not obvious after complete convergence. BDS-3 FCBs stability is lim‍it‍ed by precision products and observation data, and its PPP-AR is slightly worse than GPS.