An instantaneous and reliable precise point positioning integer ambiguity resolution method based on multistage residual tests

Rapid initialization poses a significant challenge for ambiguity resolution (AR) in precise point positioning (PPP), especially for real-time applications. The modernization of GNSS provides numerous satellite signals and brings new possibilities for PPP-AR rapid convergence. To achieve instantaneous and reliable positioning, an ambiguity resolution method based on multistage residual tests with undifferenced and ionosphere-free (IF) combined observables is proposed. This approach not only eliminates the impact of inter-frequency clock biases (IFCBs) but also decouples dual- and triple-frequency clocks. Moreover, abnormal ambiguities can be detected through multistage residual tests, including prior- and post-residuals with pseudorange and phase observables, as well as residuals of ambiguity-fixed solutions, thus expediting convergence and enhancing positioning robustness. Initially, IFCBs, alongside phase biases, which include extra-wide-lane (EWL), wide-lane (WL) and narrow-lane (NL), are estimated from a dataset in China on DOY 202 to 204, 2023. EWL and WL phase biases for GPS, Galileo, BDS-2 and BDS-3 exhibit excellent stability, with daily STDs of 0.04 and 0.07 cycles, respectively. NL phase biases using ESA final and WHU real-time products exhibit daily STDs of 0.06 and 0.1 cycles, except for BDS-2. Subsequently, intensive restarts every 15 min (totaling 8,804) are implemented to verify the effectiveness of our approach. It is important to note that the outstanding performance of GPS/Galileo/BDS-2/BDS-3 kinematic solutions, achieving horizontal convergence within 4 s at 95% confidence with an accuracy of 1.7 cm using ESA final products, and within 6 s with an accuracy of 1.8 cm using WHU real-time products, is obtained under regional positioning solutions. Overall, these results demonstrate the proposed ambiguity resolution method can achieve horizontal instantaneous convergence and 1–2 cm-level accuracy with multi-frequency and multi-constellation observables when applied within a regional positioning solution.