An ambiguity subset selection algorithm based on the variation of check factors for BDS-3/BDS-2/GPS precise point positioning

The ambiguity resolution (AR) technology effectively accelerates convergence and improves precise point positioning (PPP) accuracy. Many observations involved in the calculation can enhance the accuracy of parameter estimation. Still, it can also introduce unmodeled errors, making it difficult to fix ambiguities, especially in multiple global navigation satellite system (GNSS). This paper presents a novel PPP Partial-AR (PAR) method to enhance Precise Point Positioning (PPP) performance by selecting an ambiguity subset based on the variation of ambiguity check factors, including the ratio, ambiguity dilution of precision (ADOP), and Bootstrapping success rate. The proposed method is validated using post-processing and real-time static and kinematic datasets across five GNSS integration modes involving the global positioning system (GPS) and BeiDou navigation satellite system (BDS), demonstrating that PPP Partial-AR (PAR) outperforms the method that fixes all ambiguities, known as PPP Full-AR (FAR). The static and kinematic post-processing experiment shows that PPP-PAR, compared with PPP-FAR, increases the ambiguity epoch fixing rate from 84.6 and 79.5% to 94.2 and 91.9%, decreases the time to first fix (TTFF) from 21.4 and 31.1 min to 17.7 and 25.4 min, and reduces the root mean square error (RMSE) from 12.7/11.3/32.2 and 21.7/19.4/51.8 mm to 11.5/10.3/30.9 and 19.1/18.1/48.9 mm in the north-east-up directions, respectively. The static and kinematic real-time experiment shows that PPP-PAR, compared with PPP-FAR, increases the ambiguity epoch fixing rate from 80.1 and 71.7% to 91.8 and 86.6%, decreases the TTFF from 29.5 and 35.5 min to 25.2 and 28.7 min, and reduces the RMS from 22.4/19.4/45.9 and 33.8/26.9/65.2 mm to 18.6/17.1/42.0 and 29.2/23.6/60.5 mm in the north-east-up directions, respectively. Moreover, the real-time experiments with actual kinematic data show that the proposed method significantly improves the ambiguity epoch fixing rate from 43.3% for PPP-FAR to 50.7% for PPP-PAR, and increases the positioning accuracy with an RMS value of 0.28/0.21/0.57 m for the PPP float solution, 0.23/0.19/0.55 m for the PPP-FAR solution towards 0.21/0.18/0.53 m for the PPP-PAR solution.