Evaluation of PPP-RTK based on BDS-3/BDS-2/GPS observations: a case study in Europe

The Chinese BeiDou Navigation Satellite System (BDS) transited from regional (Asia–Pacific) to global on December 28, 2018. In this study, the performance of PPP-RTK based on BDS-3/BDS-2/GPS observations is analyzed by utilizing the observations in Europe during a calm ionospheric disturbance period with Kp-index ranging from 0o to 2-. Satellite clock offsets are first estimated and then fixed to determine the uncalibrated phase delays (UPDs) and the ionospheric/tropospheric information from the reference network. Real-time PPP and PPP AR based on raw observations are estimated at the user, in which atmospheric constraints are imported as virtual observations if available. Analysis results based on 3 days of observations reveal that centimeter-level positioning accuracy can be achieved based on GPS, BDS, or GPS + BDS observations, and the performance can be further improved by realizing PPP AR. The satellite-differenced ionospheric and tropospheric information can be predicted for the users with an accuracy of 24.6 mm and 5.6 mm, respectively. Augmented by the predicted atmospheric information, PPP-RTK can be realized based on GPS- or BDS-only observations, and the average number of epochs required for ambiguity fixing is 1.5 and 1.6, respectively. The RMS values of the positioning errors of the north, east, and up components based on GPS-only observations are 8.0, 4.7, and 19.7 mm, while 9.8, 7.3, 29.7 mm, respectively, based on BDS-only observations. Utilizing GPS and BDS observations together, the average number of epochs required decreases to 1.2, and the positioning errors become 5.6, 3.5, and 23.3 mm for the north, east, and up components, respectively. All these results suggest that BDS can provide high-accuracy positioning services independently for users in Europe. Although a small decrease in the positioning accuracy of the up component, which might be attributed to inappropriate weighting strategy between satellite systems and requires further researches in the future, the additional BDS observations can improve the performance in the time to the first fixed solution and the positioning accuracies with respect to GPS-only positioning. The performance of PPP-RTK based on BDS-3/BDS-2/GPS observations during medium and high ionospheric disturbance periods will also be estimated in the future to fully evaluate the effects of additional BDS-3 observations in high-accuracy GNSS applications.