Using Galileo and BDS-3 Quad-Frequency Signals for Long-Baseline Instantaneous Decimeter-Level Positioning

As the signals of Galileo and the global BDS-3 navigation satellite system have been accessible, positioning users can use quad-frequency even five-frequency signals nowadays. With multifrequency signals, one can form some useful combinations to improve the positioning performance, e.g., the widely used extra-wide-lane (EWL)/wide-lane (WL) in triple-frequency cases. For quad-frequency or five-frequency cases, better positioning performance can be expected since additional frequencies are introduced. In this study, we systematically analyse the benefits of Galileo and BDS-3 quad-frequency signals on long-baseline instantaneous positioning. First, the theoretical analysis of EWL/WL ambiguity resolution (AR) and satellite-station range estimation with a single-satellite geometry-free and ionosphere-free model is studied, along with the comparison with triple-frequency cases. Second, using the quad-frequency advantages, an instantaneous decimeter-level positioning model is proposed, where the geometry-free model is adopted for the first two EWL AR and the geometry-based model is adopted for the third WL AR. In the end, the AR and positioning performance are evaluated using real long-baseline date containing Galileo and BDS-3 quad-frequency observations. The results indicate that, with quad-frequency observations, both Galileo and BDS-3 EWL/WL ambiguities can be fixed reliably with a single epoch. Contributed by the resolved EWL/WL ambiguities, instantaneous decimeter-level positioning can be obtained, with the accuracies of 0.116 m/0.126 m/0.351 m in north, east, and up directions, respectively.