Multi-GNSS double/triple-frequency PPP-AR/RTK performance evaluation in the European region

With the continuous development and updates of GNSS systems, an increasing number of satellites now emit triple-frequency signals. Currently, research on triple-frequency positioning is predominantly focused on the Asian region, with limited attention given to the multi-frequency positioning performance in Europe. This study utilizes triple-frequency signals from BDS-3/GPS/Galileo satellites and employs observations from EUREF Permanent GNSS Network (EPN) to evaluate the performance of Precise Point Positioning Ambiguity Resolution (PPP-AR) and Atmosphere-augmented Real-Time Kinematics (PPP-RTK) modes in the European region. We calculate Uncalibrated Phase Delay (UPD) using 46 EPN stations and perform PPP-AR on all 138 stations to derive ionospheric and tropospheric delays. The fixing residuals of EWL/WL/NL UPD achieve 99.9%/98.2%/84.9% for BDS, 100.0%/97.1%/89.9% for Galileo, and 99.9%/94.9%/88.7% for GPS satellites within 0.15 cycles, respectively. Double and triple-frequency PPP-AR 68^th percentile results achieve 7.0/3.5 and 7.0/6.0 minutes for horizontal and vertical components using GPS/Galileo/BDS constellations. Additionally, the ionospheric delays derived from double and triple frequencies show only slight differences, measured at the centimeter-level among GPS/Galileo/BDS constellations. Relying on atmospheric delay augmentation, i.e., PPP-RTK, we further analyze the positioning performance under varying inter-station distances from 100 km to 400 km. The triple-frequency brings about a 5% improvement in convergence for BDS and Galileo satellites with respect to double-frequency solutions, while only slightly enhancing GPS satellites. Combining GPS/BDS/Galileo achieves nearly instantaneous convergence even at distances up to 400 km. Overall, the European region using GPS/Galileo/BDS constellations can achieve rapid positioning by triple-frequency signals, and instantaneous convergence can be achieved for double and triple-frequency solutions when atmosphere delays are implemented.