Enhancing the continuity and robustness of Galileo HAS PPP time transfer with a novel adaptive clock model

Abstract

Precise point positioning (PPP) is a cornerstone technology for delivering high-precision spatiotemporal transfer in Global Navigation Satellite Systems (GNSSs). Although the Galileo high accuracy service (HAS) improves static PPP timing and time transfer, practical applications remain limited by observation noise, timing discontinuities during data outages, and slow reconvergence after data recovery. To address these issues, this study proposes an adaptive receiver clock model for Galileo HAS PPP static timing and time transfer, integrating local oscillator constraints, clock-offset prediction during data outages, and progressive relaxation during recovery. Using observations from ten global International GNSS service (IGS) stations over day of year 258–290, 2023, with IGS final products used as a post-processed reference and CNES real-time products used as an independent real-time comparison, performance is evaluated in GPS-only, Galileo-only, and combined GPS/Galileo modes. The experiments follow a three-stage strategy: basic HAS product assessment, comparison between conventional processing and the proposed adaptive model under normal, outage, and recovery conditions, and validation of inter-station time transfer and frequency stability. Results show that Galileo HAS provides strong baseline performance: compared with CNES products, HAS-based GPS and combined GPS/Galileo solutions reduce average receiver-clock standard deviation (STD) by approximately 65%, while the Galileo-only solution remains only about 6% larger. The proposed model further suppresses observation noise and correction-related fluctuations, reducing Galileo-only receiver-clock STD by 6.58%. During simulated outages, it rapidly switches to clock prediction based on prior states and frequency-drift information; after data recovery, the progressive relaxation strategy substantially reduces step discontinuities and improves timing continuity under the selected static observation dataset. For inter-station time transfer, the model reduces average STD from 1.16 ns to 1.05 ns in GPS-only mode, from 2.81 ns to 0.70 ns in Galileo-only mode, and from 1.51 ns to 1.12 ns in combined GPS/Galileo mode, corresponding to improvements of 9.34%, 74.98%, and 26.32%, respectively. Modified Allan deviation analysis further confirms that frequency stability improves by 26.62%–34.34% at the short-term scale and by 15.03%–27.82% at the long-term scale, with the combined GPS/Galileo mode showing the best short-term performance. Overall, the results indicate that the adaptive receiver clock model improves the continuity and stability of Galileo HAS-based PPP timing and time transfer for the ten static stations and the simulated outage conditions considered in this study.