Satellite clock offset products are fundamental to high-precision Global Navigation Satellite Systems (GNSS) applications. Clock offsets derived from L-band Orbit Determination and Time Synchronization (ODTS) method generally exhibit good short-term stability but suffer from pronounced day-boundary discontinuities (DBDs). Furthermore, the orbit modeling errors absorbed into the clock estimates degrade their long-term stability. For BDS-3, Ka-band inter-satellite link (ISL) technology provides an additional source of clock information. Clock offsets derived from ISL geometry-free observables are almost immune to orbit errors and therefore offer superior long-term stability. However, the limited Ka-band ranging precision introduces larger random noise into ISL clocks, leading to poorer short-term stability. Consequently, combining these two clock products is a logical strategy to optimize the overall clock solution. To exploit their complementary characteristics, we apply the Vondrak-Cepek (V-C) filter to combine 90 days of ISL clock offsets with ODTS clock offsets provided by Deutsche GeoForschungsZentrum (GFZ). The results demonstrate that the V-C filter effectively suppresses observation noise without distorting the true signals. The combined clock product preserves the reduced DBDs of ISL clocks while maintaining the low noise level of the ODTS solution. After quadratic detrending, the combined clock residual is about 0.11 ns, comparable to that of ISL and smaller than the GFZ value of 0.14 ns. In terms of overlapping Allan deviation, the combined clocks closely follow the GFZ performance at short averaging times and approach or surpass the ISL stability at long intervals, achieving a balanced compromise between short- and long-term performance. Static PPP validation further shows that the combined products achieve positioning performance comparable to that of GFZ precise products. This study provides a new perspective on clock combination and a practical method for leveraging the strengths of clock products derived from different measurement technologies.
Regional atmospheric delay corrections and their uncertainty quantification are critical components for achieving fast convergence and highly reliable positioning in precise point positioning real-time kinematic (PPP-RTK) services. However, existing single-epoch regional modeling methods remain limited in exploiting the spatiotemporal structural consistency of the atmospheric field, while most uncertainty assessment approaches rely on idealized modeling assumptions. To address these issues, this study proposes a dynamic spatiotemporal Kriging (STDK) based regional atmospheric delay modeling method for the PPP-RTK. By constructing a dynamic temporal window, jointly incorporating temporal and spatial information in the trend component, the proposed method provides spatiotemporal estimation of regional atmospheric delays within the best linear unbiased prediction (BLUP) framework. On this basis, an epoch-wise leave-one-out cross-validation (ELOOCV) method is further proposed, which fully exploits historical spatiotemporal observations to adaptively calibrate the original model predicted uncertainties, ensuring statistical consistency with the actual error levels and thereby providing more reliable stochastic constraints for user-side PPP-RTK positioning. The core innovation of this study lies in introducing a spatiotemporal perspective into regional atmospheric augmentation for PPP-RTK, enabling the joint consideration of atmospheric delay evolution and uncertainty reliability within a unified framework. Experimental validation is conducted using networks in Europe and Australia under different atmospheric activity conditions. The results indicate that, compared with conventional modeling methods, the STDK approach exhibits superior stability in both ionospheric and tropospheric delay interpolation accuracy. The ELOOCV-based standard deviation calibration significantly improves the consistency between uncertainties and actual errors, increasing the coverage rate of the three-sigma error envelope to over 95
The BDS-3 utilizes the BeiDou Global Broadcast Ionospheric delay correction Model (BDGIM), which represents global ionospheric variability using nine dynamic broadcast coefficients and 17 predicted non-broadcast parameters. Because the BDS-3 monitoring network is concentrated mainly in mainland China, the global coefficient estimation is constrained by limited observational coverage. This study proposes a hierarchical two-step fusion framework that first condenses dense regional GNSS observations into compact constraints and then integrates them with globally distributed radio occultation (RO) data to estimate the nine broadcast coefficients. Evaluated over 60 days (DOY 215–274, 2024) spanning high solar activity and geomagnetic storms, the framework reduces the condition number from 1.13 × 10⁴ for direct joint inversion to 21.0. Under data-rich conditions, the fused model achieves mean RMSEs of 9.37 TECU over extended China and 9.87 TECU globally, representing reductions of 36.9
Accurate day-ahead forecasts of global ionospheric total electron content (TEC) support Global Navigation Satellite System applications and space weather services. Most deep learning models process TEC maps as planar latitude-longitude arrays, which do not explicitly preserve spherical connectivity. We developed GraphCastTEC, a spherical graph neural network that maps hourly Center for Orbit Determination in Europe (CODE) products onto an icosahedral multi-resolution mesh. The model uses the preceding 24 h of TEC maps and available geomagnetic and solar indices to generate hourly forecasts for the subsequent 24 h. In the 2018 evaluation, GraphCastTEC achieved an area-weighted mean absolute error (WMAE) of 1.114 TECU, a weighted root mean squared error (WRMSE) of 1.687 TECU, and a weighted correlation coefficient of 0.971. WMAE and WRMSE were 23.7
High solar activity can significantly impact Global Navigation Satellite Systems (GNSS) signals, leading to loss-of-lock (LoL) events in satellite-based receivers. A LoL occurs when a GNSS receiver can no longer maintain signal tracking from a satellite, resulting in degraded positioning accuracy. Here, we analyze LoL occurrence using observations from the European Space Agency Swarm satellite mission spanning 2014 to 2025. While LoL events generally correlate with solar activity, reflecting increased intensity of processes driving ionospheric irregularities during active periods, since 2023 a subset of events over Europe and western Asia has been identified that cannot be explained by ionospheric irregularities. These unexplained events coincide spatially and temporally with regions and periods where independent reports document widespread GNSS interference linked to military operations. This study highlights the capability of scientific satellite constellations to detect and characterize GNSS interference, with benefits for space weather research, technological resilience, and situational awareness in conflict regions.
