PPP can provide globally uniform high-precision positioning without dense reference stations, but it still faces slow initial convergence, slow reconvergence after signal loss, and degraded continuity in urban canyons. LEO augmentation can improve received signal power, satellite geometry, and observation redundancy, yet most Global Navigation Satellite System (GNSS)/Low Earth Orbit (LEO) precise point positioning (PPP) schemes still rely on fixed stochastic models and treat GNSS and LEO observations similarly. They often overlook LEO-specific signal-power fluctuations, Doppler shifts, short visibility arcs, and differing orbit and clock stability. FGO preserves historical constraints and suits complex environments, while learning-assisted stochastic models rarely provide direct observation-level uncertainty factors or jointly model GNSS-LEO multi-relations. Given these challenges, further research is needed to develop adaptive, heterogeneous stochastic models for integrated GNSS/LEO PPP.
Researchers at the Radar Technology Research Institute, School of Information and Electronics, Beijing Institute of Technology, and the Key Laboratory of Electronic and Information Technology in Satellite Navigation (Beijing Institute of Technology), Ministry of Education, China, published (DOI: 10.1186/s43020-026-00218-8) the study in Satellite Navigation on 29 September 2026. They developed a heterogeneous graph neural network (HetGNN)-based factor graph optimization (HetGNN-FGO) method for integrated GNSS/LEO PPP. The method learns observation-level uncertainty scale factors and applies covariance rescaling within a dual-frequency PPP-FGO framework.
The proposed framework uses a sliding-window PPP-FGO backend with dual-frequency ionosphere-free pseudorange and carrier-phase factors. A relation-aware HetGNN represents each epoch as a directed heterogeneous graph containing receiver, Global Positioning System (GPS), BeiDou Navigation Satellite System (BDS), and LEO satellite nodes. Typed graph edges represent receiver-satellite observations and geometric relationships among satellite viewing directions, both within a system and between GNSS and LEO. The network predicts pseudorange and carrier-phase uncertainty scale factors, which are fed back to the factor graph through covariance rescaling. A constrained random-walk model handles the LEO-GPS inter-system bias (ISB). Tests combined real vehicular GNSS data with simulated LEO observations in mixed, open-sky, and urban obstructed scenarios. In these three settings, the method achieved average three-dimensional (3D) positioning root mean square (RMS) errors of 3.06 m, 0.67 m, and 3.00 m, respectively. In the long-distance mixed scenario, availability reached 98.93% and 60-s continuity probability reached 91.09%, using a 5 m threshold for 3D positioning error.Compared with elevation-angle/carrier-to-noise-density ratio (C/N₀) joint weighting and residual-driven weighting, the method reduced the 3D RMS positioning error in the urban obstructed scenario by 28.4% and 10.2%, respectively. In the urban obstructed scenario, mean reconvergence time after obstruction was 47.33 s. Recovery was assessed using a 20-epoch window at 1 Hz, requiring a 3D RMS error below 6 m and a standard deviation of the 3D error below 0.1 m. Ablation tests showed that heterogeneous nodes, cross-system edges, near-neighbor edges, and relation gating all contributed.
The authors said the key advance is not simply adding more satellites but teaching the estimator how much to trust each heterogeneous observation as conditions change. They said the HetGNN acts as an observation-level risk model, inflating covariance for degraded GNSS or LEO links and preserving confidence for stable links. This keeps the physically interpretable PPP model while adding data-driven adaptability. They said the approach improved not only average accuracy but also availability, short-term continuity, and recovery after blockages, which are critical for real-world urban navigation.
The method could support autonomous driving, urban air mobility, unmanned systems, and spatiotemporal infrastructure where continuous high-precision positioning is required. By integrating LEO augmentation with adaptive stochastic modeling, it may help receivers maintain service under overpasses, viaducts, multipath, and signal blockage. The authors caution that LEO observations were simulated rather than collected from real operational navigation constellations, so further validation is needed with large-scale real LEO data. Future work will target real LEO observations, multi-sensor navigation, lightweight online deployment, cross-domain generalization, and continuous adaptation.
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References
DOI
10.1186/s43020-026-00218-8
Original Source URL
https://doi.org/10.1186/s43020-026-00218-8
Funding information
The study was supported by the National Key Research and Development Program of China (Grant 2021YFB3901400) and the National Natural Science Foundation of China (Grant 62571044). The article.
About Satellite Navigation
Satellite Navigation (ISSN: 2662-1363; ISSN: 2662-9291) Satellite Navigation is the official journal of the Aerospace Information Research Institute. The journal aims to report innovative ideas, new results, and progress in the theories, techniques, and applications of satellite navigation. The journal welcomes original articles, reviews and commentaries.