Low earth orbit satellites are increasingly recognized as valuable complements to traditional Global Navigation Satellite System (GNSS) satellites because of their stronger signals and rapidly changing observation geometry. However, maintaining accurate satellite clock bias prediction remains challenging because onboard oscillators experience complex variations that are difficult for conventional forecasting models to capture. Existing approaches often struggle with high-order trends in clock data and error accumulation during prediction reconstruction. Based on these challenges, deeper research is needed to develop more adaptive and accurate prediction methods for low earth orbit (LEO) satellite clock bias.
Researchers from the College of Surveying and GeoInformatics at Tongji University published (DOI: 10.1186/s43020-026-00215-x) their findings in Satellite Navigation in 2026, presenting a neural network-based prediction framework for LEO satellite clock bias. The study introduces advanced differencing strategies and a reconstruction fine-tuning mechanism to improve prediction accuracy, using clock bias data from the Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) mission to validate the proposed approach.
The researchers designed a framework centered on two major innovations. First, they introduced improved differencing strategies to reduce complex trends in LEO satellite clock bias data. These strategies included single differencing combined with segment-wise standardization and direct double differencing, allowing the model to suppress high-order trends without relying on additional external fitting procedures. This approach helps preserve the independence of predictions while transforming unstable clock bias sequences into forms that are easier for neural networks to learn.
Second, the team developed a reconstruction fine-tuning mechanism to solve a previously overlooked problem: the training objective in the differenced domain is not fully aligned with the final prediction objective in the original clock-bias domain, which can lead to directional error accumulation during reconstruction. To overcome this limitation, the researchers used a two-stage training process. The model was first trained using Mean Squared Error (MSE) loss in the differenced domain and then fine-tuned using a reconstruction loss function that directly optimizes prediction accuracy in the original domain.
The framework was built on the Informer model, a Transformer-based deep learning architecture designed for long-sequence time-series forecasting. The researchers evaluated the method using one year of 2021 clock bias data from the GRACE-FO C and D satellites. Experimental results showed that the proposed fine-tuning mechanism reduced overall prediction errors by approximately 6%–16%. Compared with the conventional Spectrum Analysis (SA) model, the new framework improved prediction accuracy by about 90% for 60-minute predictions and 94% for 10-minute predictions. At the 60-minute prediction point, the errors were reduced to 0.84 nanoseconds (ns) and 1.42 ns for the two GRACE-FO satellites, respectively, demonstrating strong potential for real-time navigation applications.
The authors said the study provides a more reliable approach for predicting LEO satellite clock behavior by addressing both data instability and reconstruction errors. They said that improving prediction accuracy is not only about building more powerful neural networks, but also about designing better strategies to process complex time-series signals. By combining trend suppression with reconstruction optimization, the proposed framework offers a more stable solution for future real-time satellite navigation systems.
The findings could support the development of more efficient LEO-enhanced navigation services by improving the availability and precision of satellite timing information. More accurate satellite clock bias (SCB) prediction may reduce dependence on delayed post-processing services and help enable faster positioning solutions for applications such as precise point positioning (PPP), autonomous systems, and emerging space-based navigation networks. The framework also provides a general strategy that may be adapted to other complex time-series prediction problems involving unstable measurement signals.
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References
DOI
10.1186/s43020-026-00215-x
Original Source URL
https://doi.org/10.1186/s43020-026-00215-x
Funding information
This work is supported by the National Natural Science Funds of China (42225401, 42430109), the Scientific and Technological Innovation Plan from Shanghai Science and Technology Committee (23JC1400500), Natural Science Funds of Shanghai (25ZR1402495), Basic Research Program “Explorer Program” from Shanghai Science and Technology Committee (25TS1404800), the Scientific and Technological Innovation Plan from Shanghai Science and Technology Committee (24DZ3101302), the industrial Collaborative Innovation Project (Technology) of Shanghai Municipality (XTCX-KJ-2024-03; XTCX-KJA005-2025-02), the Innovation Program of Shanghai Municipal Education Commission (2021–01-07-00-07-E00095), and the Fundamental Research Funds for the Central Universities.
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.