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<p>The traditional satellite clock offset prediction methods require continuous training data. However, due to limited distribution of the regional tracking stations, the BDS PPP-B2b satellite clock offsets represented by multiple arc segments are not continuous and cannot meet the requirement of the traditional methods. To address this issue, this study proposes a novel PPP-B2b satellite clock offset prediction method. Leveraging the high degree of statistical similarity in both the temporal variation and distribution characteristics of PPP-B2b clock offset series, the proposed method extracts historical clock offsets across multiple arc segments to train neural network-based prediction models. The model training and prediction is conducted with the Central Processing Unit (CPU) of Intel i9-13900K, Graphics Processing Unit (GPU) of Nvidia GeForce GTX 4090, and MATLAB R2022a. For seven-day training data, the model training consumes an average of 10.8/23.6 min for BDS Medium Earth Orbit (MEO)/Inclined GeoSynchronous Orbit (IGSO) satellites and 7.3 min for GPS satellites. With the trained model, real-time (RT) precise point positioning (PPP) users only need 2.6 ms to predict PPP-B2b satellite clock offsets per epoch. The accuracy of the proposed method is validated through both single-step and multi-step prediction tests. In the single-step prediction test, average prediction Root Mean Square Errors (RMSEs) for BDS MEO/BDS IGSO/GPS satelites are 9.911/7.476/31.219 × 10<sup>–3</sup> ns. In two ten-minute multi-step prediction tests, the proposed method yields PPP-B2b clock offset prediction RMSEs of 0.04/0.03 ns and 0.12/0.20 ns for BDS and GPS, respectively. Such predition accuracirs represent an average of 22.5% and 28.2% improvement compared to the traditional method. Furthermore, the simulated kinematic PPP experiment is carried out. Six clock correction interruptions are simulated at a four-hour interval on Feb 8, 2023. Comparison is made between using real and predicted PPP-B2b clock offsets. Results indicate the positioning RMSE differences in E/N/U directions are 6.4/0.8/26.1 cm during the converging stage, and less than 2.6/4.9 cm in horizontal/vertical directions after convergence. Therefore, the proposed method can not only improve satellite clock offset prediction accuracy, but also effectively maintain RT-PPP continuity during short-term interruptions of PPP-B2b satellite clock corrections.</p>

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A data-driven PPP-B2b satellite clock offset prediction method considering the cross-arc statistical similarity

  • 期刊论文

  • 发表日期：

    2025年4月22日

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  • Junbo Shi,
  • Chenhao Ouyang,
  • Cheng Hou,
  • Wenjie Peng,
  • Jiming Guo,
  • Yibin Yao

摘要

The traditional satellite clock offset prediction methods require continuous training data. However, due to limited distribution of the regional tracking stations, the BDS PPP-B2b satellite clock offsets represented by multiple arc segments are not continuous and cannot meet the requirement of the traditional methods. To address this issue, this study proposes a novel PPP-B2b satellite clock offset prediction method. Leveraging the high degree of statistical similarity in both the temporal variation and distribution characteristics of PPP-B2b clock offset series, the proposed method extracts historical clock offsets across multiple arc segments to train neural network-based prediction models. The model training and prediction is conducted with the Central Processing Unit (CPU) of Intel i9-13900K, Graphics Processing Unit (GPU) of Nvidia GeForce GTX 4090, and MATLAB R2022a. For seven-day training data, the model training consumes an average of 10.8/23.6 min for BDS Medium Earth Orbit (MEO)/Inclined GeoSynchronous Orbit (IGSO) satellites and 7.3 min for GPS satellites. With the trained model, real-time (RT) precise point positioning (PPP) users only need 2.6 ms to predict PPP-B2b satellite clock offsets per epoch. The accuracy of the proposed method is validated through both single-step and multi-step prediction tests. In the single-step prediction test, average prediction Root Mean Square Errors (RMSEs) for BDS MEO/BDS IGSO/GPS satelites are 9.911/7.476/31.219 × 10–3 ns. In two ten-minute multi-step prediction tests, the proposed method yields PPP-B2b clock offset prediction RMSEs of 0.04/0.03 ns and 0.12/0.20 ns for BDS and GPS, respectively. Such predition accuracirs represent an average of 22.5% and 28.2% improvement compared to the traditional method. Furthermore, the simulated kinematic PPP experiment is carried out. Six clock correction interruptions are simulated at a four-hour interval on Feb 8, 2023. Comparison is made between using real and predicted PPP-B2b clock offsets. Results indicate the positioning RMSE differences in E/N/U directions are 6.4/0.8/26.1 cm during the converging stage, and less than 2.6/4.9 cm in horizontal/vertical directions after convergence. Therefore, the proposed method can not only improve satellite clock offset prediction accuracy, but also effectively maintain RT-PPP continuity during short-term interruptions of PPP-B2b satellite clock corrections.