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<p>Satellite-Based Augmentation Systems (SBAS) broadcast the Grid Ionospheric Vertical Delay (GIVD) and Grid Ionospheric Vertical Error (GIVE) at Ionospheric Grid Points (IGPs), as Ionospheric Delay Correction Messages (IDCMs), to enhance GNSS positioning accuracy and integrity. As a typical representative of SBAS, the Wide Area Augmentation System (WAAS) generates IDCMs based on the Kriging method. In WAAS-Kriging, the process noise of the ionosphere is characterized by a constant variance and variogram, which are usable for mid-to-high latitude regions, but less adequate for low-latitude active regions of the ionosphere, leading to unrealistic GIVD accuracies and overly conservative GIVE values. This study presents an optimized Kriging method that adaptively models ionospheric process noise, and proposes a novel strategy for calculating GIVE, along with a Grid Ionospheric Delay Accuracy (GIVA) to characterize GIVD accuracy. In the proposed method, the variances of process noise are first determined adaptively by analyzing the statistical relationship between the Local Ionospheric Spatial Activity Indexes (LISAIs) and ionospheric modeling errors. Then a spatiotemporal-varying variogram is newly established, so that variable variances are considered when calculating the process noise covariance. Finally, the IDCMs and GIVAs are calculated using those variances and covariances. The observation data on DOY 251 of 2017 and DOY 277-280 of 2021, in which the ionosphere was active in low-latitude regions, were obtained from the Crustal Movement Observation Network of China (CMONOC) and used for experimental analyses. The results demonstrate that the estimated GIVA can effectively describe the GIVD accuracy, therefore improving the IGP availability rate with an increase of 13.16% and 33.19% at mid- and low-latitude regions, respectively; and further accelerating the convergence of static precise point positioning. The estimated GIVE is reduced by around 21.15% and can still envelop the ionospheric modeling errors successfully. These results demonstrate that the proposed method can enhance the performance of the WAAS-Kriging method in low-latitude regions.</p>

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Optimizing the WAAS-Kriging method for estimating grid ionospheric delay error and accuracy over low-latitude regions

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • Yunri Fu,
  • Ling Yang,
  • Shaojun Feng,
  • Yunzhong Shen,
  • Nan Zhi,
  • Liping Fu

摘要

Satellite-Based Augmentation Systems (SBAS) broadcast the Grid Ionospheric Vertical Delay (GIVD) and Grid Ionospheric Vertical Error (GIVE) at Ionospheric Grid Points (IGPs), as Ionospheric Delay Correction Messages (IDCMs), to enhance GNSS positioning accuracy and integrity. As a typical representative of SBAS, the Wide Area Augmentation System (WAAS) generates IDCMs based on the Kriging method. In WAAS-Kriging, the process noise of the ionosphere is characterized by a constant variance and variogram, which are usable for mid-to-high latitude regions, but less adequate for low-latitude active regions of the ionosphere, leading to unrealistic GIVD accuracies and overly conservative GIVE values. This study presents an optimized Kriging method that adaptively models ionospheric process noise, and proposes a novel strategy for calculating GIVE, along with a Grid Ionospheric Delay Accuracy (GIVA) to characterize GIVD accuracy. In the proposed method, the variances of process noise are first determined adaptively by analyzing the statistical relationship between the Local Ionospheric Spatial Activity Indexes (LISAIs) and ionospheric modeling errors. Then a spatiotemporal-varying variogram is newly established, so that variable variances are considered when calculating the process noise covariance. Finally, the IDCMs and GIVAs are calculated using those variances and covariances. The observation data on DOY 251 of 2017 and DOY 277-280 of 2021, in which the ionosphere was active in low-latitude regions, were obtained from the Crustal Movement Observation Network of China (CMONOC) and used for experimental analyses. The results demonstrate that the estimated GIVA can effectively describe the GIVD accuracy, therefore improving the IGP availability rate with an increase of 13.16% and 33.19% at mid- and low-latitude regions, respectively; and further accelerating the convergence of static precise point positioning. The estimated GIVE is reduced by around 21.15% and can still envelop the ionospheric modeling errors successfully. These results demonstrate that the proposed method can enhance the performance of the WAAS-Kriging method in low-latitude regions.