Optimizing Ionospheric Semi-variograms with Variable Correlation Parameters and Modeling Spatial Threats with Multiple Metrics for China Region

The ionosphere presents a significant challenge for satellite-based augmentation system (SBAS) due to its unpredictable ionospheric variations affecting satellite single-frequency (SF) signal propagation. The traditional grid model estimates vertical delays and uncertainties at ionospheric grid points (IGPs) but is limited in capturing spatial variations and undersampled threats when employing a constant semi-variogram. This article aims to enhance ionospheric integrity and system availability of BeiDou SBAS (BDSBAS) in China and surrounding areas by optimizing universal Kriging-based semi-variograms with spatio-temporally varying correlation parameters for both isotropic and anisotropic ionospheric models. Using observation data from 30 stations of Crustal Movement Observation Network of China (CMONOC) from January to December 2021, semi-variogram parameters, including decorrelation distance, nugget, and sill, were estimated every half hour. Results demonstrated that these parameters exhibit significant temporal dependence for both the region and each IGP, indicating that variable semi-variograms are more effective for Kriging fitting and SBAS ionospheric corrections. Additionally, the undersampled threat model was expanded by introducing a norm-based angular metric (NAM) alongside the fit radius and the relative centroid metric. Data from periods of higher geomagnetic and solar activity in 2021 and 2022 were used to identify raw undersampled threat samples for two-metric and multi-metric threat models across typical, isotropic, and anisotropic semi-variograms. Evaluations showed that variable anisotropic semi-variograms reduced the representative ionospheric threat level to 1.75 m, compared to 1.92 m for typical semi-variograms and 1.82 m for isotropic ones. Further testing, using data from nine additional stations under different solar and geomagnetic conditions, was conducted to assess BDSBAS performances based on different combinations of semi-variograms and threat models. Results demonstrated that combining variable anisotropic semi-variograms with the multi-metric threat model significantly tightened the user ionospheric vertical error (UIVE) envelope and reduced the spatial threat percentage in grid ionospheric vertical errors (GIVEs) from 88.44% to 71.68%. This approach also lowered protection levels and increased BDSBAS coverage, highlighting its capability to deal with complex ionospheric conditions.