An end-to-end approach for near real time ionosphere monitoring over mid-latitudes from GPS data using kriging interpolation and IGS products

Daily Plasmaspheric TEC Variations From COSMIC GPS Observations Based on RBF Neural Network‐Kriging Method

“…The Kriging method considers spatial autocorrelation and employs a semivariogram as a measure of spatial variability. The semivariogram is calculated by (e.g., Munyati & Sinthumule, 2021; Takka et al., 2018): $$$\gamma (h)={\gamma }_{i,j}=\frac{1}{2}E\left[{\left({Z}_{i}-{Z}_{j}\right)}^{2}\right]$$$ where $$h$$ is the separation distance between sample points, and $$Z$$ denotes the spatial variable at the sample point. During the processing of experimental data, the semivariogram is generally represented using a theoretical model.…”

“…The parameters in the theoretical model need to be estimated in the experimental data processing. Based on the ordinary kriging method, the spatial variables $$v$$ of the unsampled points can be given (e.g., Oliver & Webster, 1990): $$$v=\sum\limits _{i}^{n}{\lambda }_{i}\cdot {Z}_{i}$$$ where $$\lambda $$ is the Kriging weight coefficient calculated by solving the following linear system with $$\gamma $$, and the details of the implementation can be found in the previous study (Takka et al., 2018).…”

“…The Kriging method considers spatial autocorrelation and employs a semivariogram as a measure of spatial variability. The semivariogram is calculated by (e.g., Munyati & Sinthumule, 2021;Takka et al, 2018):…”

“…where 𝐴𝐴 𝐴𝐴 is the Kriging weight coefficient calculated by solving the following linear system with 𝐴𝐴 𝐴𝐴 , and the details of the implementation can be found in the previous study (Takka et al, 2018).…”