Improving extended Kriging with Chapman model and exponential variation function model

In the satellite-based augmentation system, the ionospheric error as one of the main error sources has a big influence on the navigation capability of single frequency user. At present, the IGD is estimated based on the distance-weighted algorithm and Kriging plane fitting algorithm with a single-layer shell model, in which ionosphere is equivalent to a thin shell at certain height. However, the error introduced by single-layer thin shell model leads to a poor precision of ionospheric delay estimation. In terms of this issue, some scholars proposed extended Kriging algorithm based on empirical model, but the accuracy is not high and are limited by experience. This paper proposes an extended tomography algorithm improving the estimation precision of extended Kriging algorithm using Chapman model instead of empirical model, and fitting the single Gaussian random delays. The analysis is made using ionospheric data collected from WAAS reference stations and CORS stations within the scope of the United States in this paper. First, we compare the fitting accuracy of Kriging algorithm and extended algorithm on each reference station, and analyze the improvement under the different ionospheric disturbance conditions and elevation angles. Then we compare the fixed delays based on the two methods. The results show that the fitting precision of the improved algorithm is increased by 10–50%, especially in the case of low elevation angle, and the UIVE is also reduced by 5–40%.