An Anisotropic Kriging for Ionospheric Delay Interpolation With a Wide Area Reference Network

Ionospheric delay is a critical error source for global navigation satellite system (GNSS) users. The kriging method is widely adopted to estimate the ionospheric delay at users’ locations based on sampling observations collected from a wide area reference network with the assumption of the isotropic ionosphere, e.g., satellite-based augmentation systems (SBASs) in North America, Japan, and India. However, the isotropy assumption may deviate from the ionosphere spatial characteristics in certain regions, compromising the SBAS performance. In this study, a modified ordinary kriging approach is presented based on the anisotropy characteristic of the ionospheric delay. First, variograms describing the spatial random characteristics for kriging are analyzed to investigate the differences along the longitude and latitude directions. It is observed that the anisotropy behavior is obvious in low- and mid-latitude regions and becomes very weak in the high-latitude region. Furthermore, the isotropic ordinary kriging (IOK) is expanded into anisotropic ordinary kriging (AOK) with regional anisotropic variogram models constructed for three regions at low, middle, and high latitudes. Experimental results show that AOK significantly improves the delay estimation accuracy compared with the previous IOK method. Specifically, based on a wide reference network in North America, the implementation of AOK reduces the magnitude of the root mean square fit residual by 24.48%, 14.92%, and 6.90% in low-, mid-, and high-latitude regions. Moreover, the AOK algorithm consistently outperforms both IOK and universal kriging (UnK) across low- and mid-latitude regions, regardless of solar activity levels. The anisotropy characteristic in the ionosphere and the AOK technology facilitates the development of high-precision ionospheric delay modeling from isotropic to anisotropic models using a wide area reference network.