Ionospheric Refined Mapping Function Construction Based on LSTM

The ionospheric mapping function (MF) is used to achieve mutual conversion between the vertical total electron content (VTEC) and the slant total electron content (STEC) and is vital to the application of ionospheric products. Currently, the typically used MFs consider only the effect of the ionospheric thin-layer height and signal elevation angle, whereas the effects of ionospheric spatiotemporal changes and the azimuth angle, which severely restrict the accuracy of the MF, are not considered. In this study, an ionospheric MF model with the modified Julian day (MJD), local time (LT), elevation angle, and azimuth angle of the ionospheric pierce point (IPP) as inputs is proposed. The MF model, which is named long short-term memory (LSTM)-MF, is constructed using data from the United States provided by the Massachusetts Institute of Technology (MIT)/Haystack Observatory from September 1, 2021 to April 30, 2022, and ionospheric grid products named Model VTEC are established based on the LSTM-MF model. On the test set, the root-mean-square errors (RMSEs) of the STEC projected using the LSTM-MF model in the elevation-angle ranges of 20°–40°, 40°–70°, and 70°–90° are 48.66%, 33.79%, and 11.36% higher than that of the single-layer MF (SLMF) model, respectively. On December 5, 2021, the STEC obtained by projecting the Model VTEC product using the LSTM-MF model is 43.8% higher in accuracy than that obtained by projecting MIT VTEC products using the SLMF model at the low elevation angles of 20°–50°. The LSTM-MF model proposed herein and the established VTEC product improved the STEC accuracy obtained from low-elevation-angle conversion.