A Neural network (NN) is a promising tool for the tomographic inversion of the ionosphere. However, existing research has adopted an unbalanced cost function for training purposes and a preset image for constraint purposes, resulting in the output image being dominated by measurements. To address these problems, we proposed an NN-based tomographic model with a balance cost function and a dynamic correction process (BCDC) for ionosphere inversion. The cost function is composed of two balance terms corresponding to the measurements and the selected constraints, respectively. The produced image in the forward process of the NN is corrected dynamically by fitting each vertical profile with orthogonal basis functions (EOFs) and the Chapman function and then by smoothing the voxels of each layer with a moving window approach horizontally. The corrected image is then used to calculate the slant total electron content (STEC) parameter, which is further translated into the term of the cost for the vertical and horizontal constraints. Experiments were carried out to validate the BCDC method and compared with a recently developed tomographic method and the international reference ionosphere (IRI) model. Results show that the parameters derived from the BCDC model demonstrate good consistency with the observations. Comparing with the reference methods, the BCDC method performs better in the validations of vertical profiles, F2 layer peak density (NmF2), STEC parameter and vertical total electron content map. Further analysis also shows that a balance cost function is of benefit to achieve an image of better quality.
The errors contained in slant total electron content (STEC) have a strong impact on the image generated by ionosphere tomography. This paper presents a method that rejects abnormal corrections and rays (RACR) in the multiplicative algebraic reconstruction technique (MART) algorithm by applying a correction threshold and a rejecting ratio threshold. The RACR algorithm was validated using ionosonde observations, Swarm satellite measurements, independent STEC observations and a vertical total electron content (TEC) map. Its performance was compared with the MART algorithm on both geomagnetically quiet days and disturbed days. The results show that the RACA algorithm is able to capture the main phase and the recovery phase of a storm and outperforms the MART algorithm under both geomagnetic conditions. The average improvements over the MART algorithm are 36.01%, 36.56%, 6.18%, 22.10% and 6.03% in the validation tests of the peak density of F2 layer, peak height of F2 layer, the electron density of the topside ionosphere, STEC and VTEC, respectively. The quality of the image produced by the RACR algorithm was controlled by the correction threshold and the rejection threshold. Smaller threshold values tend to make the image smoother. The RACR algorithm provides not only a way to produce a better tomographic image but also a means to detect abnormal rays.
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