A new three-dimensional computerized ionospheric tomography model based on a neural network

Computerized ionospheric tomography (CIT) is an ill-posed inverse problem owing to insufficient data acquisition. Therefore, the ionospheric electron density (IED) distributions cannot be reconstructed accurately. Although many attempts have been made to deal with this issue, there is still a long way to go before it can be completely overcome. Specifically, the inverted IEDs of voxels without observational information show a strong dependence on initial values, which affects the overall accuracy of CIT. Taking this into account, a new three-dimensional CIT model is developed, based on a backpropagation neural network. The neural network model is trained using the characteristics and inverted IEDs of voxels with observational information, and then, the IEDs of voxels without observational information are predicted again. Careful validation of the proposed model is performed by conducting numerical experiments with GPS simulation and real data under both quiet and disturbed ionospheric conditions. Compared with the traditional non-neural network method in the simulation experiment, the proposed method offers improvements of 62.0 and 56.89% in root mean square error and the mean absolute error for those voxels without observational information, respectively, while it offers improvements of 30.98 and 26.67% for all voxels of the whole region. In the real data experiment, the IEDs of the control groups obtained by the proposed method are compared with the target IEDs for all periods. The result presents correlation coefficient greater than 0.96 between this predicted IEDs and the target IEDs for all periods, and this further certifies the feasibility of the proposed method. Additionally, the latitude–longitude maps and profiles of the ionospheric electron density also show that the ill-posedness problem has a significantly weaker effect for those voxels without observational information.