Three-dimensional ionospheric tomography using observation data of GPS ground receivers and ionosonde by neural network

In this paper we present a new method based on a Residual Minimization Training Neural Network (RMTNN) to reconstruct the three-dimensional electron density distribution of the local ionosphere with high spatial resolution (about 50 km x 50 km in east/west and 30 km in altitude) using GPS and ionosonde observation data. In this method we reconstruct an approximate three-dimensional electron density distribution as a computer tomographic image by making use of the excellent capability of a multilayer neural network to approximate an arbitrary function. For this application the network training is carried out by minimizing the squared residuals of an integral equation. We combine several additional techniques with the new method, i.e., input space discretization, use of ionosonde observation data to improve the vertical resolution, automatic estimation of the biases of the satellite and the ground receivers by using the parameter estimation method, and estimation of plasmasphere contributions to the total electron content on the basis of an assumption of diffusive equilibrium with constant scale height. Numerical experiments for the actual positions of the GPS satellites and the ground receivers are used to validate the reliability of the method. We also applied the method to the analysis of real observation data and compared the results with ionosonde observations which were not used for the network training.