[1] 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  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.Citation: Ma, X. F., T. Maruyama, G. Ma, and T. Takeda (2005), Three-dimensional ionospheric tomography using observation data of GPS ground receivers and ionosonde by neural network,

[1] The dual-frequency signals of GPS can be used to measure the total electron content (TEC). The differential instrumental biases inherent in GPS satellite and receivers are considered as the main sources of error, and they must be removed for an accurate estimation of TEC. We aim at developing an effective method to solve the difficulties involved in the TEC measurement; there are only a few usable ground receivers, especially in lower-latitude areas near the geomagnetic equator where large ionospheric variability exists. For this purpose a new parameter estimation method based on a residual minimization training neural network is applied to determination of the GPS receiver biases. The alternative method is realized by making use of the excellent features of neural networks to approximate a wide range of mapping functions, for which the network training is carried out by minimizing squared residuals of integral equation. To determine receiver biases (unknown parameters), we used additional ''neural networks,'' each of which consists of only one neuron without an input channel. It is assumed that satellite biases have already been determined by applying the least squares method to the GEONET data gathered by a large number of receivers. Various cases of observation data for different seasons, different local times, and different geographic locations of the receiver as well as the cases of model data are analyzed, and it is confirmed that the method is very effective for a small number of receivers located in the lower-latitude areas.