Investigating the performance of wavelet neural networks in ionospheric tomography using IGS data over Europe

Ionospheric tomography is a very cost-effective method which is used frequently to modeling of electron density distributions. In this paper, residual minimization training neural network (RMTNN) is used in voxel based ionospheric tomography. Due to the use of wavelet neural network (WNN) with back-propagation (BP) algorithm in RMTNN method, the new method is named modified RMTNN (MRMTNN). To train the WNN with BP algorithm, two cost functions is defined: total and vertical cost functions. Using minimization of cost functions, temporal and spatial ionospheric variations is studied. The GPS measurements of the international GNSS service (IGS) in the central Europe have been used for constructing a 3-D image of the electron density. Three days (2009.04.15, 2011.07.20 and 2013.06.01) with different solar activity index is used for the processing. To validate and better assess reliability of the proposed method, 4 ionosonde and 3 testing stations have been used. Also the results of MRMTNN has been compared to that of the RMTNN method, international reference ionosphere model 2012 (IRI-2012) and spherical cap harmonic (SCH) method as a local ionospheric model. The comparison of MRMTNN results with RMTNN, IRI-2012 and SCH models shows that the root mean square error (RMSE) and standard deviation of the proposed approach are superior to those of the traditional method.