Ionosphere Tomography using Minimization of Objective Functions Method and Neural Networks over Iran

In the last two decades, knowledge of the distribution of the ionospheric electron density considered as a major challenge for geodesy and geophysics researchers. To study the physical properties of the ionosphere, computerized ionosphere tomography (CIT) indicated an efficient and effective manner. Usually the value of total electron content (TEC) used as an input parameter to CIT. Then inversion methods used to compute electron density at any time and space. However, CIT is considered as an inverse ill-posed problem due to the lack of input observations and non-uniform distribution of TEC data. Many algorithms and methods are presented to modeling of CIT. For the first time, 2-dimensional CIT was suggested by Austin et al., (1988). They used algebraic reconstruction techniques (ART) to obtain the electron density. Since, other researchers have also studied and examined the CIT. Although the results of all studies indicates high efficiency of CIT, but two major limitations can be considered to this first, due to poor spatial distribution of GPS stations and limitations of signal viewing angle, CIT is an inverse ill-posed problem. Second, in most cases, observations are discontinuous in time and space domain, so it is not possible determining the density profiles at any time and space around the world.
In this paper, the method of residual minimization training neural network is proposed as a new method of ionospheric reconstruction. In this method, vertical and horizontal objective functions are minimized. Due to a poor vertical resolution of ionospheric tomography, empirical orthogonal functions (EOFs) are used as vertical objective function. To optimize the weights and biases in the neural network, a proper training algorithm is used. Training of neural networks can be considered as an optimization problem whose goal is to optimize the weights and biases to achieve a minimum training error. In this paper, back-propagation (BP) and particle swarm optimization (PSO) is used as training algorithms. 3 new methods have been investigated and analyzed in this research. In residual minimization training neural network (RMTNN), 3 layer perceptron artificial neural networks (ANN) with BP training algorithm is used to modeling of ionospheric electron density. In second method, due to the use of wavelet neural network (WNN) with BP algorithm in RMTNN method, the new method is named modified RMTNN (MRMTNN). In the third method, WNN with a PSO training algorithm is used to solve pixel-based ionospheric tomography. This new method is named ionospheric tomography based on the neural network (ITNN).
The GPS measurements of the Iranian permanent GPS network (IPGN) (1 ionosonde and 4 testing stations) have been used for constructing a 3-D image of the electron density. For numerical experimentation in IPGN, observations collected at 36 GPS stations on 3 days in 2007 (2007.01.03, 2007.04.03 and 2007.07.13) are used. Also the results have been compared to that of the spherical cap harmonic (SCH) method as a local ionospheric model and ionosonde data. Relative and absolute errors, root mean square error (RMSE), bias, standard deviations and correlation coefficient computed and analyzed as a statistical indicators in 3 proposed methods. The Analyzes show that the ITNN method has a high convergence speed and high accuracy with respect to the RMTNN and MRMTNN. The obtained results indicate the improvement of 0.5 to 5.65 TECU in IPGN with respect to the other empirical methods.
The GPS measurements of the Iranian permanent GPS network (IPGN) (1 ionosonde and 4 testing stations) have been used for constructing a 3-D image of the electron density. For numerical experimentation in IPGN, observations collected at 36 GPS stations on 3 days in 2007 (2007.01.03, 2007.04.03 and 2007.07.13) are used. Also the results have been compared to that of the spherical cap harmonic (SCH) method as a local ionospheric model and ionosonde data. Relative and absolute errors, root mean square error (RMSE), bias, standard deviations and correlation coefficient computed and analyzed as a statistical indicators in 3 proposed methods. The Analyzes show that the ITNN method has a high convergence speed and high accuracy with respect to the RMTNN and MRMTNN. The obtained results indicate the improvement of 0.5 to 5.65 TECU in IPGN with respect to the other empirical methods.