Modeling and interpolation of ionosphere total electron content using artificial neural network and GPS observation



Global positioning system (GPS) signals provide valuable information about ionosphere physical structure. Using these signals, can be derived total electron content (TEC) for each line of sight between the receiver and the satellite. For historic and other sparse data sets, the reconstruction of TEC images is often performed using multivariate interpolation techniques. Recently it has become clear that the techniques derived from artificial intelligence research and modern computer science provide a number of system aids to analyze and predict the behavior of complex solar-terrestrial dynamic systems. Methods of artificial intelligence have provided tools which potentially make the task of ionospheric modeling possible. Artificial neural network (ANN) provides an inexplicit non-linear model to learn relations between inputs and outputs using training data.
Neural network is an information processing system which is formed by a large number of simple processing elements, known as artificial nerves. The input data are multiplied by the corresponding weight and the summation are entered into neurons. Each neuron has an activation function. Inputs pass to the activation function and determine the output of neurons. The behavior of neural network is related to communication between nodes. Using training data, the designed ANN can be adjusted in an iterative procedure to determine optimal parameters of ANN. Then for an unknown input, we can compute corresponding output using the trained ANN. The neurons of input and output layers are determined according to the number of input and output parameters. The number of neurons in the hidden layer can be determined by trial and error through minimizing total error of the ANN. For this minimization, each ANN parameter’s share in the total error should be computed which can be achieved by a back-propagating algorithm.
Radial basis function neural network (RBFNN) is known from the approximation theory as it is applied to the real multivariate interpolation problem. RBFNN is popularized by Moody and Darken (1989), and many researchers suggested it as an alternative ANN structure to MLP. RBFNN is very useful for function approximation and classification problems because of its more compact topology and faster learning speed. RBFNN is configured with three layers. An input layer consists of source neurons and distributes input vectors to each of the neurons in the hidden layer without any multiplicative factors. The single hidden layer has receptive field units (hidden neurons) each of which represents a nonlinear transfer function called a basis function. The output layer produces a linear weighted sum of hidden neuron outputs and supplies the response of RBFNN.
Due to the nonlinearity of ionosphere physical properties, in this paper, multi-layer perceptron artificial neural networks (MLP-ANN) and RBFNN used to model and predict the spatial and temporal variations of vertical TEC (VTEC) over Iran. The used model is able to estimate and predict the VTEC within and also near the network. For this work, observations of 22 GPS stations in northwest of Iran (360


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