عنوان مقاله [English]
The ionosphere as the upper part of Earth’s atmosphere consists of electrons and atoms affecting the signal propagation in the radio frequency domain. Nowadays, Global Navigation Satellite Systems (GNSS), like GPS, are widely used for various applications. The majority of navigation satellite receivers operate on a single frequency and experience an error due to the ionospheric delay. They compensate for the ionospheric delay using an ionospheric model which typically only corrects for 50% of the delay. An alternative approach is to map the ionosphere with a network of real-time measurements. Global Positioning System (GPS) networks prepare chance to study the dynamics and continuous variations in the ionosphere by complementary ionospheric measurements, which are usually obtained by different techniques such as ionosondes, incoherent scatter radars and satellites. The ionospheric delay is characterized by the Total Electron Content (TEC) along the signal path from the satellite to the receiver. Elimination (or reduction) of the ionosphere effects is possible using dual-frequency receivers by a very useful combination of dual-frequency data known as geometry free combination (L4) as follows:
where the L4 signature is derived from L1(1.57542 GHz) and L2(1.22760 GHz) phase observables. Single-frequency users, however cannot take advantage of this combination. So, they have to use a proper ionospheric model to correct the ionospheric delay. Ionosondes (up to an altitude of 1000 km) can determine TEC while GPS measurements give completely information about the topside ionosphere. In this paper, the suitability of Neural Networks (NNs) in order to predict the Total Electron Content (TEC) obtained from Iranian Permanent GPS Network (IPGN) during the low-solar-activity period 2006 has been investigated. TEC has many non-linear variations while the neural network has a significant ability to model and approximate it (Williscroft and Poole, 1996; Hernandez-Pajares et al., 1997; Xenos et al., 2003; Sarma and Mahdu, 2005; Leandro and Santos, 2007). The input space included the day number (DN,seasonal variation), hour (HR,diurnal variation), sunspot number (SSN,measure of the solar activity) and magnetic index (measure of magnetic activity).
To make the data continuous, the first two parameters were each split into sine and cosine components, two cyclic as follows:
where DNS, DNC, HRS and HRC are the sine and cosine components of DN and HR, respectively.
In this paper, the TEC values have been estimated using the PPP (Precise Point Positioning) module of the Bernese over Iranshahr (27˚N, 60˚E).
Optimum situation of the neural network include of single hidden layer and eight neurons of inputs layer and fifty neurons of hidden layer and one neuron of output layer. To this end, the single hidden layer feed-forward network with a back propagation algorithm has been designed.
An analysis was done by comparing predicted NN TEC(TEC values predicted by the NN model) with TEC values from the IRI2007 version of the International Reference Ionosphere, validating GPS TEC(TEC values calculated from the GPS measurements) with the maximum electron density obtained from ionosonde and calculating the performance of the NN model during equinoxes and solstices.
The results show high correlation with GPS TEC and NN TEC. Their Root-Mean-Square Error(RMSE) and coefficient of determination (R2) are 1.5273 TECU and 0.9334 respectively.
RMSE is defined as:
where N is the number of data points.
In table 3, the absolute error (Eabs) is defined as the magnitude of the difference between the NN predicted TEC and the GPS TEC, while the relative error(Erel) is the ratio of the absolute error to GPS TEC and can be represented as a percentage (Habarulema et al, 2007).These errors were calculated as follows:
is the absolute error and is the relative error respectively. The difference (100- % gives the relative correction, which indicates the approximate TEC prediction accuracy for the NN model (Leandro and Santos, 2007). An average error of ~11.41% means that the NN can predict about 88.58% of the GPS TEC on average. Results show that the neural network works better rather than the IRI model for IRAN.