Modeling of ionosphere TEC using gated recurrent unit neural network model and comparison against other models

The ionosphere is a layer of the earth's atmosphere that extends from an altitude of 80 km to more than 1000 km above the earth. Due to its electrical properties, this layer of the atmosphere has very important and fundamental effects on the waves passing through it. The ionosphere exhibits temporary and intermittent variations such as daily, 27-day, seasonal, six-monthly, annual and 11-year changes. Ionosphere disturbances can cause distance error, cycle slips and phase fluctuations of satellite systems signals, which leads to degradation of the performance, accuracy and reliability of these systems. A parameter that can be used to study the ionosphere is the total electron content (TEC). This parameter is the sum of free electrons in a cylinder with a cross section of one square meter between the satellite and the receiver in the ground and its unit is ele./m2. If the TEC is along the vertical (zenith direction), it is called VTEC. Usually, TEC is expressed in terms of TECU, which is equal to 1016 ele/m2. Various methods have been developed to model the TEC. The simplest and at the same time the most practical method is to use observations of two-frequency receivers. If there is a proper station distribution, it is possible to obtain accurate TEC and model the ionosphere.

Materials & Methods:

In this paper, the idea of using the gated recurrent unit (GRU) for spatio-temporal modeling of the ionospheric total electron content (TEC) is proposed as a new model. In this type of neural network model, unlike normal neural networks, there is no gradient vanishing problem and it is very simple in terms of computations. The efficiency of the new model has been evaluated using the observations of 15 global positioning system (GPS) stations in the northwest of Iran. To calculate the accuracy of the GRU model, two interior and three exterior control stations are considered. It should be noted that the training of GRU model is done using the parameters of longitude and latitude of the GPS station, day of year (DOY), time (universal time), geomagnetic indices AP, KP and DST and solar activity index (F10.7). Also, the TEC in the direction of the zenith (VTEC) related to the input parameters are considered as the desired output. The results of the new model are compared with the results of artificial neural network (ANN), global ionosphere maps (GIM) and IRI2016 model. Also, the effect of the modeled TEC in precise point positioning (PPP) has been investigated.

Results & Discussion:

After training ANN and GRU models and selecting the optimal structure, these models can be used to estimate of VTEC. In this step, with the trained models, the VTEC is estimated at interior control stations and compared with the VTEC obtained from GPS. In the evaluation step of interior control stations, the averaged value of root mean square error (RMSE) of ANN, GRU, GIM and IRI models is to 2.42, 1.76, 3.02 and 6.91 TECU, respectively. Also, the averaged relative error of the models is 12.93%, 10.75%, 16.82% and 26.56%, respectively. In the control stations outside the GPS network area (exterior control stations), two scenarios were investigated: using the observations of these stations in the training step and not using the observations in the training. The evaluations showed that if the observations of exterior control stations are used in the training step of ANN and GRU models, the error of these models will be reduced. In all three exterior control stations, the accuracy of GRU model was higher than other models. The analysis of positioning error by PPP method also showed that by using the GRU model, positioning accuracy has improved by 7 to 45 mm. After evaluating the accuracy of the new model in interior and exterior control stations, the VTEC time series is estimated with the new model and compared with the time series obtained from other models and GPS. This comparison showed that the time series obtained from the GRU model correctly models the VTEC variations in both high and low solar and geomagnetic activities.

In this paper, the gated recurrent unit (GRU) neural network model was used for the first time in Iran for the spatio-temporal modeling of the total electron content of the ionosphere. In this model, unlike standard neural network models, there is no gradient vanishing problem, and as a result, the computation speed and accuracy of the model have increased. The results of this paper showed that the GRU model has the ability to estimate the spatio-temporal variations of VTEC with very high accuracy and can replace global and empirical models in the study area of this research.