Modeling and prediction of the ionospheric total electron content time series using support vector machine in 2007-2018

The ionosphere is a layer of the Earth's atmosphere that extends from an altitude of 60 km to an altitude of 1,500 km. Knowledge of electron density distribution in the ionosphere is very important and necessary for scientific studies and practical applications. Observations of global navigation satellite system (GNSS) such as the global positioning system (GPS) are recognized as an effective and valuable tool for studying the properties of the ionosphere. Studies on ionosphere modeling in the Iranian region have shown that the global ionosphere maps (GIM) model as well as empirical models such as IRI2016 and NeQuick have low accuracy in this region. The main reason for the low accuracy of these models is the lack of sufficient observations in the Iranian region. For this reason, this paper presents the idea of using learning-based methods to generate a local ionosphere model using observations of GNSS stations. Therefore, the main purpose of this paper is to use three models of artificial neural networks (ANNs), adaptive neuro-fuzzy inference system (ANFIS) and support vector machine (SVM) to model and predict the time series of ionospheric TEC variations in Tehran GNSS station.An adaptive neuro-fuzzy inference system (ANFIS) is a kind of ANN that is based on Takagi–Sugeno fuzzy inference system. The technique was developed in the early 1990s (Jang, 1993). Since it integrates both neural networks and fuzzy logic principles, it has potential to capture the benefits of both in a single framework. Its inference system corresponds to a set of fuzzy IF–THEN rules that have learning capability to approximate nonlinear functions. Hence, ANFIS is considered to be a universal estimator. ANFIS architecture consists of five layers: fuzzy layer, product layer, normalized layer, defuzzy layer, and total output layer.In machine learning, support-vector machines (SVM) are supervised learning models with associated learning algorithms that analyze data used for classification and regression analysis. More formally, a SVM constructs a hyperplane or set of hyperplanes in a high- or infinite-dimensional space, which can be used for classification, regression, or other tasks like outliers detection (Vapnik, 1995). In SVM method, using nonlinear functions φ(x), the input vector (x) is depicted from N-dimensional space to M-dimensional space (M>N). The number of hidden units (M) is equal to the number of support vectors that are the learning data points, closest to the separating hyperplane.The results of this paper show that the SVM has a very high accuracy and capability in modeling and predicting the ionosphere TEC time series. This model has a higher accuracy in the period of severe solar activity than GIM and IRI2016 models, which are the traditional ionospheric models in the world. Due to the fact that global models in the region of Iran do not have acceptable accuracy due to lack of sufficient observations, therefore, the SVM can be used as a local ionosphere model with high accuracy. Using this model, the TEC value can be predicted with high accuracy for different times and during periods of severe solar activity. This model can be used in studies related to the physics of the ionosphere as well as its temporal variations.