Modeling and forecasting of ionosphere TEC using least squares SVM in central Europe

Abstract

We propose a new method for spatio-temporal modeling of ionosphere total electron content (TEC) using least squares support vector machine (LS-SVM). In the SVM model, dual programming is used to solve the system of equations. Therefore, large-scale problem solving with the SVM greatly increases computation time and decreases accuracy. To overcome these limitations, a LS-SVM method is proposed. This method uses simple linear equations to solve the system of equations. As a result, the complexity of the computational algorithm is reduced. In addition, the convergence speed and accuracy of the results increase. To evaluate the new method, observations of 30 GNSS stations in the central Europe are used. The observations are for 80 days from 2014, with different solar (F10.7) and geomagnetic activity (KP and DST) indices. The results of the LS-SVM model at three control stations are compared with the vertical TEC (VTEC) of the GPS and also with the VTEC of the SVM, NeQuick and global ionosphere map (GIM) models. On all days considered, the averaged RMSE of the LS-SVM, SVM, GIM and NeQuick models at the control stations are calculated as 2.45, 3.13, 4.61 and 7.48 TECU, respectively. In precise point positioning (PPP) analysis and at the high geomagnetic activity, the maximum RMSE of LS-SVM, SVM, GIM and NeQuick models are computed 52.34, 63.22, 70.21 and 79.55 mm, respectively. During periods of low geomagnetic activity, the RMSE of the LS-SVM model is lower than the other models. Seasonal error analysis of all 4 models shows that the LS-SVM model has less error in different seasons compared to the other models. The results also show that the proposed model has a higher speed and accuracy than the SVM, GIM and NeQuick. Therefore, it can be considered a regional model of the ionosphere in the European region.