Prediction of ionospheric vertical total electron content from GPS data using ordinary kriging-based surrogate model

  • R. MukeshEmail author
  • P. Soma
  • V. Karthikeyan
  • P. Sindhu
Original Article


The total electron content (TEC) is the number of electrons present in a ray path between satellite and receiver. TEC affects the propagation of radio signal from satellite to receiver, which causes a ranging error. In the case of single frequency user receiver, the prediction of TEC helps to correct the range errors. TEC is measured using TEC unit (TECU), where \(1~\text{TECU} = 1 \times 10^{16}~\text{electrons}/\text{m}^{2}\). The vertical total electron content (VTEC) of the L1 band is estimated by using data collected from GPS receiver which is installed at the ACSCE station Bangalore. In this work, an ordinary kriging (OK)-based surrogate model algorithm and Matlab code is developed and used to predict the hourly basis ionospheric VTEC. Six parameters such as time, sun spot number (SSN), the solar flux index at 10.7 cm (F10.7), Kp and Ap and observed TEC are used to build the surrogate model. These parameters are related to the ionospheric diurnal variations, solar cycle and geomagnetic activities. In order to cover all regions of the world during different solar activity periods six input parameters are collected from low-, mid- and high-latitude regions during low, medium and high solar activity periods. The root mean square error (RMSE) of the OK-based surrogate model ranges from 0.6–3.6 TECU, and the correlation coefficient varies between 0.79–0.99 and range error varies from 0.04654–0.3017244 m at three regions.

The TEC prediction results from the OK-based surrogate model are compared with results obtained from (i) a genetic algorithm-based neural network (GA-NN), (ii) a back-propagation neural network (BP-NN) and (iii) the IRI-2012 model at the CHAN station. For a typical dataset the RMSE of the OK-based surrogate model is 4.523 TECU and the correlation coefficient is 0.9733. The RMSE values for the GA-NN, BP-NN and IRI-2012 models are 5.3529, 6.2913 and 6.7179 TECU and The correlation coefficients are 0.8343, 0.7869 and 0.7797, respectively. The OK model is also compared with a time series method for the CHAN station; it is observed that, for 3 days (7-1-2008 to 9-1-2008) prediction, the OK model gives a 75% result for \(\Delta \textit{TEC} <1~\text{TECU}\) condition, the time series method gives 39% for the same condition. The results indicate that the OK-based surrogate model is suitable for applications in ionospheric TEC predictions.


Ionosphere Vertical total electron content Ordinary kriging Surrogate model GPS TEC prediction 



The research work presented in this paper has been carried out under the project entitled “Surrogate model for ionospheric studies using IRNSS/GPS Data”, funded by SAC, ISRO, Ahmadabad.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringACS College of EngineeringBangaloreIndia
  2. 2.Department of Aeronautical EngineeringACS College of EngineeringBangaloreIndia
  3. 3.Department of ECEDr. MGR Educational and Research InstituteChennaiIndia

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