Improving IRI-2016 global total electron content maps using ELM neural network

Abstract

The International Reference Ionosphere (IRI) is the most widely used empirical model for presenting ionosphere parameters like Vertical Total Electron Content (VTEC) or electron density indices. This model is suitable for studying long-term ionospheric conditions. However, for precise applications like Precise Point Positioning (PPP), the obtained VTEC values cannot provide the required precision. Artificial Neural Networks (ANNs) have become the burgeoning case of studies in all scientific fields. This is due to their capability to simply parametrize a relation between non-linear physical parameters and several independent variables. The goal of this study is to implement an Extremely Learning Machine (ELM) to improve the IRI-2016 model accuracy using historical Spherical Harmonic (SH) coefficients of the IGS Global Ionosphere Maps (GIMs). The choice of ELM was due to their decreased convergence time and not falling in the local minimum solution. For the considered supervised learning process, the IRI-2016 and IGS GIMs SH coefficients (256 coefficients up to degree and order 15) were chosen as the variables for the input and output layer of the ELM, respectively. Then, after the training of the ANN, one can input SH coefficients of the IRI-2016 and derive improved SH coefficients, which can be transformed into the GIMs. The results showed that between several considered cases for training and prediction intervals, the one with 365 and 7 days for training and prediction time intervals had shown a mean Root Mean Square Error (RMSE) of about 1.6 TECU compared to IGS GIMs, which was 56% better than the corresponding IRI-2016 RMSE value. Also, the kinematic Precise Point Positioning (kinematic-PPP) using single frequency observation of 6 IGS stations has been done using ELM derived VTEC values. The calculated mean 3D positions error of about 1.85 m showed that the ELM-derived VTEC values might be implemented for high precision real-time applications.