Using TensorFlow-based Neural Network to estimate GNSS single frequency ionospheric delay (IONONet)

In the last 20?years, and in particular in the last decade, the availability of propagation data for GNSS has increased substantially. In this sense, the ionosphere has been sounded with a large number of receivers that provide an enormous amount of ionospheric data. Moreover, the maturity of the models has also been increased in the same period of time. As an example, IGS has ionospheric maps from GNSS data back to 1998, which would allow for the correlation of these data with other quantities relevant for the user and space weather (such as Solar Flux and Kp). These large datasets would account for almost half a billion points to be analyzed. With the advent and explosion of Big Data algorithms to analyze large databases and find correlations with different kinds of data, and the availability of open source code libraries (for example, the TensorFlow libraries from Google that are used in this paper), the possibility of merging these two worlds has been widely opened. In this paper, a proof of concept for a single frequency correction algorithm based in GNSS GIM vTEC and Fully Connected Neural Networks is provided. Different Neural Network architectures have been tested, including shallow (one hidden layer) and deep (up to five hidden layers) Neural Network models. The error in training data of such models ranges from 50% to 1% depending on the architecture used. Moreover, it is shown that by adjusting a Neural Network with data from 2005 to 2009 but tested with data from 2016 to 2017, Neural Network models could be suitable for the forecast of vTEC for single frequency users. The results indicate that this kind of model can be used in combination with the Galileo Signal-in-Space (SiS) NeQuick G parameters. This combination provides a broadcast model with equivalent performances to NeQuick G and better than GPS ICA for the years 2016 and 2017, showing a 3D position Root Mean Squared (RMS) error of approximately 2?m.