A Causal Long Short-Term Memory Sequence to Sequence Model for TEC Prediction Using GNSS Observations

The necessity of predicting the spatio-temporal phenomenon of ionospheric variability is closely related to the requirement of many users to be able to obtain high accuracy positioning with low cost equipment. The Precise Point Positioning (PPP) technique is highly accepted by the scientific community as a means for providing high level of position accuracy from a single receiver. However, its main drawback is the long convergence time to achieve centimeter-level accuracy in positioning. Hereby, we propose a deep learning-based approach for ionospheric modeling. This method exploits the advantages of Long Short-Term Memory (LSTM) Recurrent Neural Networks (RNN) for timeseries modeling and predicts the total electron content per satellite from a specific station by making use of a causal, supervised deep learning method. The scope of the proposed method is to compare and evaluate the between-satellites ionospheric delay estimation, and to aggregate the Total Electron Content (TEC) outcomes per-satellite into a single solution over the station, thus constructing regional TEC models, in an attempt to replace Global Ionospheric Maps (GIM) data. The evaluation of our proposed recurrent method for the prediction of vertical total electron content (VTEC) values is compared against the traditional Autoregressive (AR) and the Autoregressive Moving Average (ARMA) methods, per satellite. The proposed model achieves error lower than 1.5 TECU which is slightly better than the accuracy of the current GIM products which is currently about 2.0–3.0 TECU.