LSTM-based short-term ionospheric TEC forecast model and position accuracy analysis

Abstract Ionospheric delay is one of the major error sources in global navigation satellite system (GNSS) single point positioning (SPP). Some empirical models have been proposed to correct ionospheric delay, which, however, are limited by the low accuracy. The single-point time-series-based ionospheric total electron content (TEC) forecast method theoretically introduces model error and the accumulation of forecast error increases during a day. Therefore, based on the regular variation characteristics of the ionosphere, to improve the forecast accuracy of the ionosphere, we propose a long short-term memory (LSTM) short-term forecast model using discrete GNSS data and ionospheric space environment data in the same period of multiple days. The LSTM ionospheric forecast model is constructed based on the 2014 single-site GNSS data from different regions (low, mid, and high latitude regions) of the Crustal Movement Observation Network of China (CMONOC). The results are compared with the Klobuchar model, CMONOC regional ionosphere maps (RIM) data, and GNSS derived TEC measurements. The performance of each model in the SPP is also compared and analyzed to further examine the feasibility of the LSTM ionospheric forecast model. The comprehensive statistical analysis shows that: i) LSTM forecast model is consistent with GNSS-TEC observations at high, mid, and low latitudes, and the forecast error is less than 3 TECu, which is much better than that of the Klobuchar model and RIM model, and is robust to anomalous values. The mean absolute error (MAE) and root mean square error (RMSE) of the LSTM forecast model decrease with increasing latitude. ii) When being used in SPP, the LSTM forecast model brings significant improvement to position accuracy, which is overall better than the RIM and Klobuchar models. The RMSE of 3D position error is 2–4 m for the LSTM forecast model, 2–5 m for the RIM model, and 4–5 m for the Klobuchar model. iii) In terms of geographic location, for 3D position accuracy, it is highest at mid-latitudes followed by high latitudes and worst at low latitudes. For the percentage of 3D position corrections relative to the reference, it is highest at high latitudes followed by mid-latitudes, and lowest at low latitudes. The percentage of LSTM forecast model is 85%-90% at low latitudes, which is better than Klobuchar's 40%-80% and RIM's 75%-85%. Such percentage is over 90% at mid-latitudes, which is comparable to the RIM and about 50% better than the Klobuchar model. It is noteworthy that the LSTM performs even better than the reference data at high latitudes.