Regional/Single Station Zenith Tropospheric Delay Combination Prediction Model Based on Radial Basis Function Neural Network and Improved Long Short-Term Memory

Abstract

Atmospheric water vapor is an essential source of information that predicts global climate change, rainfall, and disaster-natured weather. It is also a vital source of error for Earth observation systems, such as the global navigation satellite system (GNSS). The Zenith Tropospheric Delay (ZTD) plays a crucial role in applications, such as atmospheric water vapor inversion and GNSS precision positioning. ZTD has specific temporal and spatial variation characteristics. Real-time ZTD modeling is widely used in modern society. The conventional back propagation (BP) neural network model has issues, such as local, optimal, and long short-term memory (LSTM) model needs, which help by relying on long historical data. A regional/single station ZTD combination prediction model with high precision, efficiency, and suitability for online modeling was proposed. The model, called K-RBF, is based on the machine learning algorithms of radial basis function (RBF) neural network, assisted by the K-means cluster algorithm (K-RBF) and LSTM of real-time parameter updating (R-LSTM). An online updating mechanism is adopted to improve the modeling efficiency of the traditional LSTM. Taking the ZTD data (5 min sampling interval) of 13 international GNSS service stations in southern California in the United States for 90 consecutive days, K-RBF, R-LSTM, and K-RBF were used for regions, single stations, and a combination of ZTD prediction models regarding research, respectively. Real-time/near real-time prediction results show that the root-mean-square error (RMSE), mean absolute error (MAE), coefficient of determination (R2), and training time consumption (TTC) of the K-RBF model with 13 station data are 8.35 mm, 6.89 mm, 0.61, and 4.78 s, respectively. The accuracy and efficiency of the K-RBF model are improved compared with those of the conventional BP model. The RMSE, MAE, R2, and TTC of the R-LSTM model with WHC1 station data are 6.74 mm, 5.92 mm, 0.98, and 0.18 s, which improved by 67.43%, 66.42%, 63.33%, and 97.70% compared with those of the LSTM model. The comparison experiments of different historical observation data in 24 groups show that the real-time update model has strong applicability and accuracy for the time prediction of small sample data. The RMSE and MAE of K-RBF with 13 station data are 4.37 mm and 3.64 mm, which improved by 47.70% and 47.20% compared to K-RBF and by 28.48% and 31.29% compared to R-LSTM, respectively. The changes in the temporospatial features of ZTD are considered, as well, in the combination model.