基于Keras平台的LSTM模型的对流层延迟预测

对流层延迟是影响全球卫星导航系统（GNSS）测量精度的重要因素. 针对现有对流层延迟模型稳定性差，精度较低等问题，在无实测气象参数条件下，提出一种基于Keras平台的长短期记忆神经网络（LSTM）的对流层延迟预测模型. 选取全球均匀分布的8个测站，使用其2016年第90-131年积日共42 天的整点对流层延迟数据预测其第132-136年积日的整点数据. 以国际GNSS服务（IGS）中心提供的对流层产品为真值，分析比较LSTM模型和反向传播（BP）神经网络模型的预测效果. 研究表明，LSTM模型预测结果的均方根误差基本达到mm级，其平均绝对误差和平均绝对百分比误差均比BP模型低，LSTM模型在精度和稳定性上较BP模型均有明显提高；LSTM模型在中高纬区域的均方根误差（RMSE）均值达到7.82 mm，中高纬地区更适合使用该模型. 

Prediction of tropospheric delay based on the LSTM model of Keras platform

Tropospheric delay is a vital factor that influence the measurement accuracy of GNSS. To solve the problems of poor stability and low accuracy of existing tropospheric delay model, a prediction model of tropospheric delay based on the Long-Short Term Memory neural network (LSTM) of Keras platform is proposed in the absence of measured meteorological parameters. Eight stations evenly distributed around the world were selected to use their 42-day hourly tropospheric delay data from the 90th to 131st day of 2016 to predict their hourly data of 132nd to 136th day. Based on the troposphere products provided by International GNSS Service (IGS) center, the prediction effects of LSTM model and back propagation neural network (BP) model were analyzed and compared. The result shows that the root mean square error of LSTM model basically reaches mm level, and the mean absolute error and mean absolute percentage error of LSTM model are lower than those of BP model, and the accuracy and stability of LSTM model are significantly improved compared with BP model. LSTM model has an average RMSE of 7.82 mm in mid and high latitude, which shows it is more suitable for mid and high latitude.