基于LSTM的改进模型在电离层TEC预报中的应用
doi: 10.11728/cjss2025.05.2024-0112 cstr: 32142.14.cjss.2024-0112
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黄灿 女, 1997年6月出生于广西壮族自治区钦州市, 桂林理工大学测绘地理信息学院在读硕士研究生, 主要研究电离层参数预测方法. E-mail: can_huangcc@163.com -
黎峻宇 男, 1989年2月出生于广西壮族自治区玉林市, 现为桂林理工大学测绘地理信息学院副教授, 硕士生导师, 主要从事GNSS空间环境监测研究. E-mail: yl_lijunyu@163.com
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Application of Improved Model Based on LSTM in Ionospheric TEC Forecast
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摘要: 电离层延迟是全球卫星导航定位中重要的误差源之一, 提高电离层总电子含量(Total Electron Content, TEC)预报精度对改善卫星导航定位精度极其重要. 本文联合滑动窗口(Sliding Window)和长短时记忆(Long Short-Term Memory, LSTM))神经网络, 以滑动窗口算法对输入序列数据集不断更新并测试不同输入序列长度对应模型的精度, 最后以预测值来更新输入数据序列的最后10%, 进而构建TEC预报模型. 验证结果表明, 该模型在平静期和磁暴期预测残差绝对值小于5 TECU的比例均达85%以上, 较传统LSTM模型对应值占比增加了49%, 71%, 均方根误差(RMSE)低31%, 35%; 其预报结果的平均绝对误差(MAE)减少25%, 32%; SLSTM模型预测结果的RMSE均值、MAE均值均比传统LSTM模型、BP模型小.Abstract: Ionospheric delay is one of the most important sources of error in global satellite navigation and positioning. Improving the prediction accuracy of ionospheric Total Electron Content (TEC) is very important to improve the positioning accuracy of satellite navigation. In this paper, we combine sliding window and Long Short-Term Memory (LSTM) neural network, and use sliding window algorithm to continuously update the input time series data set. We tested the accuracy of the models corresponding to different input sequence lengths and recorded them, and found that the accuracy of the last 10% of the input data series was the best when the predicted value was updated. Finally, we used the sliding window method to update the last 10% of the input data series with the predicted value to build the TEC prediction model. The newly constructed model, traditional LSTM model and BP model are used to predict the same TEC time series data, and Root Mean Square Error (RMSE), absolute residual error and mean absolute error (MAE) are used to evaluate the accuracy of the model prediction results, and verify the prediction performance of the new model. The experimental results show that the proportion of residual absolute value less than 5 TECU predicted by the newly constructed model in both the calm period and the magnetic storm period exceeds 85%, and the proportion of predicted residual absolute value less than 5 TECU corresponding to the traditional LSTM model increases by 49% and 71%. On the other hand, compared with the traditional LSTM model, the root-mean-square error of the new model is reduced by 31% and 35% respectively, and the average absolute error is reduced by 25% and 32% respectively. In addition, we can also see that the RMSE mean values and MAE mean values of SLSTM model are smaller than those of traditional LSTM model and BP model.
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表 1 Dst指数对应地磁活动强度
Table 1. Intensity of geomagnetic activity corresponding to the Dst index
Dst /nT ≤ –100 –(100, –50] (–50–30] >–30 地磁活动强度 强 中 弱 平静 
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表 2 SLSTM/LSTM模型对20个格网预测结果的MAE(单位: TECU)
Table 2. MAE of SLSTM/LSTM model for prediction results of 20 grids (Unit: TECU)
纬度/(º)N 经度/(º)E (平静期) 经度/(º)E (磁暴期) 95 100 105 110 95 100 105 110 30 2.9/2 1.0/1.8 1.4/2.4 2.0/2.4 2.7/3.4 3.5/3.8 2.1/2.6 2.8/2.8 27.5 1.6/2.1 1.4/3.3 1.6/2.4 3.3/2.8 2.7/3.4 1.6/2.9 1.6/2.6 3.5/2.9 25 2.6/3.2 3.4/2.3 2.2/3.2 1.6/4.6 3.3/3.6 3.2/3.4 2.1/2.8 2.4/3.9 22.5 1.6/3.1 1.5/2.5 2.1/1.9 3.4/2.6 1.1/4.1 1.7/2.3 2.2/2.7 2.1/3.3 20 1.1/4 1.5/3 2.8/3.0 2.2/4 2.2/5.7 2.0/3.8 2.9/3.3 1.2/4 均值 2.1/2.8 2.3/3.4
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表 3 SLSTM/LSTM模型对20个格网预测结果的RMSE (单位: TECU)
Table 3. RMSE of SLSTM/LSTM model for prediction results of 20 grids (Unit: TECU)
纬度/(º)N经度/(º)E (平静期) 经度/(º)E (磁暴期) 95 100 105 110 95 100 105 110 30 3.5/2.5 1.3/2.3 2.4/2.7 3.1/2.8 3.6/4.3 4.0/4.6 3.1/3.4 3.6/3.7 27.5 1.9/2.4 2.1/3.7 2.2/3.3 3.8/3.7 3.4/4.5 2.5/3.3 1.7/3.2 4.3/4.1 25 3.2/3.7 4.0/3.2 3.2/4 1.9/5.5 3.8/4.5 3.7/4.3 2.3/3.5 2.8/4.9 22.5 1.7/3.8 1.7/3.5 2.5/2.4 3.7/3.4 1.5/5.2 1.8/3.1 2.6/3.7 2.7/4.1 20 1.2/4.7 1.6/4.3 3.1/4 3.2/5.1 2.8/7.1 2.1/4.8 3.0/4.6 1.4/5.2 均值 2.5/3.6 2.8/4.3
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表 4 SLSTM, LSTM, BP模型对4个格网预测结果的RMSE均值和MAE均值(单位: TECU)
Table 4. RMSE mean and MAE mean values by SLSTM, LSTM and BP models for the prediction results of four grids (Unit: TECU)
模型 RMSE均值 MAE均值 平静期 磁暴期 下半年 平静期 磁暴期 下半年 SLSTM 2.7 2.8 2.7 2.0 2.2 2.1 LSTM 3.7 5.0 3.8 3.1 4.0 3.3 BP 3.7 5.1 4.0 3.3 4.2 3.6
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