Modeling and accuracy analysis of GNSS ionospheric error in EU-China based on GA-BP
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摘要:
电离层误差是全球卫星导航系统 (GNSS)的主要误差来源之一，改正电离层误差的关键在于确定电离层的总电子含量(TEC)。针对现有电离层误差改正模型中存在的经验模型精度较低、球谐函数模型计算繁琐及其他模型存在的计算效率不足等问题，提出了基于遗传算法优化反向传播神经网络(GA-BP)的中欧GNSS电离层误差建模方法，并对模型精度进行了评估。通过国际GNSS服务组织(IGS)提供的TEC数据训练所提模型，挖掘了基于GA-BP模型的GNSS电离层TEC预测规则，并对不同时间和位置处的TEC值进行了短期、中期和长期预测。实验结果表明：基于GA-BP的电离层误差模型的短期预测均方根误差(RMSE)在不同纬度位置相比于自回归移动平均(ARIMA)模型分别提高了67.61%、36.33%、73.68%；在中期预测过程中的提升比例分别达到54.07%、22.36%、78.48%；在长期预测过程中的提升比例分别达到45.53%、43.78%、48.50%，能够更好地预测和拟合TEC随时间的变化情况。
Abstract:Ionospheric error is one of the main error sources of global navigation satellite system (GNSS). The key to correct ionospheric error is to determine the total electron content (TEC) of ionosphere. Aiming at the problems of low accuracy of empirical model, cumbersome calculation of spherical harmonic function model and insufficient calculation efficiency of other models in the existing ionospheric error correction model, an EU-China GNSS ionospheric error modeling method based on genetic algorithm optimized back propagation neural network (GA-BP) is proposed, and its model accuracy is evaluated. By training the model based on TEC data provided by International GNSS Service (IGS), the GNSS ionospheric TEC prediction rules based on GA-BP model are mined, and the short-term, medium-term and long-term prediction of TEC values at different time and locations are realized. The experimental results show that compared with other models, the root mean square error (RMSE) of short-term prediction of GA-BP model proposed in this paper are 67.61%, 36.33% and 73.68%, higher than that of autoregressive integrated moving average (ARIMA) model in different latitudes. In the medium-term prediction, the improvement has reached 54.07%, 22.6% and 78.48% respectively; in the long-term prediction, the results have reached 45.53%, 43.78% and 48.50% respectively, which can better predict and fit the change of TEC with time.
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图 1 基于GA-BP的GNSS电离层误差建模方法流程
Figure 1. Modeling algorithm of GNSS ionospheric error based on GA-BP
图 2 各模型短期（1周）预测结果对比
Figure 2. Comparison of short-term (one week) prediction results of each model
图 3 各模型中期（1月）预测结果对比
Figure 3. Comparison of medium-term (one month) prediction results of each model
图 4 各模型长期（1年）预测结果对比
Figure 4. Comparison of long-term (one year) prediction results of each model
表 1 各数据集样本数量
Table 1. Number of samples per dataset
数据集 样本数量 样本总数 低纬度 中纬度 高纬度 训练集 28 496 28 496 28 496 85 488 测试集 4745 4745 4745 14235 
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表 2 实验设计
Table 2. Experimental design
实验模型 实验1 实验2 实验3 Klobuchar 分别在3个不同纬度点处 分别在3个不同纬度点处 分别在3个不同纬度点处 ARIMA 利用各模型预测 利用各模型预测 利用各模型预报 GA-BP 未来1周的TEC变化 未来1月的TEC变化 未来1年的TEC变化
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表 3 各模型短期（1周）预测精度对比
Table 3. Comparison of short-term (one week) prediction accuracy of each model
预测模型 RMSE/TECU 低纬度 中纬度 高纬度 Klobuchar 105.48 114.19 71.21 ARIMA 11.30 2.67 2.85 GA-BP 3.66 1.70 0.75
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表 4 GA-BP模型短期（1周）预测精度提升率
Table 4. Improvement rate of short-term (one week) prediction accuracy of GA-BP model
% 类型 RMSE提升率 低纬度 中纬度 高纬度 相对Klobuchar模型的提升率 96.53 98.51 98.95 相对ARIMA模型的提升率 67.61 36.33 73.68
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表 5 各模型中期（1月）预测精度对比
Table 5. Comparison of medium-term (one month) prediction accuracy of each model
预测模型 RMSE/TECU 低纬度 中纬度 高纬度 Klobuchar 105.07 113.76 70.92 ARIMA 14.50 3.31 3.95 GA-BP 6.66 2.57 0.85
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表 6 GA-BP模型中期（1月）预测精度提升率
Table 6. Improvement rate of medium-term (one month) prediction accuracy of GA-BP model
% 类型 RMSE提升率 低纬度 中纬度 高纬度 相对Klobuchar模型的提升率 93.66 97.74 98.80 相对ARIMA模型的提升率 54.07 22.36 78.48
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表 7 各模型长期（1年）预测精度对比
Table 7. Comparison of long-term (one year) prediction accuracy of each model
预测模型 RMSE/TECU 低纬度 中纬度 高纬度 Klobuchar 103.53 98.23 67.95 ARIMA 10.52 6.67 4.33 GA-BP 5.73 3.75 2.23
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表 8 GA-BP模型长期（1年）预测精度提升率
Table 8. Improvement rate of long-term (one year) prediction accuracy of GA-BP model
% 类型 RMSE提升率 低纬度 中纬度 高纬度 相对Klobuchar模型的提升率 94.47 96.18 96.72 相对ARIMA模型的提升率 45.53 43.78 48.50
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