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摘要:
为评估现有全球导航卫星系统(GNSS)中广播电离层模型性能，利用国际GNSS服务(IGS)分析中心提供的事后全球电离层图(GIM)产品，对北斗系统、全球定位系统(GPS)、Galileo系统的广播电离层模型进行了电离层总电子含量(TEC)域及定位域的长期精度评估。发现在太阳活动爬坡过程中，北斗Klobuchar八参数模型（BDSK8）、GPS Klobuchar八参数模型(GPSK8)、北斗全球广播电离层模型(BDGIM)及NeQuickG 4种模型的精度均有一定程度的下降，在不同纬度带也表现出不同的特性。结果表明：BDGIM性能最优，在3个纬度带的误差均方根(RMS)均值分别上升至7.27、4.43、4.00 TECU，三维定位误差分别上升至6.62、2.81、3.51 m；BDSK8受太阳活动影响最大，RMS的放大系数可达4～5倍。利用Bagging回归树学习器对各广播电离层模型误差和空间物理参数进行了建模和预报，其中，BDGIM模型预测效果最优，3个纬度带的均方根误差(RMSE)分别为2.13、1.23、1.47 TECU，相对误差(RE)分别为18%、15%、14%；NeQuickG模型次之，RMSE分别为4.60、2.27、1.47 TECU，RE分别为17%、18%、21%；2种Klobuchar模型精度的预报效果不佳。
Abstract:To evaluate the performance of broadcast ionospheric models in existing global navigation satellite systems (GNSS), post-processed global ionospheric map (GIM) products provided by the International GNSS Service (IGS) Analysis Center are used. Long-term accuracy evaluations of ionospheric total electron content (TEC) and positioning domains are conducted for the BeiDou system, global positioning system (GPS), and Galileo broadcast ionospheric models. It is observed that during the solar activity ramp-up, the accuracy of all four models (BeiDou system Klobuchar 8-parameter model (BDSK8), GPS Klobuchar 8-parameter model (GPSK8), BeiDou global ionospheric model (BDGIM), NeQuickG) declines to varying extents, with distinct characteristics observed in different latitude bands. The results indicate that the BDGIM exhibits the best performance, with root mean square (RMS) increasing to 7.27, 4.43, and 4.00 TECU in the three latitude bands, and three-dimensional positioning errors increasing to 6.62, 2.81, and 3.51 meters, respectively. The BDSK8 is most influenced by solar activity, with an RMS amplification factor reaching up to 4 to 5 times. Finally, a Bagging regression tree learner is used to model and predict errors in various broadcast ionospheric models based on space physics parameters. The BDGIM model demonstrates the best predictive performance, with root mean square errors (RMSE) of 2.13, 1.23, and 1.47 TECU for the three latitude bands, and relative errors (RE) of 18%, 15%, and 14%, respectively. The NeQuickG model ranks second, with RMSE values of 4.60, 2.27, and 1.47 TECU, and RE of 17%, 18%, and 21%, respectively. The predictive accuracy of the two Klobuchar models is unsatisfactory.
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图 2 BDSK8、GPSK8、BDGIM、NeQuickG低纬度区域VTEC RMS时间序列
Figure 2. VTEC RMS time series in low-latitude region for BDSK8, GPSK8, BDGIM, and NeQuickG
图 3 BDSK8、GPSK8、BDGIM、NeQuickG中纬度区域VTEC RMS时间序列
Figure 3. VTEC RMS time series in mid-latitude region for BDSK8, GPSK8, BDGIM, and NeQuickG
图 4 BDSK8、GPSK8、BDGIM、NeQuickG高纬度区域VTEC RMS时间序列
Figure 4. VTEC RMS time series in high-latitude region for BDSK8, GPSK8, BDGIM, and NeQuickG
图 6 低纬度带平静日与活动日BDSK8、GPSK8、BDGIM、NeQuickG、IF三维定位精度
Figure 6. Three-dimensional positioning accuracy on quiet and active days in low-latitude zone for BDSK8, GPSK8, BDGIM, NeQuickG, and IF
图 7 中纬度带平静日与活动日BDSK8、GPSK8、BDGIM、NeQuickG、IF三维定位精度
Figure 7. Three-dimensional positioning accuracy on quiet and active days in mid-latitude zone for BDSK8, GPSK8, BDGIM, NeQuickG, and IF
图 8 高纬度带平静日与活动日BDSK8、GPSK8、BDGIM、NeQuickG、IF三维定位精度
Figure 8. Three-dimensional positioning accuracy on quiet and active days in high-latitude zone for BDSK8, GPSK8, BDGIM, NeQuickG, and IF
表 1 Bagging回归树对各广播电离层模型预报误差
Table 1. Forecast errors of Bagging regression tree for various broadcast ionospheric models
模型 纬度 RMSE RE/% BDSK8 低 5.20 36 中 1.43 15 高 3.23 26 GPSK8 低 6.20 46 中 3.90 31 高 5.30 42 NeQuickG 低 4.60 17 中 2.27 18 高 1.47 21 BDGIM 低 2.13 18 中 1.23 15 高 1.47 14 
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