小波分解与Prophet框架融合的电离层VTEC预报模型

doi:10.12305/j.issn.1001-506X.2021.03.03

摘要/Abstract

摘要：

在全球导航卫星系统(global navigation satellite system, GNSS)的应用中, 电离层垂直总电子含量(vertical total electron content, VTEC)是直接决定电离层延迟误差的重要参数。为提高其短期预报精度, 在综合考虑地磁扰动影响的基础上, 提出了小波分解与Prophet框架融合的时间序列预报模型, 并基于全球电离层模型(global ionosphere model, GIM)格网数据进行了对比实验。通过均方根误差、平均绝对误差、平均绝对百分比误差3项指标评估了预测结果, 并分析其预报残差。结果表明在不同条件(电离层平静期与活跃期)下, 该模型的预报精度均较高, 优于未改进的Prophet框架, 显著优于自回归移动平均(autoregressive integrated moving average, ARIMA)模型, 在中、高纬度地区有良好的适用性。

关键词: 电离层垂直总电子含量, 时间序列预测, 小波分解, Prophet框架, 地磁扰动

Abstract:

In the application of global navigation satellite system (GNSS), the ionosphere vertical total electron content (VTEC) is an important parameter that directly determines the ionosphere delay error. In order to improve its short-term prediction accuracy, a time series prediction model fused with the wavelet decomposition and Prophet framework is proposed on the basis of considering the influence of geomagnetic disturbance. The comparative experiments are carried out based on the global ionosphere model (GIM) grid data. The indicator of root mean square error, mean absolute error and mean absolute percentage error are used to evaluate the prediction results and analyze the prediction residual. The results show that under different conditions (ionosphere quiet period and active period), the prediction accuracy of the model is higher, which is better than the unimproved Prophet frame, significantly better than the autoregressive integrated moving average (ARIMA) model, and has good applicability in middle and high latitudes.

Key words: ionosphere vertical total electron content, time series prediction, wavelet decomposition, Prophet framework, geomagnetic disturbance

中图分类号:

P288

田睿, 董绪荣. 小波分解与Prophet框架融合的电离层VTEC预报模型[J]. 系统工程与电子技术, 2021, 43(3): 610-622.

Rui TIAN, Xurong DONG. Ionosphere VTEC prediction model fused with wavelet decomposition and Prophet framework[J]. Systems Engineering and Electronics, 2021, 43(3): 610-622.

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小波基函数	正交性	双正交性	对称性	消失距	支撑长度
Haar	是	是	对称	1	1
Daubechies (db N)	是	是	近似对称	N	2N-1
Symlets (sym N)	是	是	近似对称	N	2N-1
Coiffets (Coif N)	是	是	近似对称	2N	6N-1
meyer	是	是	对称	无	无限
morlet	否	否	对称	无	无限

实验区域	纬度范围	经度范围
低纬度地区	2.5°N~17.5°N	75°E~125°E
中纬度地区	32.5°N~47.5°N	75°E~125°E
高纬度地区	62.5°N~77.5°N	75°E~125°E

参数	说明	设置值
τ	通过changepoint_prior_scale属性进行设置	活跃期低纬度	高频:0.50 低频:0.35
		活跃期中纬度	高频:0.50 低频:0.30
		活跃期高纬度	高频:0.05 低频:0.05
		平静期低纬度	高频:0.50 低频:0.05
		平静期中纬度	高频:0.05 低频:0.05
		平静期高纬度	高频:0.05 低频:0.03
增长模型	Linear(即分段线性模型)	通过Growth属性进行设置
N	3	通过add_seasonality方法中的fourier_order进行设置
σ	10	通过Seasonality_prior_scale属性进行设置
υ	10	通过holidays_prior_scale属性进行设置
参数估计方法	MAP	默认设置, 无需改动

预报模型	预报天数	低纬度地区			中纬度地区			高纬度地区
预报模型	预报天数	RMSE/TECu	MAE/TECu	MAPE/%	RMSE/TECu	MAE/TECu	MAPE/%	RMSE/TECu	MAE/TECu	MAPE/%
本文改进	1	2.047	1.575	11.32	0.673	0.566	7.75	0.620	0.523	16.97
	2	1.827	1.489	10.73	0.858	0.745	11.05	0.685	0.593	20.43
	3	2.272	1.789	13.38	1.095	0.978	13.70	1.069	0.953	40.44
Prophet	1	2.065	1.624	12.50	0.732	0.624	8.72	0.665	0.568	18.45
	2	1.827	1.510	11.92	0.973	0.854	12.71	0.804	0.711	24.81
	3	2.437	1.980	15.83	1.255	1.147	16.11	1.267	1.143	48.38
ARIMA	1	3.459	2.878	25.14	1.915	1.569	18.96	1.111	0.886	25.84
	2	3.927	3.328	28.64	2.120	1.839	23.45	1.446	1.233	36.73
	3	4.657	3.842	35.04	2.142	1.828	24.02	1.619	1.470	56.17

预报模型	预报天数	低纬度地区			中纬度地区			高纬度地区
预报模型	预报天数	RMSE/TECu	MAE/TECu	MAPE/%	RMSE/TECu	MAE/TECu	MAPE/%	RMSE/TECu	MAE/TECu	MAPE/%
本文改进	1	2.306	1.831	11.01	1.169	0.977	10.01	0.663	0.539	10.80
	2	3.232	2.620	15.58	1.086	0.919	8.65	0.782	0.608	11.08
	3	2.581	2.152	13.70	1.386	1.078	9.70	0.916	0.806	13.18
Prophet	1	2.342	1.864	11.43	1.310	1.121	11.62	0.678	0.554	11.17
	2	3.277	2.649	15.72	1.305	1.156	11.01	0.796	0.623	11.51
	3	2.600	2.136	13.63	1.651	1.359	12.84	0.921	0.809	13.38
ARIMA	1	5.581	4.700	30.55	2.628	2.278	23.39	1.782	1.522	29.75
	2	5.980	4.906	36.12	2.824	2.484	24.48	2.115	1.845	34.53
	3	5.898	5.004	34.79	3.826	3.296	31.67	2.345	1.979	32.24