基于地球物理因素与多模型融合的GNSS高程时间序列预测方法

doi:10.11947/j.AGCS.2025.20250257

摘要/Abstract

摘要：

针对当前只考虑时间因素或固定地球物理因素进行GNSS高程时序预测时存在的不足，本文顾及多种地球物理因素，提出多模型融合（BO-BiLSTM-A-Bootstrap）的GNSS高程时序预测模型及结果不确定分析方法。针对GNSS高程变化影响因素空间差异显著的特点，提出物理因素优选策略。利用贝叶斯优化算法（BO）优化双向长短期记忆网络-注意力机制（BO-BiLSTM-A）参数并进行GNSS高程预测，同时基于Bootstrap算法估计预测结果的置信区间，进而分析预测结果的不确定性。从全球4个区域选择56个GNSS站数据验证了本文方法的有效性。试验结果表明，不同区域的GNSS高程变化影响因素差异明显，基于地球物理因素优选策略建立的GNSS高程预测方法比采用固定影响因素和仅考虑时间因素方法具有更好的预测精度和普适性；本文方法对全球56个测站预测结果的RMSE和MAE分别为4.60和3.62 mm，相比自适应提升、极端梯度提升、门控循环单元、长短期记忆网络模型分别提高3.6%~25.8%和4.2%~ 29.7%，精度指标分布更为集中，并且本文方法在不同月份的预测平均精度总体上优于其他方法，结果更加稳定；在95%置信水平下，本文方法预测结果的平均覆盖宽度的标准为25.95，平均连续排名概率得分为2.67，总体上优于其他模型，表明本文方法预测结果具有较好的精度及可靠性。

关键词: GNSS高程时间序列, 多模型融合, 地球物理因素, 预测方法

Abstract:

In response to the shortcomings of current GNSS elevation time series prediction that only considers time factors or fixed geophysical factors, this paper proposes a new GNSS elevation time series prediction model and result uncertainty analysis method based on multi-model fusion (BO-BiLSTM-A-Bootstrap) considering multiple geophysical factors. A physical factor optimization strategy is proposed to address the significant spatial differences in factors affecting GNSS elevation changes. Using Bayesian optimization algorithm (BO) to optimize the parameters of bidirectional long short-term memory network attention mechanism (BO-BiLSTM-A) and perform GNSS elevation prediction, while estimating the confidence interval of the prediction results based on Bootstrap algorithm, and then analyzing the uncertainty of the prediction results. Validate the effectiveness of the new method using data from 56 GNSS stations selected from 4 global regions. The experimental results show that there are significant differences in the influencing factors of GNSS elevation changes in different regions. The GNSS elevation prediction method based on physical factor optimization strategy has better prediction accuracy and universality than the methods using fixed influencing factors and only considering time factors. The RMSE and MAE of the new model for predicting 56 stations worldwide are 4.60 and 3.62 mm, respectively. Compared with adaptive boosting, extreme gradient boosting, gated recurrent unit, and long short-term memory models, the RMSE and MAE of the new model are improved by 3.6% to 25.8% and 4.2% to 29.7%, respectively. The accuracy index distribution is more concentrated, and the average prediction accuracy of the new method in different months is generally better than other methods, resulting in more stable results. At a 95% confidence level, the standard for the average coverage width of the new method's predicted results is 25.95, and the average continuous ranking probability score is 2.67, which is generally better than other models, indicating that the new method's predicted results have good accuracy and reliability.

Key words: GNSS elevation time series, multi-model fusion, geophysical factors, prediction method

中图分类号:

P228

罗亦泳, 占奥文, 冯小欢, 鲁铁定. 基于地球物理因素与多模型融合的GNSS高程时间序列预测方法[J]. 测绘学报, 2025, 54(10): 1769-1785.

Yiyong LUO, Aowen ZHAN, Xiaohuan FENG, Tieding LU. A GNSS elevation time series prediction method based on geophysical factors and multi-model fusion[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(10): 1769-1785.

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测站	隐藏层神经元	训练次数	批数量	学习率
P043	93	85	125	0.006 53
HOLM	83	104	16	0.000 1
NNOR	112	124	110	0.009 59
SCOR	71	89	34	0.000 1

测站	方法	RMSE	MAE
P043	时间变量建模	5.8	4.82
	部分物理因素建模	4.93	4.14
	多物理因素特征筛选建模	3.63	2.89
NNOR	时间变量建模	4.87	4.81
	部分物理因素建模	3.87	3.12
	多物理因素特征筛选建模	3.6	2.88
HOLM	时间变量建模	6.67	5.33
	部分物理因素建模	6.33	5.22
	多物理因素特征筛选建模	5.7	4.8
SCOR	时间变量建模	6.35	5.38
	部分物理因素建模	5.69	4.75
	多物理因素特征筛选建模	4.5	3.63

评估指标	数据增强前/mm	数据增强后/mm	ARI/（%）
RMSE	4.822	4.614	4.3
MAE	3.821	3.637	4.8

区域	方法	RMSE	MAE
美国	AdaBoost	5.90	4.9
	XGBoost	5.60	4.63
	GRU	4.71	3.74
	LSTM	4.66	3.69
	本文方法	4.44	3.51
澳大利亚	AdaBoost	4.51	3.61
	XGBoost	4.4	3.50
	GRU	4.47	3.55
	LSTM	4.63	3.69
	本文方法	4.28	3.36
加拿大	AdaBoost	6.74	5.57
	XGBoost	6.67	5.58
	GRU	5.12	4.02
	LSTM	5.01	3.91
	本文方法	4.76	3.66
格陵兰岛	AdaBoost	10.64	9.56
	XGBoost	10.67	9.56
	GRU	5.16	4.26
	LSTM	4.82	3.95
	本文方法	4.61	3.67

测站	方法	RMSE	MAE
NLIB	AdaBoost	8.1	6.52
	XGBoost	8.28	6.56
	GRU	8.48	6.73
	LSTM	8.06	6.49
	本文方法	7.60	6.10
CHWK	AdaBoost	6.8	5.62
	XGBoost	6.8	5.61
	GRU	7.32	6.04
	LSTM	7.25	5.98
	本文方法	6.44	5.15
INVK	AdaBoost	9.61	7.69
	XGBoost	8.73	6.87
	GRU	8.91	6.23
	LSTM	8.67	6.24
	本文方法	8.32	6.17
VNDP	AdaBoost	6.84	4.96
	XGBoost	6.73	4.86
	GRU	6.72	4.85
	LSTM	6.95	5.15
	本文方法	6.56	4.85
PICL	AdaBoost	8.71	6.7
	XGBoost	7.19	5.3
	GRU	7.11	5.24
	LSTM	7.77	5.95
	本文方法	6.97	5.16