A GNSS elevation time series prediction method based on geophysical factors and multi-model fusion

doi:10.11947/j.AGCS.2025.20250257

Abstract

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

CLC Number:

P228

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