基于Swarm卫星数据与三维勒让德多项式的中国区域地磁场模型

doi:10.11947/j.AGCS.2025.20240379

摘要/Abstract

摘要：

区域地磁场模型可以描述地磁场的细节信息，在精准导航、目标探测等领域具有重要的应用价值。为了建立高精度中国区域地磁场模型，本文结合Swarm卫星数据，对三维勒让德多项式模型进行了研究，提出了基于奇异值分解的改进求解方法，提高了模型在高阶数时的求解精度，同时，采用K折交叉验证的方式，确定了勒让德多项式模型各地磁分量的最佳截止阶数。通过与泰勒多项式模型、拉盖尔多项式模型、切比雪夫多项式模型的对比试验，验证了勒让德多项式模型在模型截止阶数、计算速度、建模精度和边界效应等方面的优势，其各分量的整体拟合误差最低可以达到0.055 nT，模型边界误差可以达到0.074 nT。通过与其他区域地磁场模型和WMM2020模型计算结果的对比分析，进一步验证了本文方法的有效性和区域地磁场模型的精度优势。

关键词: 区域地磁场模型, 勒让德多项式, 奇异值分解, K折交叉验证, Swarm卫星, WMM2020

Abstract:

Regional geomagnetic field models can provide detailed information about the geomagnetic field, with significant applications in precise navigation and target detection. To establish a high-precision regional geomagnetic field model for China, this study integrates Swarm satellite data to investigate the 3D Legendre polynomial model and proposes an enhanced solution method based on singular value decomposition to improve accuracy at higher degrees. Concurrently, the optimal truncation degree of the Legendre polynomial model for each geomagnetic component is determined using K-fold cross-validation. Comparative experiments with Taylor polynomial models, Laguerre polynomial models, and Chebyshev polynomial models validate the advantages of the Legendre polynomial model in terms of truncation degree, computational speed, modeling accuracy, and boundary effects; with overall fitting errors for each component as low as 0.055 nT and boundary errors reaching a minimum of 0.074 nT. Further comparisons with other regional geomagnetic field models and WMM2020 calculation results confirm both the effectiveness and precision advantages of the proposed method along with its corresponding regional geomagnetic field model.

Key words: regional geomagnetic field model, Legendre polynomials, singular value decomposition, K-fold cross-validation, Swarm satellite, WMM2020

中图分类号:

P318

朱博, 李厚朴, 朱立波, 边少锋, 陈成. 基于Swarm卫星数据与三维勒让德多项式的中国区域地磁场模型[J]. 测绘学报, 2025, 54(3): 461-472.

Bo ZHU, Houpu LI, Libo ZHU, Shaofeng BIAN, Cheng CHEN. A regional geomagnetic field model for China based on Swarm satellite data and 3D Legendre polynomials[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(3): 461-472.

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多项式模型	地磁分量	最佳截止阶数	平均拟合误差/nT	平均预测误差/nT
泰勒	总强度F	4	41.515	41.597
	X分量	4	23.980	24.010
	Y分量	4	30.560	30.609
	Z分量	4	41.346	41.407
拉盖尔	总强度F	17	0.379	0.384
	X分量	15	0.603	0.611
	Y分量	15	0.942	0.954
	Z分量	15	2.978	2.989
切比雪夫	总强度F	22	0.112	0.117
	X分量	18	0.304	0.313
	Y分量	17	0.561	0.575
	Z分量	13	2.946	2.963
勒让德	总强度F	26	0.052	0.073
	X分量	23	0.209	0.233
	Y分量	23	0.451	0.489
	Z分量	15	2.929	2.961

模型	总场强F	X分量	Y分量	Z分量
泰勒多项式模型	41.525	23.989	30.562	41.392
拉盖尔多项式模型	0.321	0.743	0.868	3.023
切比雪夫多项式模型	0.111	0.289	0.555	2.946
勒让德多项式模型	0.055	0.207	0.452	2.934

多项式模型	总场强F	X分量	Y分量	Z分量
泰勒	113.885	50.643	41.073	97.788
拉盖尔	0.331	1.208	1.143	2.857
切比雪夫	0.213	0.228	0.386	0.480
勒让德	0.074	0.131	0.360	0.377

模型	总场强F	X分量	Y分量	Z分量
文献[30]泰勒多项式模型	20.28	22.38	14.52	32.06
文献[31]泰勒多项式模型	54.1	19.1	48.8	67.9
本文泰勒多项式模型	41.525	23.989	30.562	41.392
本文勒让德多项式模型	0.055	0.207	0.452	2.934
WMM2020	46.581	161.924	45.932	133.256