基于ico_HEALPix网格的超高阶地球重力场建模方法

doi:10.11947/j.AGCS.2024.20230151

测绘学报 ›› 2024, Vol. 53 ›› Issue (8): 1531-1539.doi: 10.11947/j.AGCS.2024.20230151

基于ico_HEALPix网格的超高阶地球重力场建模方法

张展鹏¹(), 李新星¹^,²^,³(), 刘长建¹, 范昊鹏¹, 裴宪勇¹

^1.信息工程大学地理空间信息学院，河南　郑州　450001
^2.地理信息工程国家重点实验室，陕西　西安　710054
^3.智慧地球重点实验室，北京　100020

收稿日期:2023-05-15 发布日期:2024-09-25
通讯作者: 李新星 E-mail:zhanpeng1109@163.com;zhanpeng1109@163.com;minibad@126.com
作者简介:张展鹏（2000—），男，硕士生，研究方向为测量数据处理理论与方法。E-mail：zhanpeng1109@163.com
基金资助:
国家自然科学基金(U23A2028);地理信息工程国家重点实验室基金(SKLGIE2023-Z-1-1)

Ultra-high-order Earth gravity field modeling method based on ico_HEALPix grid

Zhanpeng ZHANG¹(), Xinxing LI¹^,²^,³(), Changjian LIU¹, Haopeng FAN¹, Xianyong PEI¹

^1.Institute of Surveying and Mapping, Information Engineering University, Zhengzhou 450001, China
^2.State Key Laboratory of Geographic Information Engineering, Xi'an 710054, China
^3.Key Laboratory of Smart Earth, Beijing 100020, China

Received:2023-05-15 Published:2024-09-25
Contact: Xinxing LI E-mail:zhanpeng1109@163.com;zhanpeng1109@163.com;minibad@126.com
About author:ZHANG Zhanpeng (2000—), male, postgraduate, majors in measulement data processing theory and method. E-mail: zhanpeng1109@163.com
Supported by:
The National Natural Science Foundation of China(U23A2028);The State Key Laboratory of Geo-Information Engineering(SKLGIE2023-Z-1-1)

摘要/Abstract

摘要：

本文针对传统地理网格数据剖分的重力场模型构建在高纬度区域出现数据冗余的问题，将分层等积等纬度像素化（HEALPix）网格结构引入地球重力场解算中，提出了利用二十面体HEALPix（ico_HEALPix）网格的超高阶地球重力场建模方法，实现了全球3600阶次球谐位系数的高效构建，同时针对ico_HEALPix网格在球谐分析过程中法矩阵不是严格块对角化结构的问题，设计了迭代算法，有效提高模型构建的精度。试验表明，ico_HEALPix网格数据在数据量小于地理网格500万的前提下，通过迭代方法构建的全球地球重力场模型精度可达到优于地理网格的效果，球谐位系数误差阶RMS提升1~2个数量级，还解决了地理网格南北极点畸变和数据冗余的问题，提高了网格的数据利用率。

关键词: HEALPix网格, ico_HEALPix网格, 超高阶地球重力场模型, 迭代算法, 最小二乘法, XGM2019e

Abstract:

Aiming at the problem of data redundancy in the high latitude region in the construction of gravity field model based on traditional geographic grid data subdivision, this paper introduces the hierarchical equal area isolatitude pixelation (HEALPix) grid structure into the calculation of the Earth's gravity field for the first time, and proposes the construction theory of ultra-high-degree Earth's gravity field model using icosahedral HEALPix (ico_HEALPix) grid. The efficient construction of the global 3600-degree spherical harmonic coefficient is realized, which solves the problems of uneven distribution of traditional geographic grid points and redundancy of high-latitude data. At the same time, the normal matrix of the ico_HEALPix grid is not a strict block diagonalization structure in the process of spherical harmonic analysis. An iterative algorithm is designed to effectively improve the accuracy of model construction. Experiments show that the accuracy of the global Earth gravity field model constructed by the iterative method can be better than that of the geographic grid under the premise that the data volume of the ico_HEALPix grid data is less than about 5 million of the geographic grid, and the error order RMS of spherical harmonic coefficient is increased by 1~2 orders of magnitude. It also solves the problems of north and south pole distortion and data redundancy of the geographic grid, and improves the data utilization of the grid.

Key words: HEALPix grid, ico_HEALPix grid, ultra-high-degree Earth gravity field model, iterative algorithm, least squares method, XGM2019e

中图分类号:

P223

张展鹏, 李新星, 刘长建, 范昊鹏, 裴宪勇. 基于ico_HEALPix网格的超高阶地球重力场建模方法[J]. 测绘学报, 2024, 53(8): 1531-1539.

Zhanpeng ZHANG, Xinxing LI, Changjian LIU, Haopeng FAN, Xianyong PEI. Ultra-high-order Earth gravity field modeling method based on ico_HEALPix grid[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(8): 1531-1539.

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基于ico_HEALPix网格的超高阶地球重力场建模方法

Ultra-high-order Earth gravity field modeling method based on ico_HEALPix grid

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