引力不变量曲线坐标系及在定位导航上的应用

doi:10.11947/j.AGCS.2021.20200216

测绘学报 ›› 2021, Vol. 50 ›› Issue (2): 153-159.doi: 10.11947/j.AGCS.2021.20200216

引力不变量曲线坐标系及在定位导航上的应用

于锦海^1,2, 徐焕^1,2, 万晓云³

1. 中国科学院计算地球动力学重点实验室, 北京 100049;
2. 中国科学院大学地球与行星科学学院, 北京 100049;
3. 中国地质大学(北京)土地科学与技术学院, 北京 100083

收稿日期:2020-06-02 修回日期:2020-10-20 发布日期:2021-03-03
作者简介:于锦海(1961-),男,博士,教授,主要从事物理大地测量研究。E-mail:yujinhai@ucas.edu.cn
基金资助:
国家重点研究计划（2016YFB0501702）；国家自然科学基金（41774089）

Curvilinear coordinates from the gravitational field and the related application in orientation and navigation

YU Jinhai^1,2, XU Huan^1,2, WAN Xiaoyun³

1. Key Laboratory of Computational Geodynamics, Chinese Academy of Sciences, Beijing 100049, China;
2. College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
3. School of Land Science and Technology, China University of Geosciences(Beijing), Beijing 100083, China

Received:2020-06-02 Revised:2020-10-20 Published:2021-03-03
Supported by:
The National Key Research and Development Program of China (No. 2016YFB0501702);The National Natual Science Foundation of China (No. 41774089)

摘要/Abstract

摘要： 本文基于引力与引力梯度不变量引入了3个仅是点位的独立函数，从而构成了空间的曲线坐标系。在此基础上，讨论了引入的不变量坐标系在定位导航方面的潜在应用。事实上，利用观测所得的引力与引力梯度不变量，可直接构建关于观测点的方程组。由于该方程组是非线性的，所以求解过程中必须进行线性化处理以及迭代计算。为了展示如何使用该曲线坐标系进行定位导航计算，本文借助于EGM2008模型进行了仿真计算。结果表明，本文提出的算法稳定，能较好地对点位坐标进行恢复。

关键词: 曲线坐标系, 引力场不变量, 线性化, 定位与导航

Abstract: Three independent functions are introduced from the gravimetry and gradiometry, so a curvilinear system of coordinates from the gravitational field can be constructed. Then potential applications of the coordinates in orientation or navigation are discussed. To realize orientation or navigation for some object, the observation equations are established by using the gravimetry and gradiometry, and the coordinates of the object can be solved from the equations. Since the observation equations are nonlinear, the linearization for them and the iterative arithmetic are required. To examine the accuracies of the orientation or navigation by using the curvilinear coordinates proposed in the paper, some arithmetic examples are given with the help of EGM2008 gravity field model, and the computational results illustrate that the proposed method is feasible.

Key words: curvilinear coordinates, invariants of gravitational field, linearization, positioning and navigation

中图分类号:

P228

于锦海, 徐焕, 万晓云. 引力不变量曲线坐标系及在定位导航上的应用[J]. 测绘学报, 2021, 50(2): 153-159.

YU Jinhai, XU Huan, WAN Xiaoyun. Curvilinear coordinates from the gravitational field and the related application in orientation and navigation[J]. Acta Geodaetica et Cartographica Sinica, 2021, 50(2): 153-159.

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引力不变量曲线坐标系及在定位导航上的应用

Curvilinear coordinates from the gravitational field and the related application in orientation and navigation

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