Exact and heuristic formulae to compute the geodetic height from the ellipse equation

IF 2.8 4区地球科学 Q2 GEOCHEMISTRY & GEOPHYSICS

Geodesy and Geodynamics Pub Date : 2023-10-01 DOI:10.1016/j.geog.2023.05.007

Mohamed Eleiche, Ahmed Mansi

引用次数: 0

Abstract

The conversion of the cartesian coordinates of a point to its geodetic equivalent coordinates in reference to the geodetic ellipsoid is one of the main challenges in geodesy. The ellipse equation in the meridian plane significantly influences the value of the geodetic coordinates. This research analyzes this influence and how it can contribute to their solutions. The study investigates the mathematical relation between them and presents an exact formula relating to the geodetic height and the ellipse equation. In addition, a heuristic formula for the relation between the geodetic height and the ellipse equation is proposed, which is independent of the geodetic latitude and has a relative accuracy better than 99.9 %. The calculation is stable, and the cost is low.

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从椭圆方程计算大地高度的精确启发式公式

将点的笛卡儿坐标转换成参照大地椭球体的大地等效坐标是大地测量学中的主要挑战之一。子午线平面上的椭圆方程对大地坐标系的取值有重要影响。本研究分析了这种影响以及它如何有助于他们的解决方案。研究了它们之间的数学关系，提出了大地高度与椭圆方程的精确关系式。此外，还提出了一种不受大地纬度影响的大地高度与椭圆方程关系的启发式公式，其相对精度优于99.9%。计算稳定，成本低。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Geodesy and Geodynamics GEOCHEMISTRY & GEOPHYSICS-

CiteScore

4.40

自引率

4.20%

发文量

566

审稿时长

69 days

期刊介绍： Geodesy and Geodynamics launched in October, 2010, and is a bimonthly publication. It is sponsored jointly by Institute of Seismology, China Earthquake Administration, Science Press, and another six agencies. It is an international journal with a Chinese heart. Geodesy and Geodynamics is committed to the publication of quality scientific papers in English in the fields of geodesy and geodynamics from authors around the world. Its aim is to promote a combination between Geodesy and Geodynamics, deepen the application of Geodesy in the field of Geoscience and quicken worldwide fellows'' understanding on scientific research activity in China. It mainly publishes newest research achievements in the field of Geodesy, Geodynamics, Science of Disaster and so on. Aims and Scope: new theories and methods of geodesy; new results of monitoring and studying crustal movement and deformation by using geodetic theories and methods; new ways and achievements in earthquake-prediction investigation by using geodetic theories and methods; new results of crustal movement and deformation studies by using other geologic, hydrological, and geophysical theories and methods; new results of satellite gravity measurements; new development and results of space-to-ground observation technology.