大椭圆航线设计的空间矢量方法

doi:10.11947/j.AGCS.2015.20130799

测绘学报 ›› 2015, Vol. 44 ›› Issue (7): 741-746.doi: 10.11947/j.AGCS.2015.20130799

大椭圆航线设计的空间矢量方法

刘文超, 卞鸿巍, 王荣颖, 温朝江

海军工程大学导航工程系, 湖北武汉 430033

收稿日期:2014-01-21 修回日期:2014-10-29 发布日期:2015-07-28
作者简介:刘文超(1988-),男,博士生,研究方向为舰船导航技术。E-mail:wenchao19880102@126.com
基金资助:
国家自然科学基金(41406212;41201478);航空科学基金(20120816001)

Great Ellipse Route Planning Based on Space Vector

LIU Wenchao, BIAN Hongwei, WANG Rongying, WEN Chaojiang

Department of Navigation Engineering, Naval University of Engineering, Wuhan 430033, China

Received:2014-01-21 Revised:2014-10-29 Published:2015-07-28
Supported by:
The National Natural Science Foundation of China (Nos.41406212;41201478);Aerospace Science Foundation of China (No.20120816001)

摘要/Abstract

摘要： 针对传统大圆航线设计采用的球体模型和现代导航设备采用的椭球体模型不统一引起航行误差的问题,研究了基于空间矢量的大椭圆航线设计方法。通过采用空间矢量代数方法直接求解大椭圆顶点,并提出依据长轴矢量和短轴矢量的大椭圆描述方法,应用两个基本矢量推导大椭圆航线方位和航程计算公式,进而研究了大椭圆航线设计算法,重点提出了基于Newton-Raphson(N-R)的等距离航线设计算法。对比算例表明,大圆航线与大椭圆航线设计结果差异明显,大椭圆航线设计算法与航行阶段采用的地球模型一致,可消除大圆航线设计引起的误差,提高航海计算精度。

关键词: 大圆航线, 大椭圆航线, 航线设计, 空间矢量, Newton-Raphson法

Abstract: Aiming at the problem of navigation error caused by unified earth model in great circle route planning using sphere model and modern navigation equipment using ellipsoid mode, a method of great ellipse route planning based on space vector is studied. By using space vector algebra method, the vertex of great ellipse is solved directly, and description of great ellipse based on major-axis vector and minor-axis vector is presented. Then calculation formulas of great ellipse azimuth and distance are deduced using two basic vectors. Finally, algorithms of great ellipse route planning are studied, especially equal distance route planning algorithm based on Newton-Raphson(N-R) method. Comparative examples show that the difference of route planning between great circle and great ellipse is significant, using algorithms of great ellipse route planning can eliminate the navigation error caused by the great circle route planning, and effectively improve the accuracy of navigation calculation.

Key words: great circle, great ellipse, route planning, space vector, Newton-Raphson method

中图分类号:

P228

刘文超, 卞鸿巍, 王荣颖, 温朝江. 大椭圆航线设计的空间矢量方法[J]. 测绘学报, 2015, 44(7): 741-746.

LIU Wenchao, BIAN Hongwei, WANG Rongying, WEN Chaojiang. Great Ellipse Route Planning Based on Space Vector[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(7): 741-746.

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大椭圆航线设计的空间矢量方法

Great Ellipse Route Planning Based on Space Vector

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