基于四元数的椭球面距离计算方法  

A quaternion based calculation method of ellipsoid distance

作　　者：兰田 张春玲 胡松[1] LAN Tian;ZHANG Chunling;HU Song(College of Marine Science,Shanghai Ocean University,Shanghai 201306,China)

机构地区：[1]上海海洋大学海洋科学学院,上海201306

出　　处：《海洋测绘》2022年第5期78-82,共5页Hydrographic Surveying and Charting

基　　金：国家自然科学基金联合基金(U1811464);国家重点研发计划子课题(2021YFC3101702)。

摘　　要：针对现有椭球面上两点距离公式使用范围有限,以及测算方法抽象冗杂、计算效率低等问题,基于四元数可以描述多个定位姿态的性质,提出了一种具有普适性,且可以有效减少积分误差,提高测算精度和效率的方法。针对不同的地理位置,采用不同的椭球模型,以获取更接近真实地理位置的坐标数据。结果表明,四元数可以将位置的移动和转动融为一体,通过相对位置的选择角度,方便地表达两点间的弧长距离。并且由四元数确定的椭球上两点间极坐标距离公式,可以在保持高计算效率的同时,有效提高计算精度。At present, the commonly used calculation formula of ellipsoid distance is abstract and complicated.Based on the property that quaternions can describe multiple rotation attitude, this paper proposes a universal method that can effectively improve the calculation accuracy and efficiency.Different ellipsoid models are used for different geographic locations to obtain the coordinates data that are closer to the real ocean location.The results show that quaternions can integrate position movement and rotation, and express the arc distance between two points conveniently by selecting angle of relative position.The distance formula of polar coordinates between two points on the ellipsoid determined by quaternion can not only maintain the calculation efficiency, but also effectively improve the calculation accuracy.

关 键 词：海洋定位 大地线长计算 椭圆积分 四元数运算 积分算法 

分 类 号：P226[天文地球—大地测量学与测量工程]