球坐标系在导航定位中的推广应用  

A generalized application of spherical coordinate in navigation and positioning

作　　者：刘倩[1] 滕吉红[1] 王习文 LIU Qian;TENG Jihong;WANG Xiwen(Department of Basic Course,Information Engineering University,Zhengzhou 450001,China)

机构地区：[1]信息工程大学基础部,河南郑州450001

出　　处：《高师理科学刊》2021年第1期52-55,共4页Journal of Science of Teachers＇College and University

基　　金：信息工程大学2020年教育教学研究自筹项目(JXYJ2020D013)。

摘　　要：在卫星导航系统定位问题的研究中,需要将目标的定位结果在某置信水平下进行精度分析,这就涉及到m维球体上的实m维向量的积分.为解决这类问题,从R^3中球坐标系入手,推广到R^m中的高维球坐标系,并从坐标变换的角度推导出了求此类积分的通用公式.When the problem of location in satellite navigation system is studied,it is needed to do precision analysis about the location result within a given confidence level,which is related to the m-dimension real vector calculus on m-sphere.To resolve this problem,the spherical coordinate in R^3 is introduced and generalized to the spherical coordinate in R^m.Furthermore,a general formula about this kind of integral is deduced from the point of view of coordinate transformation.

关 键 词：球坐标系 向量积分 坐标变换 高维 

分 类 号：O172[理学—数学] G642.0[理学—基础数学]