正交三角函数导出的最小GDOP定位构型解集  

Positioning Configurations with Minimum GDOP from Orthogonal Trigonometric Functions

作　　者：薛树强[1,2] 杨元喜[3,4] 陈武[5] 党亚民[2] 

机构地区：[1]长安大学地测学院,陕西西安710054 [2]中国测绘科学研究院,北京100830 [3]地理信息工程国家重点实验室,陕西西安710054 [4]西安测绘研究所,陕西西安710054 [5]香港理工大学

出　　处：《武汉大学学报（信息科学版）》2014年第7期820-825,共6页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金资助项目(41020144004;41104018);国家科技支撑计划资助项目(2012BAB16B01);国家863计划资助项目(2009AA121405;2013AA122501);北斗全球连续监测评估系统资助项目(GFZX0301040309)~~

摘　　要：由正交三角函数导出了一类最小GDOP测距单点定位构型集。导出了测距单点定位构型的GDOP极小值条件,并由此引入了最小GDOP测距单点定位构型解集的概念,揭示了最小GDOP测距单点定位构型的性质——旋转不变性和叠加不变性。对于任意给定的控制点数目n,由正交三角函数导出了最小GDOP构型的正多边形解。最后在最小GDOP二维测距单点定位构型的基础上,导出了三种三维最小GDOP测距单点定位构型:圆锥构型(锥角108.48°)、笛卡尔构型、Walker构型(轨道倾角54.74°),这些构型的几何条件为讨论GNSS星座设计提供了参考。In this paper,single-point-positioning configurations with minimum GDOP employing orthogonal trigonometric functions are presented.The preconditions for minimizing the GDOP are introduced,and the set composed of all configurations with minimal GDOP is defined.Some properties of the minimum GDOP configurations,including the invariance of rotation and superposition,are detailed.For arbitrary given number n of control points,regular polygon solutions are immediately deduced from the orthogonal trigonometric functions.Based on the two dimensional configurations with minimum GDOP,three kinds of three dimensional configurations with minimum GDOP,including the cone configuration with cone angle 108.48°,the Descartes configuration,and the Walker configuration with inclination angle 54.74°,are discussed.The geometrical conditions of these configurations provide us some knowledge for GNSS constellation design.

关 键 词：定位构型 GDOP 三角函数 圆锥构型 笛卡尔构型 Walker构型 

分 类 号：P221[天文地球—大地测量学与测量工程] P207[天文地球—测绘科学与技术]