最小GDOP定位构型的一种嵌套圆锥结构  

Nested Cones for Single-Point-Positioning Configuration with Minimal GDOP

作　　者：薛树强[1,2] 杨元喜 

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]地理空间信息工程国家重点实验室,陕西西安710054

出　　处：《武汉大学学报（信息科学版）》2014年第11期1369-1374,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;2013AA122501);国家863计划资助项目(2009AA121405);北斗全球连续监测评估系统资助项目(GFZX0301040309)~~

摘　　要：在圆锥构型的基础上,定义了一种嵌套圆锥构型,并导出了最小PDOP嵌套圆锥构型所应满足的条件。讨论了构造最小GDOP(几何精度衰减因子)构型的方法。在最小PDOP嵌套圆锥构型的基础上给出了最小GDOP嵌套圆锥构型。在此基础上,由最小GDOP嵌套圆锥构型导出了数学上仅有的5种正多面体构型,证明了5种正多面体均满足GDOP极值条件。Dilutions of precision （DOP） is a key criterion to measure the geometric strength of singlepoint-positioning configuration. Revealing the configuration set composed of configurations with minimal DOPs has practical significance in geodetic positioning design and application. A kind of nested cones composed of many single cones was provided and the precondition of minimizing the PDOP （position dilution of precision） was deduced based on the cone configuration. A general method of structuring configurations with minimal GDOP （geometric dilution of precision） is given. The nested cones with minimal GDOP structured by the nested cones with minimal PDOP are discussed. At last, five regular polyhedrons are deduced by the nested cones with minimal GDOP. It was shown that any regular polyhedron has minimal GDOP. Moreover, the configurations with minimal GDOP are more numerous than the known polyhedrons.

关 键 词：GNSS星座 定位构型 圆锥 测距方程 正多面体 最优构型 

分 类 号：P228[天文地球—大地测量学与测量工程]