中文摘要：

几何精度衰减因子是衡量定位构型优劣的重要指标,因此研究最小几何精度衰减因子定位图形对提高导航定位精度具有重要作用。针对这一问题,该文主要介绍目前最小几何精度衰减因子定位图形的研究进展。首先由单点定位测距观测方程引入两类几何精度衰减因子的定义,并由此引出一类最小几何精度衰减因子的二维定位图形解;在最小几何精度衰减因子二维定位图形的基础上,分别介绍3种无约束条件下的三维最小几何精度衰减因子测距单点定位构型：圆锥构型、笛卡尔构型、Walker构型;在圆锥构型的基础上扩展一类嵌套圆锥构型,可解决约束条件下的最小几何精度衰减因子定位构型问题。研究表明,最小几何精度衰减因子定位图形解的几何结构异常丰富。

英文摘要：

Geometric dilutions of precision（GDOP）is a key criterion to measure the graphic intensity of single-point-positioning configurations,so revealing the geometry of configurations with minimal GDOP has practical significance.Firstly,the paper introduced the first-kind and second-kind GDOP,and then revealed a class of twodimensional geometric structure with the lowest GDOP.The classification of three-dimensional geometric structure with the lowest GDOP was proposed,such as cones,Descartes configuration and Walker configuration.At last,under the constraint conditions,a kind of the nested cones could solve the configuration with minimal GDOP.It showed that the solution of the geometry of configurations with minimal GDOP was very rich.