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中文摘要：
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。
英文摘要：
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.
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