positioning configurations with minimum gdop from orthogonaltri gonometric functions
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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Abstract: in this papersin gle －point －positioning confi gurations with minimum gdop emplo ying orthogonal tri gonometric functions are presented．the preconditions for minimizing the gdop are intro－ducedand the set composed of all confi gurations with minimal gdop is defined．some properties ofthe minimum gdop confi gurationsincluding the invariance of rotation and super position are de－tailed．for arbitrar y given number n of control pointsre gular pol ygon solutions are immediately deduced from the orthogonal tri gonometric functions．based on the two dimensional confi gurations with minimum gdopthree kinds of three dimensional confi gurations with minimum gdopincluding the cone confi guration with cone angle 108．48°the descartes confi gurationand the walker confi gurationwith inclination angle 54．74°are discussed．the geometrical conditions of these confi gurations provide us some knowledge for gnss constellation design
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