方向后交最佳点位研究

Research on Optimum Point Position of Direction Resection

文中推导出方向后交点位精度的显函数公式 ;用解析法导出对称交会时最佳交会角和最佳点位精度 ;用无约束最优化共轭梯度法 ,求出一般情况下方向后交最佳交会角和点位精度 ;对同一三角形三个内角分别作顶角进行后交定位的最佳精度作了比较 ,得出三角形内只有一个最佳点位的结论 ;最后提出一种选择近似最佳点位的方法。

In the paper,an explicit function formula of point position accuracy in direction resection is derived,the optimum intersection angle and point position accuracy in symmetrical intersection is also derived with analysis,and the optimum intersection angle and point position accuracy in direction resection under general condition is as well derived with unconfined optimization conjugate gradient method. What's more,a comparison is made to the optimum accuracy of resection position when three inside angles of the same triangle act as the vertex angle respectively,which gets to a conclusion that there is only one optimum point position in a triangle. In the end,a method of selecting quasi-optimal point position is put forward in the paper.