三维坐标转换参数求解的一种直接搜索法
A Kind of Direct Search Method Adapted to Solution of 3D Coordinate Transformation Parameters
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摘要: 采取了两步措施简化三维坐标转换非线性模型:①旋转矩阵的3个旋转角用一个反对称矩阵的3个独立元素代替,将旋转矩阵由反对称矩阵构成Lodrigues矩阵;②将坐标转换7参数模型变换成基线向量模型,消去平移3参数。然后,采用遗传算法与模式搜索法相结合的一种直接搜索法求解参数。算例表明,该算法是可行的。最后,从坐标转换精度的角度对基线向量模型原点与公共点的选取进行了分析,结论是原点选取的点的精度相对较高时坐标转换精度相对较高,公共点的选取以3~5个精度高的点为宜。Abstract: In view of 3D coordinate transformation nonlinear model,in order to adapt direct search method to solve the transformation parameters,it is necessary to make the model simple and operand small by way of two step measurements as follows.One is to transform the 7 parameters model to 4 parameters model by eliminating translation 3 parameters;the other is to replace 3 rotation angles of rotation matrix with antisymmetric matrix 3 independent elements.A kind of direct search method which integrates genetic algorithm and pattern search method is used to solve the transformation parameters;and it is suitable to rotation of random angle.The example indicates the algorithm is feasible.Lastly,for some factors effecting coordinate transformation precision,some conclusions are made by analysis,including the higher coordinate precision of original point of baseline vector model the better coordinate transformation precision and 3-5 common points are fit to solve the parameters.
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