顾及病态的融合解算坐标转换模型研究

Research on Coordinate Transformation Model of Fusion Solution Taking Into Account Ill-condition

针对传统Bursa坐标转换模型存在法方程矩阵病态与不适用于大旋转角的问题,基于坐标中心化与罗德里格矩阵融合模型,探讨各种类型旋转角对坐标转换精度的影响。通过坐标重心化减小了参与计算的坐标数值,弱化数值之间的复共线性,分两步解算旋转参数、尺度因子与平移参数,通过正则化解算平移参数,弱化旋转参数与平移参数的复共线性,利用罗德里格矩阵求解旋转参数。结合算例分析,验证了该融合算法的可行性与适用性。

Aiming at the problem that the traditional Bursa coordinate conversion model has the normal equation matrix ill-conditioned and which is not suitable for large rotation angles,based on the coordinate centering and Rodrigue matrix fusion model,the influence of various types of rotation angles on the coordinate conversion accuracy is discussed.The coordinate value involved in the calculation is reduced by the coordinate centroidization,the complex collinearity between the values is weakened,the rotation parameter,the scale factor and the translation parameter are solved in two steps,and the translation parameter is solved by regularization,which weakens the rotation parameter and the translation parameter,complex collinearity,using Rodrigues matrix to solve the rotation parameters.Combined with the analysis of the calculation examples,the feasibility and applicability of the fusion algorithm are verified.