大角度三维基准转换的解析封闭解

传统大地测量应用中的基准转换往往涉及小角度旋转,可只考虑旋转角的一阶量采用线性化方法求解。现代空间测量技术成果应用的基准转换涉及大角度旋转,通过将旋转矩阵所有元素作为未知数并利用旋转矩阵正交条件采用附约束条件平差法迭代求解。本文以空间三维基准转换为例,采用多元模型的矩阵形式将多点坐标组成矩阵处理,并利用旋转矩阵的正交条件导出了大角度三维基准转换的解析分步解。同时引入两套公共点坐标误差对传统三维基准转换模型扩展,导出了同时顾及两套公共点坐标误差的大角度三维基准转换模型的解析解。试验表明:给出的大角度三维基准转换解析解能在实现与传统迭代解等效转换结果的同时,有效避免复杂耗时的迭代计算,提高计算效果。

Analytical Close-form Solutions for Three-dimensional Datum Transformation with Big Rotation Angles

The small rotation angles are typically involved in the traditional geodetic datum transformation,for which one can iteratively solve for its linearized model with ignoring its second-smaller terms.However,the big rotation angles are introduced to transform the outcomes from the advanced space surveying techniques.For this transformation model with big rotation angles,all elements of rotation matrix are usually parameterized as unknown parameters and then solved with the constrained adjustment theory by using the orthogonal condition of rotation matrix.With three-dimensional datum transformation with big rotation angles as example,this paper derives the analyticalclose-form solutions by formularizing the coordinates of multi-points as a matrix and using the orthogonal condition of rotation matrix.Expanding the transformation model with introducing the errors to common points of both datum,we derive out its analytical solutions as well.The results of simulation computations show that the presented three-dimensional datum transformation can realize the comparable transformation result while the new method can outcome the complicated and time-consuming iterations,therefore improving the computation efficiency.