顾及协方差阵的三维基准非线性变换

A Weighted Non-linear 3-Dimensional Datum Transformation Algorithm

三维基准变换需要解算3个平移、1个尺度和3个旋转参数.顾及控制点坐标协方差阵时,根据最小二乘准则,导出了平移参数、尺度参数与旋转参数分别求解的计算公式和方法;通过引入重心坐标,将7个转换参数解算转化为先解算3个旋转参数,然后计算尺度与平移参数.采用单纯形法进行迭代计算旋转参数,避免了对目标函数进行复杂函数的求导运算,且对初始值依赖性小.最后通过实例验证了本文的方法.

3-Dimensional datum transformation needs a computation of the transformation parameters including three translations, one scale factor and three rotations. With a consideration of the eovariance matrices of transformed coordinates, this paper presents the method and formulae for separately computing rotation, scale and translation parameters based on the least squares criterion. With the introduction of the barycenter coordinates, the solutions of seven transformation parameters are converted to computing the rotation parameters, the scale parameter and the translation parameters sequentially. The rotation parameters are computed with simplex method, which can avoid complicated derivation operation and is less dependent on the initial values. Last but not least, the algorithm is verified with numerical examples.