罗德里格矩阵在三维坐标转换严密解算中的应用

Applications of Lodrigues Matrix in 3D Coordinate Transformation

利用反对称矩阵和罗德里格矩阵的性质,把传统的三个旋转角参数用反对称矩阵的三个独立元素代替,推导了用三个公共点计算任意旋转角情况下的7个参数的直接计算公式,并建立了相应的平差模型。

In the 3D coordinate transformation, change of two datum system origins △X, △Y,△Z, scale change factor λ and three rotate angle θ,φ,ψ are generally used as parameters, a total of seven changes is called seven-parameter transformation. There are three transformation models, the Buras-Wolf model and the Molodensky model and the WTUSM model, generally used between two datum systems transformation. The linear models is used when the rotate angles are small; howev er, when the rotate angles are bigger, model errors will be produced relatively.