罗德里格矩阵总体最小二乘法的应用研究

Study on the application of Rodrigues matrix total least squares method

针对最小二乘法用于相似模型试验坐标转换时不能综合考虑系数矩阵误差的问题,提出采用总体最小二乘法用于相似模型试验的坐标转换,该方法以罗德里格矩阵为基础,同时顾及坐标转换方程中系数矩阵和观测向量中的误差,通过一定准则删除数据中的粗差或异常点,从而获得高精度的参数估计值。用近景摄影测量方法获取相似材料模型试验数据对该方法进行试验,结果验证了该方法的有效性和实用性。

When the traditional least-squares are used in the similar model test of a coordinate transformation,it assumes that the errors do not exist in the data matrix. The total least-squares method is employed for the similar model test of a coordinate transformation. The proposed method is based on a Rodrigues matrix. The total least-squares is a more general model wherein both the observation matrix and the data matrix are considered to delete outliers from point clouds in some other methods,and thus obtains a fitting parameter of high precision. A comparative study was also made between the proposed and traditional methods,such as the solution precision of a photogrammetric system,as well as the least-squares and total least-squares method. The results show that the method is valid and practical.