直接利用旋转矩阵进行空间后方交会的原理和方法

Principle and Method of Space Resection Using Orientation Matrix

空间后方交会是摄影测量学的基本内容,其解算的理论基础是共线条件方程及其线性化。传统的解算方法是直接以6个外方位元素为未知参数,使用泰勒级数展开进行线性化,然后迭代求解。而这里则直接以旋转矩阵为未知数进行迭代求解,这样既可直接解算出旋转矩阵,又避免欧拉角和旋转矩阵相互转换所引起的计算误差和时间耗费。试验结果表明该方法切实可行,求解精度高,而且迭代次数更少、迭代速度更快。

Space resection is a fundamental element in photogrammetry which is based on the collinearity equations and linearization. Directly as unknown variables, six elements of exterior orientation were expanded by Taylor series to realize linearization and then were solved by iterative algorithm in traditional method, but the orientation matrix was directly as unknown variables to solve iteratively in the paper. The new method could not only solve the orientation matrix, but also avoid time consumption and rounding-error accumulation which were caused by the mutual transfor- mations between Eulerian angles and orientation matrix. A test proved that the method was feasible because of less iterative times, faster iterative speed and higher resolution precision.