单位四元数在航空摄影测量解算中的应用与实践

The application and practice of unit quaternion method in aerial triangulation

研究了单位四元数方法在航摄空中三角测量各个步骤中的应用,并对其算法稳定性和适用性作了评价。首先叙述了基于单位四元数构造旋转矩阵的方法,及基于单位四元数的相对定向模型的建立和解求方法;构建了基于单位四元数的光束法区域网平差模型。然后利用大量实际航空影像数据进行了相对定向和光束法区域网平差试验,并同传统的基于欧拉角构建旋转矩阵的方案进行了比较。试验结果表明,在相对定向试验中,若采取P-H算法,只需要最少控制点就能保证所有试验数据均可得到正确的解。而在光束法平差中,基于单位四元数的方法比传统方法的稳定性差,对摄影比例尺和控制点的数量较为敏感,导致部分试验数据无法正确收敛。

In this paper, the unit quaternion method is introduced into the aerial triangulation applications and the empirical results are assessed. Firstly, the rotation matrix is constructed with unit quateruion and the expressions for calculating 3 rotation angles from rotation matrix are given, and P-H algorithm is introduced to solve relative orientation functions and the accuracy expressions of coplanarity equations are given. Then the bundle block adjustment model is constructed with unit quaternion and the error equation and its coefficient matrix are given. At last, relative orientation and bundle block adjustment tests were done using actual aerial images, which were compared with the traditional Euler angles-based rotation matrix construction. The test results showed that in the relative orientation test, if P-H algorithm is engaged, that is, anti-symmetric matrix are used to help solve the unit quaternion parameters, all the test data could get right results. While in the bundle adjustment, method based on unit quaternion shows poorer stability than the traditional one, and the unit quaternion method is influenced greatly by the scale of photography and number of control points, which results in that some test data could not be convergent correctly.