四元数微分方程的高分辨率卫星遥感影像外方位元素求解

Solution of Exterior Orientation Parameters for High-resolution Satellite Imagery Based on Quaternion Differential Equation

通过对高分辨率卫星遥感影像成像机理进行分析,提出一种基于四元数微分方程的外方位元素求解方法。该方法采用四元数描述影像成像姿态,建立基于四元数微分方程的成像几何模型。为求解该模型,引入3个独立的解算参数,计算过程中不直接求解姿态四元数,而是解算参数,使得未知数个数与现有方法相同,并采用Tikhonov正则化理论进一步求解方程。试验结果表明该方法正确可靠,具有很好的稳定性和适应性,解算参数的引入效果显著,对定位精度有一定的提高,并且完全避免了三角函数运算。

According to analyzing the imaging mechanism of high-resolution satellite imagery, a solution of exterior orientation parameters based on quaternion differential equation is presented. In this solution the unit quaternion is used to describe the attitude of the image, and then the rigorous geometric model based on quaternion differential equation is established. In order to solve this rigorous geometric model, three independent parameters are introduced to this solution. So that, it is not should to solve the unknown quaternion directly, but these three independent parameters, and the unknown number keeps the same as the existed method in photogrammetry. In addition, Tikhonov regularization theory is also used to solve the rigorous geometric model. Experimental results indicate that this solution, which can avoid computation of trigonometric functions completely, is right, stable and adaptive, and the orientation precision can be improved when these three independent parameters are used.