线阵卫星遥感影像外方位元素对偶四元数求解法

基于对偶四元数可统一描述位置与姿态的特点,提出了利用对偶四元数求解线阵卫星遥感影像外方位元素的方法。该方法使用对偶四元数的实部描述传感器的姿态,并利用对偶部和实部共同描述成像传感器的位置。通过对位置和姿态的内插建立了基于对偶四元数的外方位元素模型。为减少运算,将球面线性插值进行化简,进而建立了基于线性插值的成像几何模型。为求解外方位元素,首先对共线条件方程进行了线性化,然后通过矩阵微分运算推导了线元素的虚拟观测方程,并根据误差传播定律确定其权值,最终采用具有约束条件的参数平差法求解外方位元素。试验结果表明本文方法正确可靠,与采用欧拉角和单位四元数的外方位元素求解方法相比,有更高的参数解算精度,同时也表明了准确的初值和虚拟观测方程对外方位元素求解的必要性。

Dual Quaternion Method to Solve Exterior Orientation Parameters for Satellite Linear Array Images

According to the characteristics that dual quaternion can describe the position and orientation simultaneously,a method using dual quaternion to calculate the exterior orientation parameters for satellite linear array images is proposed.In this method the real part of dual quaternion is used to represent attitude of the sensor,and both the real part and the dual part are used to represent the position of the sensor.The model describing exterior parameters is established by interpolating the position and attitude. To reduce calculation,the simplified spherical linear interpolation algorithm is proposed,and the geometric model is established.In order to calculate the exterior parameters,the collinear equation is linearized at first.Then the virtual observation equations for position parameters are deduced according to the theory of matrix derivative,and the weight of the equation is calculated using error propagation principle.The exterior orientation parameters are calculated iteratively using parameter adjustment with constraints at last.Experimental results indicate that the proposed method is reliable and correct,and the precision of parameter estimation is higher than traditional methods using Euler angles or unit quaternion. The necessity of accuracy initial values and virtual observation equations for calculating exterior parameters is also revealed.