On total least squares for quadratic form estimation
On total least squares for quadratic form estimation
复制标题
关于二次形式估计的总最小二乘法
DOI：
10.1007/s11200-014-0267-x
复制
发表时间：
2015-07-01
影响因子：
0.9
通讯作者：
Yao, Yibin
中科院分区：
文献类型：
--
作者：
Fang, Xing;Wang, Jin;Yao, Yibin
在大地测量学中，用连续函数（如二次型）对扫描数据进行数学近似是监测人造和自然物体变形的常见任务。我们使用高次结构变量误差齐次方程来模拟二次型。根据欧拉-拉格朗日定理，设计了一种迭代调整二次型模型的总体最小二乘算法。与现有方法相比，该算法被证明是二维和三维空间中二次型判定的通用公式。最后，我们展示了该算法在变形监测中的适用性。
The mathematical approximation of scanned data by continuous functions like quadratic forms is a common task for monitoring the deformations of artificial and natural objects in geodesy. We model the quadratic form by using a high power structured errors-in-variables homogeneous equation. In terms of Euler-Lagrange theorem, a total least squares algorithm is designed for iteratively adjusting the quadratic form model. This algorithm is proven as a universal formula for the quadratic form determination in 2D and 3D space, in contrast to the existing methods. Finally, we show the applicability of the algorithm in a deformation monitoring.