On Linear Transformations of Spatial Data Using the Structured Total Least Norm Principle
On Linear Transformations of Spatial Data Using the Structured Total Least Norm Principle
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DOI：
10.1559/152304006779077273
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发表时间：
2006-01
影响因子：
2.5
通讯作者：
Y. Felus
中科院分区：
文献类型：
--
作者：
Y. Felus
坐标变换是将空间数据从源坐标系转换到目标坐标系的过程。在两个坐标系中测量的一组控制点被用于估计变换参数。一般来说，会测量更多的控制点，并使用最小二乘法对超定系统进行调整。然而，标准最小二乘法假定误差仅存在于在一个坐标系中进行的测量，或者存在于观测向量（y）中。在许多物理系统中情况并非如此，在源坐标系和目标坐标系中进行的所有测量都存在误差。结构化总体最小范数（STLN）方法是一种相对较新的数学概念，用于解决所谓的变量含误差（EIV）模型的估计问题。该方法特别适用于处理变换问题，因为它能够处理数据矩阵（A）的特殊结构。STLN方法专门用于计算常见线性坐标变换（仿射和相似）的参数。给出了一个数值示例，以证明该技术在精度方面的优越性，并比较标准最小二乘法、广义最小二乘法和STLN方法。
Coordinate transformation is the process of converting spatial data from a source coordinate to a target coordinate system. A set of control points, measured in the two coordinate systems, is used to estimate the transformation parameters. In general, more control points are measured, and the over-determined system is adjusted using the least squares method. However, the standard least squares method assumes that errors exist only in the measurements made at one coordinate system, or at the observation vector (y). This is not the case in many physical systems where errors exist in all the measurements made in both the source coordinate and the target coordinate systems. The Structured Total Least Norm (STLN) method is a relatively new mathematical concept developed to solve estimation problems of so-called Error-In-Variables (EIV) models. The method is specifically suitable for dealing with transformation problems, since it can handle the special structure of the data matrix (A). The STLN method is uniquely used to compute the parameters of common linear coordinate transformations (affine and similarity). A numerical example is presented to demonstrate the superiority of this technique in terms of accuracy and to compare the standard LS method, the generalized LS algorithm, and the STLN approach.