General Total Least Squares Theory for Geodetic Coordinate Transformations
General Total Least Squares Theory for Geodetic Coordinate Transformations
复制标题
大地坐标变换的一般总最小二乘理论
DOI：
10.3390/app10072598
复制
发表时间：
2020-04-01
影响因子：
2.7
通讯作者：
Wang, Bin
中科院分区：
文献类型：
--
作者：
Qin, Yuxin;Fang, Xing;Wang, Bin
基准转换是大地测量学、全球定位系统（GPS）科学技术、地理信息科学（GIS）以及其他研究领域中的一个基本问题。在本研究中，我们建立了一种通用的整体最小二乘（TLS）理论，该理论允许具有不同约束条件的变量含误差模型构建所有转换模型，包括仿射、正交、相似和刚体转换。通过将转换模型适配到受约束的TLS问题，解析推导出非线性约束正规方程，并且可以通过定点公式迭代估计转换参数。我们还给出了参数估计量的统计特性以及控制点的精度单位。给出了两个实例，并分析了当约束数量增加时估计量如何变化的结果。
Datum transformations are a fundamental issue in geodesy, Global Positioning System (GPS) science and technology, geographical information science (GIS), and other research fields. In this study, we establish a general total least squares (TLS) theory which allows the errors-in-variables model with different constraints to formulate all transformation models, including affine, orthogonal, similarity, and rigid transformations. Through the adaptation of the transformation models to the constrained TLS problem, the nonlinear constrained normal equation is analytically derived, and the transformation parameters can be iteratively estimated by fixed-point formulas. We also provide the statistical characteristics of the parameter estimator and the unit of precision of the control points. Two examples are given, as well as an analysis of the results on how the estimated quantities vary when the number of constraints becomes larger.