Abstract
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.
Highlights
Transformations are a frequently encountered procedure in geodesy, Global Positioning System (GPS) science and technology, geographical information science (GIS), and other scientific fields.For example, (1) a 3D similarity transformation is usually applied to transform GPS- (World GeodeticSystem 84) WGS84-based coordinates to those in a local coordinate system using a bunch of common points with coordinate values in both systems. (2) In GIS, digital data produced by tracing old paper maps over a digitizing tablet need to be converted from the tablet’s non-georeferenced plane data into georeferenced plane data that can be georegistered with other digital data layers. (3) For the purpose of monitoring a whole dam, the combining of multiple point clouds from different laser stations is needed by transformations
Adaptation of the Transformation Models to the Stochastic Model of the total least squares (TLS) Problem In Sections 2.2 and 2.3, we showed that the four kinds of transformation models can be formulated using a constrained or unconstrained EIV model
We presented transformation models in the context of the TLS method, developed the corresponding algorithm based on constrained nonlinear normal equations, and provided a statistical assessment of the TLS adjustment results, including the cofactor matrix of the parameter estimator and the a posteriori variance factor
Summary
Transformations are a frequently encountered procedure in geodesy, Global Positioning System (GPS) science and technology, geographical information science (GIS), and other scientific fields. (3) For the purpose of monitoring a whole dam, the combining of multiple point clouds from different laser stations is needed by transformations This process is called registration of the scans/images in photogrammetry and remote sensing. No one has solved the constrained TLS problem using a Gauss–Newton (GN)-type solver, which is much easier than SQP, and the statistical characteristics of the parameter estimates are straightforwardly available. 2. Adaptation of the Transformation Models to the Constrained/Unconstrained TLS Problem.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
