Generalization of total least-squares on example of unweighted and weighted 2D similarity transformation

Neitzel, Frank
December 2010
Journal of Geodesy;Dec2010, Vol. 84 Issue 12, p751
Academic Journal
In this contribution it is shown that the so-called 'total least-squares estimate' (TLS) within an errors-in-variables (EIV) model can be identified as a special case of the method of least-squares within the nonlinear Gauss-Helmert model. In contrast to the EIV-model, the nonlinear GH-model does not impose any restrictions on the form of functional relationship between the quantities involved in the model. Even more complex EIV-models, which require specific approaches like 'generalized total least-squares' (GTLS) or 'structured total least-squares' (STLS), can be treated as nonlinear GH-models without any serious problems. The example of a similarity transformation of planar coordinates shows that the 'total least-squares solution' can be obtained easily from a rigorous evaluation of the Gauss-Helmert model. In contrast to weighted TLS, weights can then be introduced without further limitations. Using two numerical examples taken from the literature, these solutions are compared with those obtained from certain specialized TLS approaches.


Related Articles

  • ADFE Simulation for Anisotropic Convection Diffusion Problems with Moving Boundaries. Xia Cui; Jing-Yan Yue; Xi-Jun Yu // World Congress on Engineering 2009 (Volume 2);2009, p1046 

    Alternating direction finite element (ADFE) simulation for moving boundary anisotropic convection diffusion problems is studied. Through the coordinate transformation of the spatial variants, a new domain independent of the time is obtained on which two ADFE algorithms are designed by...

  • Comparing of Coordinate Transformation based on Total Least Squares and Least Squares. Qing wu Meng; Lu Meng // Applied Mechanics & Materials;2014, Issue 522-524, p1211 

    The coordinate transformation models based on least square method and total least square are built and discussed. The least square model only includes the errors of observation vectors, the total least square model simultaneously takes into consideration to the errors of observation vectors and...

  • An Extension of the Coordinate Transformation Method for Open-Loop Nash Equilibria. Carlson, D. A.; Leitmann, G. // Journal of Optimization Theory & Applications;Oct2004, Vol. 123 Issue 1, p27 

    In Leitmann (Ref. 1), a coordinate transformation method was introduced to obtain global solutions for free problems in the calculus of variations. This direct method was extended and broadened in Carlson (Ref. 2) and later in Leitmann (Ref. 3). The applicability of the original work of Leitmann...

  • DEVELOPMENT OF COORDINATES CONVERSION AND TRANSFORMATION STANDARDS FOR THE DANUBE WATER PROJECT. Rus, Tiberiu; Moldoveanu, Constantin; Danciu, Valentin; Kaltchev, Ivan // Proceedings of the International Multidisciplinary Scientific Ge;2014, Vol. 2, p215 

    Romania and Bulgaria started to develop in partnership a system of monitoring, warning and dissemination of data on the quality of environment in the border-area counties. The project it is achieved under the strategic project WATER - integrated water management and is financed under the Romania...

  • EVOLVENT KONÄ°K DÄ°ÅžLÄ° ÇARKLARIN BÄ°LGÄ°SAYAR SÄ°MÃœLASYONU. Cüneyt^Fetvaci, M. // Engineer & the Machinery Magazine;Mar2010, Issue 602, p12 

    This paper studies the equations of rack cutters for generating conical gears with asymmetric involute teeth. By applying the equations of designed profile of rack cutter, the principle of coordinate transformation, the theory of differential geometry, and the theory of gearing, the mathematical...

  • Controlled Line Smoothing by Snakes. Burghardt, Dirk // GeoInformatica;Sep2005, Vol. 9 Issue 3, p237 

    A major focus of research in recent years has been the development of algorithms for automated line smoothing. However, combination of the algorithms with other generalization operators is a challenging problem. In this research a key aim was to extend a snakes optimization approach, allowing...

  • Estimating an Autoregressive Current Effects Model of Sales Response When Observations are Aggregated Over Time: Lease Squares Versus Maximum Likelihood. Vanhonacker, Wilfried R. // Journal of Marketing Research (JMR);Aug1988, Vol. 25 Issue 3, p301 

    Estimating autoregressive current effects models is not straightforward when observations are aggregated over time. The author evaluates a familiar iterative generalized least squares (IGLS) approach and contrasts it to a maximum likelihood (ML) approach. Analytic and numerical results suggest...

  • KOORDINÄ€TU SISTÄ’MAS UN KOORDINÄ€TU TRANSFORMÄ€CIJA STARP TÄ€M. Novada, Inese // Geomatics;2007, Issue 2, p20 

    There are different coordinate systems used in the world nowadays and between them are those used in Latvia also. Coordinate systems can be refer to concrete limited are, for example, LKS 92 can be used only in Latvia, but ETRS 89is European scale system, and also refer to all world scale as in...

  • Understanding Coordinate Reference Systems, Datums and Transformations. Janssen, V. // International Journal of Geoinformatics;Dec2009, Vol. 5 Issue 4, p41 

    Spatial professionals are required to deal with an increasingly wide range of positioning information obtained from various sources including terrestrial surveying, Global Navigation Satellite System (GNSS) observations and online GNSS processing services. These positions refer to a multitude of...


Read the Article


Sign out of this library

Other Topics