On ill-conditioning in 3D similarity transformation
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TLDR
In this study, it is indicated how the ill-condition structure is reduced to acceptable level by means of choosing at different unit of unknown parameters the unknown coefficient matrix in normal equations.Abstract:
D similarity transformations are often used for datum transformation in Geomatic Engineering. The transformations are routinely performed between the point coordinates evaluated from GNSS (Global Navigation Satellite Systems) observations and the point coordinates given in national datum. A mathematical model established among two different 3D coordinate systems contains tree type datum parameters which are translations, rotations and a scale. Coefficients of the parameters reflect large variations from each other's. So, the unknown coefficient matrix in normal equations is to be ill-conditioned. In this study, it is indicated how the ill-condition structure is reduced to acceptable level by means of choosing at different unit of unknown parameters. Finally, the transformation from Kocaeli Metropolitan Municipality GNSS network coordinates to Turkish Geodetic Datum is used as a numerical example.read more
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Journal ArticleDOI
An integrated solution for reducing ill-conditioning and testing the results in non-linear 3D similarity transformations
TL;DR: In this article, a combined solution is proposed to reduce ill-conditioning and to perform precision analysis and global outlier test in linearized least squares (LLS) and direct (non-iterative) least squares.
References
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Numerical Recipes in C: The Art of Scientific Computing
TL;DR: Numerical Recipes: The Art of Scientific Computing as discussed by the authors is a complete text and reference book on scientific computing with over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, with many new topics presented at the same accessible level.
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Global Positioning System: Theory and Practice
TL;DR: In this paper, the origins of GPS are discussed and the development of global surveying techniques are discussed. But the authors focus on the use of global positioning techniques and do not address the issues of accuracy and access of GPS data.
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GPS satellite surveying
TL;DR: Elements of Satellite Surveying The Global Positioning System Adjustment Computations Least Squares Adjustment Examples Links to Physical Observations The Three-Dimensional Geodetic Model GPS Observables Propagation Media, Multipath, and Phase Center Processing GPS Carrier Phases Network Adjustments Ellipsoidal and Conformal Mapping Models Useful Transformations Datums, Standards, and Specifications Appendices References Abbreviations for Frequently Used References Indexes as discussed by the authors.