Year 2015, Volume 2 , Issue 1, Pages 47 - 53 2015-03-02

On ill-conditioning in 3D Similarity Transformation

Orhan Kurt [1]


3D 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.

3D similarity transformation, linear equation system, ill-conditioning
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Primary Language en
Subjects Engineering
Journal Section Research Articles
Authors

Author: Orhan Kurt

Dates

Publication Date : March 2, 2015

Bibtex @research article { ijegeo302761, journal = {International Journal of Environment and Geoinformatics}, issn = {}, eissn = {2148-9173}, address = {}, publisher = {Cem GAZİOĞLU}, year = {2015}, volume = {2}, pages = {47 - 53}, doi = {10.30897/ijegeo.302761}, title = {On ill-conditioning in 3D Similarity Transformation}, key = {cite}, author = {Kurt, Orhan} }
APA Kurt, O . (2015). On ill-conditioning in 3D Similarity Transformation. International Journal of Environment and Geoinformatics , 2 (1) , 47-53 . DOI: 10.30897/ijegeo.302761
MLA Kurt, O . "On ill-conditioning in 3D Similarity Transformation". International Journal of Environment and Geoinformatics 2 (2015 ): 47-53 <https://dergipark.org.tr/en/pub/ijegeo/issue/28164/302761>
Chicago Kurt, O . "On ill-conditioning in 3D Similarity Transformation". International Journal of Environment and Geoinformatics 2 (2015 ): 47-53
RIS TY - JOUR T1 - On ill-conditioning in 3D Similarity Transformation AU - Orhan Kurt Y1 - 2015 PY - 2015 N1 - doi: 10.30897/ijegeo.302761 DO - 10.30897/ijegeo.302761 T2 - International Journal of Environment and Geoinformatics JF - Journal JO - JOR SP - 47 EP - 53 VL - 2 IS - 1 SN - -2148-9173 M3 - doi: 10.30897/ijegeo.302761 UR - https://doi.org/10.30897/ijegeo.302761 Y2 - 2014 ER -
EndNote %0 International Journal of Environment and Geoinformatics On ill-conditioning in 3D Similarity Transformation %A Orhan Kurt %T On ill-conditioning in 3D Similarity Transformation %D 2015 %J International Journal of Environment and Geoinformatics %P -2148-9173 %V 2 %N 1 %R doi: 10.30897/ijegeo.302761 %U 10.30897/ijegeo.302761
ISNAD Kurt, Orhan . "On ill-conditioning in 3D Similarity Transformation". International Journal of Environment and Geoinformatics 2 / 1 (March 2015): 47-53 . https://doi.org/10.30897/ijegeo.302761
AMA Kurt O . On ill-conditioning in 3D Similarity Transformation. International Journal of Environment and Geoinformatics. 2015; 2(1): 47-53.
Vancouver Kurt O . On ill-conditioning in 3D Similarity Transformation. International Journal of Environment and Geoinformatics. 2015; 2(1): 53-47.