Research Article

### Investigation on the effects of number of common points in 2D transformation problem

Year 2019, Volume: 4 Issue: 2, 58 - 62, 01.06.2019

### Abstract

Coordinate transformation from one datum to another is the basic problem in geodesy. Generally, the problem may be expressed by converting coordinates in a cartesian coordinate system with defined origin provided by the intersection of two or three axes into another system using mathematical equations. To compute the transformation parameters, a sufficient number of coordinates of the common points should be known in two systems. The problem involves either 2D or 3D coordinate systems. Traditionally the commonly used model for the estimation of the transformation parameters is the Least Squares (LS) method refers as to Helmert Transformation. This study aims to compare the performance of the spatial distribution and quantity of the common points in LS method for coordinate transformation problems. For this purpose, a geodetic network with 25 points, whose coordinates are commonly known in two datum are used to compute the performance of the transformation problem under the different scenarios. To compare the cases, the sum of the absolute coordinate differences is provided by subtracting the original coordinates of test points from computed coordinates by using estimated transformation parameters. The results show that increasing control points one by one to estimate the transformation parameters improve the results of the transformation parameters and reliable transformation parameters have been estimated when a homogeneously distributed 8 points are taken as common points for about a region as 1500 km2.

### References

• Akyilmaz, O. (2007). Total Least Squares Solution of Coordinate Transformation. Survey Review, 39 (303), 68-80
• Chen, W. and Hill, C. (2005). Evaluation Procedure for Coordinate Transformation. J. Surv. Eng., 131 (2), 43-49
• Koch, K.R. (1999). Parameter Estimation in Linear Models. In: Parameter Estimation and Hypothesis Testing in Linear Models. Springer, Berlin, Heidelberg
• Kutoglu, H.S. and Ayan, T. (2006). The role of common point distribution in obtaining reliable parameters for coordinate transformation, Applied Mathematics and Computation, 176, 751–758
• Kutoglu, H.S. and Vaníček, P. (2006). Effect of Common Point Selection on Coordinate Transformation Parameter Determination, Stud. Geophys. Geod., 50, 525−536
• Tan, Q., Lu, N., Dong, M., Zhu, L. (2013). Influence of geometrical distribution of common points on the accuracy of coordinate transformation, Applied Mathematics and Computation 221, 411–423
Year 2019, Volume: 4 Issue: 2, 58 - 62, 01.06.2019

### References

• Akyilmaz, O. (2007). Total Least Squares Solution of Coordinate Transformation. Survey Review, 39 (303), 68-80
• Chen, W. and Hill, C. (2005). Evaluation Procedure for Coordinate Transformation. J. Surv. Eng., 131 (2), 43-49
• Koch, K.R. (1999). Parameter Estimation in Linear Models. In: Parameter Estimation and Hypothesis Testing in Linear Models. Springer, Berlin, Heidelberg
• Kutoglu, H.S. and Ayan, T. (2006). The role of common point distribution in obtaining reliable parameters for coordinate transformation, Applied Mathematics and Computation, 176, 751–758
• Kutoglu, H.S. and Vaníček, P. (2006). Effect of Common Point Selection on Coordinate Transformation Parameter Determination, Stud. Geophys. Geod., 50, 525−536
• Tan, Q., Lu, N., Dong, M., Zhu, L. (2013). Influence of geometrical distribution of common points on the accuracy of coordinate transformation, Applied Mathematics and Computation 221, 411–423

### Details

Primary Language English Articles Taylan ÖCALAN Yildiz Technical University 0000-0003-0861-013X Türkiye June 1, 2019 Year 2019 Volume: 4 Issue: 2

### Cite

 Bibtex @research article { ijeg446962, journal = {International Journal of Engineering and Geosciences}, eissn = {2548-0960}, address = {}, publisher = {Murat YAKAR}, year = {2019}, volume = {4}, number = {2}, pages = {58 - 62}, doi = {10.26833/ijeg.446962}, title = {Investigation on the effects of number of common points in 2D transformation problem}, key = {cite}, author = {Öcalan, Taylan} } APA Öcalan, T. (2019). Investigation on the effects of number of common points in 2D transformation problem . International Journal of Engineering and Geosciences , 4 (2) , 58-62 . DOI: 10.26833/ijeg.446962 MLA Öcalan, T. "Investigation on the effects of number of common points in 2D transformation problem" . International Journal of Engineering and Geosciences 4 (2019 ): 58-62 Chicago Öcalan, T. "Investigation on the effects of number of common points in 2D transformation problem". International Journal of Engineering and Geosciences 4 (2019 ): 58-62 RIS TY - JOUR T1 - Investigation on the effects of number of common points in 2D transformation problem AU - TaylanÖcalan Y1 - 2019 PY - 2019 N1 - doi: 10.26833/ijeg.446962 DO - 10.26833/ijeg.446962 T2 - International Journal of Engineering and Geosciences JF - Journal JO - JOR SP - 58 EP - 62 VL - 4 IS - 2 SN - -2548-0960 M3 - doi: 10.26833/ijeg.446962 UR - https://doi.org/10.26833/ijeg.446962 Y2 - 2018 ER - EndNote %0 International Journal of Engineering and Geosciences Investigation on the effects of number of common points in 2D transformation problem %A Taylan Öcalan %T Investigation on the effects of number of common points in 2D transformation problem %D 2019 %J International Journal of Engineering and Geosciences %P -2548-0960 %V 4 %N 2 %R doi: 10.26833/ijeg.446962 %U 10.26833/ijeg.446962 ISNAD Öcalan, Taylan . "Investigation on the effects of number of common points in 2D transformation problem". International Journal of Engineering and Geosciences 4 / 2 (June 2019): 58-62 . https://doi.org/10.26833/ijeg.446962 AMA Öcalan T. Investigation on the effects of number of common points in 2D transformation problem. IJEG. 2019; 4(2): 58-62. Vancouver Öcalan T. Investigation on the effects of number of common points in 2D transformation problem. International Journal of Engineering and Geosciences. 2019; 4(2): 58-62. IEEE T. Öcalan , "Investigation on the effects of number of common points in 2D transformation problem", International Journal of Engineering and Geosciences, vol. 4, no. 2, pp. 58-62, Jun. 2019, doi:10.26833/ijeg.446962