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Comparative Analysis of Least-squares Approaches for 3D Datum Transformation in Western Turkey

Year 2017, Volume: 17 Issue: 3, 1019 - 1029, 29.12.2017

Mevlut Gullu, Mustafa Yılmaz Tamer Baybura

Abstract

In Turkey, the national reference frame was changed for geodetic applications in parallel with the increasing use of Global Navigation Satellite System technology. Due to the reference frame change, the three-dimensional (3D) datum transformation has become compulsory between ED50 and WGS84. Several 3D datum transformation algorithms have been developed for geodetic applications. The well-known technique is the Least-Squares (LS) method. In this study, alternative 3D datum transformation approaches (including the Total Least-Squares (TLS) and the Weighted TLS (WTLS) methods) were compared with the LS method over a test area. The results showed that the WTLS transformed 3D coordinates with better accuracy than the LS and TLS methods.

Keywords

3D datum transformation Least-Squares (LS) Total Least-Squares (TLS) Weighted Total Least-Squares (WTLS).

References

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  • Ayhan, ME., Demir, C., Lenk, O., Kilicoglu, A., Aktug, B., Acıkgoz, M., Fırat, O., Sengun, Y.S., Cingoz, A., Gurdal, M.A., Kurt, A., Ocak, M., Turkezer, A., Yıldız, H., Bayazıt, N., Ata, M., Caglar, Y., Ozerkan, A., 2002. Turkish National Fundamental GPS Network-1999A (TNGFN-99A). J Mapp (Spec Issue) 16, 1-73 (in Turkish).
  • Aydin, C., 2016. How to solve errors-in-variables model for coordinate transformations in a classical adjustment way?. J Geod Geoinf, 3, 49-57 (in Turkish).
  • Caglar, Y., 2005. National report of Turkey - 2005. Symposium of the IAG Subcommission for Europe (EUREF). Vienna. Austria.
  • Fang, X., 2011. Weighted Total Least Squares Solutions for Applications in Geodesy. PhD dissertation. Leibniz University. Hannover. Germany.
  • Fang, X., 2014. A total least squares solution for geodetic datum transformations. Acta Geod Geophys 49(2): 189-207.
  • Felus, Y.A., 2004. Application of Total Least Squares for spatial point process analysis. J Surv Eng, 130, 126-133.
  • Felus, Y.A. and Schaffrin, B., 2005. Performing similarity transformations using the errors-in-variables-model. ASPRS 2005 Annual Conference, “Geospatial Goes Global: From Your Neighborhood to the Whole Planet”, March 7-11, 2005, Baltimore, Maryland.
  • GCM, General Command of Mapping (2014) Turkish National Fundamental GPS Network.
  • Ghilani, C.D. and Wolf, P.R., 2006. Adjustment Computations: Spatial Data Analysis, 4th edn. Wiley, Hoboken.
  • Golub, G.H. and Van Loan C.F., 1980. An analysis of the Total Least Squares problem. SIAM J Numer Anal, 17, 883-893.
  • Gullu, M., Yilmaz, I., Erdogan, O.A., 2003. Geodetic Network Design. Afyon Kocatepe University Publications, Afyonkarahisar, (in Turkish).
  • Gullu, M., 2016. Soft computing model in geodetic coordinate transformation. AKU J Sci Eng, 16, 655-659, (in Turkish).
  • Jazaeri, S., Amiri-Simkooei, A.R., Sharifi, M.A., 2013. Iterative algorithm for weighted total least squares adjustment. Surv Rev, 46, 19-27. Lan, D., Hanwei, Z., Quingyong, Z., Ruopu, W., 2012. Correlation of coordinate transformation parameters. Geod Geodyn, 3, 34-38.
  • Li, B., Shen, Y., Zhang, X., Li, C., Lou, L., 2013. Seamless multivariate affine error-in-variables transformation and its application to map rectification. Int J Geogr Inf Sci , 27, 1572-1592.
  • Markovsky, I. and Van Huffel, S., 2005. High-performance numerical algorithms and software for structured total least squares. J Comput Appl Math, 180, 311-331.
  • Markovsky, I. and Van Huffel, S., 2006. On weighted structured total least squares. In: Lirkov I, Margenov S, Waśniewski J (eds) Large-Scale Scientific Computing. Lecture Notes in Computer Science, Vol. 3743. Springer, Berlin, Heidelberg, pp. 695-702.
  • Mahboub, V., 2012. On weighted total least-squares for geodetic transformations. J Geod, 86, 359-367.
  • Mihajlović, D. and Cvijetinović, Ž., 2016. Weighted coordinate transformation formulated by standard least-squares theory. Surv Rev. doi: 10.1080/00396265.2016.1173329.
  • NGA, National Geospatial-Intelligence Agency, 2002. Addendum to NIMA TR 8350.2: Implementation of the World Geodetic System 1984 (WGS 84) Reference Frame G1150.
  • Pearlman, M., Altamimi, Z., Beck, N., Forsberg, R., Gurtner, W., Kenyon, S., Behrend, D., Lemoine, F.G., Ma, C., Noll, C.E., Pavlis, E.C., Malkin, Z., Moore, A.W., Webb, F.H., Neilan, R.E., Ries, .JC, Rothacher, M., Willis, P., 2006. Global Geodetic Observing System-considerations for the geodetic network infrastructure. Geomatica 60(2): 193-204.
  • Ren, Y., Lin, J., Zhu, J., Sun, B., Ye, S., 2015. Coordinate transformation uncertainly analysis in large-scale metrology. IEEE Trans Instrum Meas, 64, 2380-2388.
  • Schaffrin, B. and Feuls, Y., 2008. On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms. J Geod, 82, 272-283.
  • Schwieger, V., Lilje, M., Sarib, R., 2009. GNSS CORS - Reference Frames and Services. 7th FIG Regional Conference Spatial Data Serving People: Land Governance and the Environment – Building the Capacity, 19-22 October 2009, Hanoi, Vietnam.
  • Sisman, Y., 2014. Coordinate transformation of cadastral maps using different adjustment methods. J Chin Inst Eng, 37, 869-882.
  • Teunissen, P.J.G., 1988. The non-linear 2D symmetric Helmert transformation: an exact non-linear least-squares solution. Bull Geod, 62, 1-15.
  • Tong, X.H., Jin, Y., Li, L., 2011. An improved weighted total least squares method with applications in linear fitting and coordinate transformation. J Surv Eng, 137, 120-128.
  • Turgut, B., 2010. A back-propagation artificial neural network approach for three-dimensional coordinate transformation. Sci Res Essays, 5, 3330-3335.
  • Van Huffel, S. and Vandewalle, J., 1991. The Total Least Squares Problem: Computational Aspects and Analysis. SIAM, Philadelphia.
  • Van Huffel, S., 1997. Recent advances in total least squares techniques and errors-in-variables modelling. Proceedings of the Second International Workshop on TLS and EIV, SIAM, Philadelphia.
  • Yilmaz, M. and Gullu, M., 2014. A comparative study for the estimation of geodetic point velocity by artificial neural networks. J Earth Syst Sci, 123, 791-808.
  • Wang, B., Li, J., Liu, C., 2016. A robust weighted total least squares algorithm and its geodetic applications. Stud Geophys Geod, 60, 177-194.
  • Zhao, J., 2016. Efficient weighted total least-squares solution for partial errors-in-variables model. Surv Rev. doi: 10.1080/00396265.2016.1180753.

Year 2017, Volume: 17 Issue: 3, 1019 - 1029, 29.12.2017

Mevlut Gullu, Mustafa Yılmaz Tamer Baybura

Abstract

References

  • Akyilmaz, O., 2007. Total least squares solution of coordinate transformation. Surv Rev, 39(303), 68-80.
  • Ayhan, ME., Demir, C., Lenk, O., Kilicoglu, A., Aktug, B., Acıkgoz, M., Fırat, O., Sengun, Y.S., Cingoz, A., Gurdal, M.A., Kurt, A., Ocak, M., Turkezer, A., Yıldız, H., Bayazıt, N., Ata, M., Caglar, Y., Ozerkan, A., 2002. Turkish National Fundamental GPS Network-1999A (TNGFN-99A). J Mapp (Spec Issue) 16, 1-73 (in Turkish).
  • Aydin, C., 2016. How to solve errors-in-variables model for coordinate transformations in a classical adjustment way?. J Geod Geoinf, 3, 49-57 (in Turkish).
  • Caglar, Y., 2005. National report of Turkey - 2005. Symposium of the IAG Subcommission for Europe (EUREF). Vienna. Austria.
  • Fang, X., 2011. Weighted Total Least Squares Solutions for Applications in Geodesy. PhD dissertation. Leibniz University. Hannover. Germany.
  • Fang, X., 2014. A total least squares solution for geodetic datum transformations. Acta Geod Geophys 49(2): 189-207.
  • Felus, Y.A., 2004. Application of Total Least Squares for spatial point process analysis. J Surv Eng, 130, 126-133.
  • Felus, Y.A. and Schaffrin, B., 2005. Performing similarity transformations using the errors-in-variables-model. ASPRS 2005 Annual Conference, “Geospatial Goes Global: From Your Neighborhood to the Whole Planet”, March 7-11, 2005, Baltimore, Maryland.
  • GCM, General Command of Mapping (2014) Turkish National Fundamental GPS Network.
  • Ghilani, C.D. and Wolf, P.R., 2006. Adjustment Computations: Spatial Data Analysis, 4th edn. Wiley, Hoboken.
  • Golub, G.H. and Van Loan C.F., 1980. An analysis of the Total Least Squares problem. SIAM J Numer Anal, 17, 883-893.
  • Gullu, M., Yilmaz, I., Erdogan, O.A., 2003. Geodetic Network Design. Afyon Kocatepe University Publications, Afyonkarahisar, (in Turkish).
  • Gullu, M., 2016. Soft computing model in geodetic coordinate transformation. AKU J Sci Eng, 16, 655-659, (in Turkish).
  • Jazaeri, S., Amiri-Simkooei, A.R., Sharifi, M.A., 2013. Iterative algorithm for weighted total least squares adjustment. Surv Rev, 46, 19-27. Lan, D., Hanwei, Z., Quingyong, Z., Ruopu, W., 2012. Correlation of coordinate transformation parameters. Geod Geodyn, 3, 34-38.
  • Li, B., Shen, Y., Zhang, X., Li, C., Lou, L., 2013. Seamless multivariate affine error-in-variables transformation and its application to map rectification. Int J Geogr Inf Sci , 27, 1572-1592.
  • Markovsky, I. and Van Huffel, S., 2005. High-performance numerical algorithms and software for structured total least squares. J Comput Appl Math, 180, 311-331.
  • Markovsky, I. and Van Huffel, S., 2006. On weighted structured total least squares. In: Lirkov I, Margenov S, Waśniewski J (eds) Large-Scale Scientific Computing. Lecture Notes in Computer Science, Vol. 3743. Springer, Berlin, Heidelberg, pp. 695-702.
  • Mahboub, V., 2012. On weighted total least-squares for geodetic transformations. J Geod, 86, 359-367.
  • Mihajlović, D. and Cvijetinović, Ž., 2016. Weighted coordinate transformation formulated by standard least-squares theory. Surv Rev. doi: 10.1080/00396265.2016.1173329.
  • NGA, National Geospatial-Intelligence Agency, 2002. Addendum to NIMA TR 8350.2: Implementation of the World Geodetic System 1984 (WGS 84) Reference Frame G1150.
  • Pearlman, M., Altamimi, Z., Beck, N., Forsberg, R., Gurtner, W., Kenyon, S., Behrend, D., Lemoine, F.G., Ma, C., Noll, C.E., Pavlis, E.C., Malkin, Z., Moore, A.W., Webb, F.H., Neilan, R.E., Ries, .JC, Rothacher, M., Willis, P., 2006. Global Geodetic Observing System-considerations for the geodetic network infrastructure. Geomatica 60(2): 193-204.
  • Ren, Y., Lin, J., Zhu, J., Sun, B., Ye, S., 2015. Coordinate transformation uncertainly analysis in large-scale metrology. IEEE Trans Instrum Meas, 64, 2380-2388.
  • Schaffrin, B. and Feuls, Y., 2008. On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms. J Geod, 82, 272-283.
  • Schwieger, V., Lilje, M., Sarib, R., 2009. GNSS CORS - Reference Frames and Services. 7th FIG Regional Conference Spatial Data Serving People: Land Governance and the Environment – Building the Capacity, 19-22 October 2009, Hanoi, Vietnam.
  • Sisman, Y., 2014. Coordinate transformation of cadastral maps using different adjustment methods. J Chin Inst Eng, 37, 869-882.
  • Teunissen, P.J.G., 1988. The non-linear 2D symmetric Helmert transformation: an exact non-linear least-squares solution. Bull Geod, 62, 1-15.
  • Tong, X.H., Jin, Y., Li, L., 2011. An improved weighted total least squares method with applications in linear fitting and coordinate transformation. J Surv Eng, 137, 120-128.
  • Turgut, B., 2010. A back-propagation artificial neural network approach for three-dimensional coordinate transformation. Sci Res Essays, 5, 3330-3335.
  • Van Huffel, S. and Vandewalle, J., 1991. The Total Least Squares Problem: Computational Aspects and Analysis. SIAM, Philadelphia.
  • Van Huffel, S., 1997. Recent advances in total least squares techniques and errors-in-variables modelling. Proceedings of the Second International Workshop on TLS and EIV, SIAM, Philadelphia.
  • Yilmaz, M. and Gullu, M., 2014. A comparative study for the estimation of geodetic point velocity by artificial neural networks. J Earth Syst Sci, 123, 791-808.
  • Wang, B., Li, J., Liu, C., 2016. A robust weighted total least squares algorithm and its geodetic applications. Stud Geophys Geod, 60, 177-194.
  • Zhao, J., 2016. Efficient weighted total least-squares solution for partial errors-in-variables model. Surv Rev. doi: 10.1080/00396265.2016.1180753.
There are 33 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Mevlut Gullu, This is me

Mustafa Yılmaz This is me

Tamer Baybura

Publication Date December 29, 2017
Submission Date August 3, 2017
Published in Issue Year 2017 Volume: 17 Issue: 3

Cite

APA Gullu, M., Yılmaz, M., & Baybura, T. (2017). Comparative Analysis of Least-squares Approaches for 3D Datum Transformation in Western Turkey. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 17(3), 1019-1029.
AMA Gullu, M, Yılmaz M, Baybura T. Comparative Analysis of Least-squares Approaches for 3D Datum Transformation in Western Turkey. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. December 2017;17(3):1019-1029.
Chicago Gullu, Mevlut, Mustafa Yılmaz, and Tamer Baybura. “Comparative Analysis of Least-Squares Approaches for 3D Datum Transformation in Western Turkey”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 17, no. 3 (December 2017): 1019-29.
EndNote Gullu, M, Yılmaz M, Baybura T (December 1, 2017) Comparative Analysis of Least-squares Approaches for 3D Datum Transformation in Western Turkey. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 17 3 1019–1029.
IEEE M. Gullu, M. Yılmaz, and T. Baybura, “Comparative Analysis of Least-squares Approaches for 3D Datum Transformation in Western Turkey”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 17, no. 3, pp. 1019–1029, 2017.
ISNAD Gullu,, Mevlut et al. “Comparative Analysis of Least-Squares Approaches for 3D Datum Transformation in Western Turkey”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 17/3 (December 2017), 1019-1029.
JAMA Gullu, M, Yılmaz M, Baybura T. Comparative Analysis of Least-squares Approaches for 3D Datum Transformation in Western Turkey. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2017;17:1019–1029.
MLA Gullu, Mevlut et al. “Comparative Analysis of Least-Squares Approaches for 3D Datum Transformation in Western Turkey”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 17, no. 3, 2017, pp. 1019-2.
Vancouver Gullu, M, Yılmaz M, Baybura T. Comparative Analysis of Least-squares Approaches for 3D Datum Transformation in Western Turkey. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2017;17(3):1019-2.