Performance Evaluation of Applying Fuzzy Multiple Regression Model to TLS in the Geodetic Coordinate Transformation
Keywords:
Transformation, weighted least squares, weighted total least squares, singular value decomposition, Linear Regression, Fuzzy Multiple Regression Model.Abstract
It is known that the classical technique for solving the linear regression problem of the geodetic transformation process is using least squares approach (LS). On the contrary, this research explores the application of total least squares (TLS) approach to solve linear regression with and without fuzzy multiple regression model in Bursa-Wolf similarity transformation process. In this research two groups of data sets are used; the first group is the solution points which are used to compute the values of the transformation parameters. The second is the check points that were used to assess the accuracy of the applied methods (in terms of mean and Root Mean Squares Errors RMSE). The applied four solutions show how the accuracy of TLS is relatively better than LS. The weight has a better effect on improving the accuracy of both cases, LS and TLS; however, its effects are greater on TLS. By using the fuzzy multiple regression models, the results improved further and the need for accurate weights/confidence is eliminated.
References
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[2] B.Schaffrin and A.Vieser "On weighted total least squares adjustment for linear regression". J. Geod Vol. 82, pp. 415-421, 2008.
[3] F. Neitzel "Generalization of total least squares on example of unweighted and weighted 2D similarity transformation". Journal of Geodesy, 84: 751-762, 2010.
[4] P. I. Xu, J. Liu and C. Shi "Total Least Squares Adjustment in Partial Errors in Variables Models: algorithm and statistical analysis". Journal of Geodesy. Vol.86, pp. 661-675, 2012.
[5] X.Tong, Y. Jin, and L. Li. "An Improved Weighted Total Least Squares Method with Applications in Linear Fitting and Coordinate Transformation". Journal Surveying Engineering, 10.1061/ (ASCE) SU.1943-5428.0000055,pp. 120-128, 2011
[6] G. Pan, Y. Zhou, H. Sun and W. Guo "Linear Observation Based Total Least Squares", Survey Review, Vol.47,No. 340, pp. 18-27, 2015.
[7] Y. Zhou, X. Kou, J. Li, and X. Fang "Comparison of Structured and Weighted Total Least-Squares Adjustment Methods for Linearly Structured Errors-in-Variables Models". Journal Surveying Engineering, 10.1061/ (ASCE) SU.1943-5428.0000190, 04016019, 2016.
[8] Y.Felus. and B. Schaffrin "Performing similarity transformation using the error in variables model", ASPRS Annual Conference, 2005.
[9] O.Akyilmaz "Total Least Squares Solution of Coordinate Transformation", Survey Review Vol.39 No.303, pp.68-80 • January 2007.
[10] B. Schafflin "Coordinate transformation corresponding to O. Akyilmaz's article". Survey Review, pp. 40-102, 2008.
[11] B. Schaffrin., I.P.Lee, Y.S Choi and Y.Felus "Total Least Squares for Geodetic Straight Line and Plane adjustment". Bollettino die Geodesia e Science Affini, Vol.65, pp.141-168, 2006.
[12] P.Teng Chang and E. Stanley Lee "A Generalized Fuzzy Weighted Least Squares Regression". Fuzzy Sets and Systems Vol. 82, No. 3, pp. 289- 298, 23 September 1996.
[13] S. Jazaeri, A.R.Amiri- I and M. A.Sharifi, "Iterative algorithm for weighted total least squares adjustment". Survey Review, 2014.
[14] H. Tanaka, S. Vegima, and K. Asai, “Linear regression analysis with fuzzy model”. IEEE Trans. Systems Man Cybernet. Vol.12, PP 903–907, 1982.
[15] A. Ubale and S. Sananse, "A comparative study of fuzzy multiple regression model and least square method". International Journal of Applied Research Vol. 2, No. 7, pp.11-15, 2016.
[16] Y. Yuanxi and X. Tianhe "Combined method of datum transformation between different coordinate systems", Geo-Spatial Information Science, Vol.5, No. 4, pp. 5-9, 2012.
[17] S.Yunzhang, B. Li and Y.Chen "An iterative solution of weighted total least squares adjustment". Springer- Verlag, Vol. 85, pp. 229-238, 2011.
[18] O. Okwuashi and A. Eyoh "3D Coordinate Transformation Using Total Least Squares". Academic Research International, 2012. www.journals.Savap.org.pk.
[19] I. Markovsky and S. Van Huffel "Overview of Total Least Squares Methods". Signal Processing 87- 2007, PP. 2283-2302, 2007.
[20] M.Acar, M. Ozludemir and O. Akyilmaz "Total Least Squares in Geodetic Coordinate Transformation", 2006. http//www.researchgate.net/publication/25280267.
[21] A. F. Shapiro "Fuzzy regression models". Penn State University, 2005.
[22] P. Tang Chang and E. Stanley Lee "A Generalized Fuzzy Weighted Least Squares Regression". Journal of Fuzzy Sets and Systems, Vol.82, No. 3, 23, PP. 289- 298, September 1996.
[23] V. Marza and M. A. Seyyedi "Fuzzy Multiple Regression Model for Estimating Software Development Time". International Journal of Engineering Business Management, Vol. 1, No. 2, pp. 79-82, 2009.
[24] A. Saad and M. Elsayed "Simple Model for Improving the Accuracy of Geodetic Triangulation Network in Egypt Using Accurate GPS Coordinates". Accepted in Civil Engineering Research Magazine (CERM).2005.
[25] ESA, "Introducing the new Egyptian datum -1995". Final Seminar Schedule, ESA, Cairo, Egypt.
[26] Aviation Authority "Aviation Authority Report for the Airports Project". Aviation Authority, Cairo, Egypt, 1997.
[27] S. M. Powell "Results of the Final Adjustment of the new National Geodetic". ESA, Cairo, Egypt, 1997.
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Published
2016-09-18
How to Cite
S. ElSayed, M., & H. Ali, A. (2016). Performance Evaluation of Applying Fuzzy Multiple Regression Model to TLS in the Geodetic Coordinate Transformation. American Scientific Research Journal for Engineering, Technology, and Sciences, 25(1), 36–50. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/2074
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