Application of Multivariate Adaptive Regression Spline (MARS) Approach for 2D Coordinate Transformation

Yao Yevenyo Ziggah, Prosper Basommi Laari


Coordinate transformation is still an on-going research area in the geodetic sciences. It allow coordinates to be transformed from a source datum onto a target datum and vice versa for practical geodetic applications. Multivariate Adaptive Regression Spline (MARS) is a machine learning technique that has been successfully applied to solve function estimation problems in several disciplines. However, its application in geodetic sciences for coordinate transformation is yet to be explored. In this study, an attempt has been made to explore the performance of MARS as a novel alternative technique for coordinate transformation. The MARS was applied in this study to transform two-dimensional (2D) coordinates between the two national geodetic datums (Accra 1929 and Leigon 1977) used in Ghana. The results were further analysed and compared with Backpropagation Neural Network (BPNN) and Radial Basis Function Neural Network (RBFNN) as well as two classical transformation methods namely, 2D conformal and 2D affine models, respectively. The analyses were based on the horizontal positional residuals obtained between the observed and estimated horizontal coordinates. The statistical findings revealed that a maximum horizontal positional error of 0.628, 0.509 and 1.624 m were respectively produced by the MARS, RBFNN and BPNN. While, 2.153 and 2.642 m were correspondingly given by 2D affine and 2D conformal models. In addition, a minimum horizontal positional error of 0.017, 0.005 and 0.040 m were obtained by the MARS, RBFNN and BPNN. In contrast, the 2D affine and 2D conformal models had 0.109 and 0.199 m, respectively. Furthermore, in terms of the precision of the estimated horizontal coordinates, the MARS obtained a standard deviation of 0.139 m while 0.119 and 0.273 m were achieved correspondingly by RBFNN and BPNN. The 2D affine and 2D conformal produced 0.468 and 0.510 m. It was therefore concluded that the proposed MARS can be a promising technique for coordinate transformation in the Ghana geodetic reference network.


Multivariate Adaptive Regression Spline; Radial Basis Function Neural Network; Backpropagation Neural Network; Coordinate Transformation

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