Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm

In order to solve numerous practical navigational, geodetic and astro-geodetic problems, it is necessary to transform geocentric cartesian coordinates into geodetic coordinates or vice versa. It is very easy to solve the problem of transforming geodetic coordinates into geocentric cartesian coordinates. On the other hand, it is rather difficult to solve the problem of transforming geocentric cartesian coordinates into geodetic coordinates as it is very hard to define a mathematical relationship between the geodetic latitude (φ) and the geocentric cartesian coordinates (X, Y, Z). In this paper, a new algorithm, the Differential Search Algorithm (DS), is presented to solve the problem of transforming the geocentric cartesian coordinates into geodetic coordinates and its performance is compared with the performances of the classical methods (i.e., Borkowski, 1989, Bowring, 1976, Fukushima, 2006, Heikkinen, 1982, Jones, 2002, Zhang et al., 2005, Borkowski, 1987, Shu and Li, 2010 and Lin and Wang, 1995) and Computational-Intelligence algorithms (i.e., ABC, JDE, JADE, SADE, EPSDE, GSA, PSO2011, and CMA–ES). The statistical tests realized for the comparison of performances indicate that the problem-solving success of DS algorithm in transforming the geocentric cartesian coordinates into geodetic coordinates is higher than those of all classical methods and Computational-Intelligence algorithms used in this paper.

► A new method has been proposed for transformation of the geocentric cartesian coordinates into geodetic coordinates. ► The proposed method is able to give more robust and accurate results than Bowring’s Method. ► The proposed method is developed based on evolutionary computing. ► The proposed method is an application of modern data processing techniques in geodetic applications.