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Error Estimates for WGS-84 and Everest (India-1956) Transformation
Definition of WGS-84 Co-ordinates system
The WGS-84 (World Geodetic System-1984) is a Conventional Terrestrial System (CTS), realised by modifying the Navy Navigation Satellite System (NNSS), or TRANSIT, Doppler Reference Frame in origin and scale, and rotating it to bring its reference meridian into coincidence with the Bureau International de l`Heure (BIH)-defined Zero meridian. The origin of WGS-84 System is the centre of mass of the earth. Its Z-axis lies along the direction of Conventional Terrestrial Pole (CTP) for polar motion and the X-axis lies along inter-section of the WGS-84 Reference Meridian Plane and the Plane of the CTP's Equator. The Y-axis of this system completes a right-handed, Earth-Centred, Earth-Fixed (ECEF) orthogonal co-ordinates system, measured in the plane of CTP Equator 900 East of X-axis. The origin and orientation of co-ordinates axis in WGS-84 have been defined by the X, Y, Z co-ordinates established under the control of the 5 GPS monitoring stations located at Hawaii, Colorado Springs, Ascension, Diego Garcia and Kwajalein. WGS-84 is an earth-fixed global reference frame, including an earth model and is defined by a set of primary and secondary parameters. The primary parameters are as follows;1 
Conversion Softwares 4 For conversion of geographical coordinates from one datum to other, 7 transformation parameters are required to be taken into account. They are three translation parameters (i.e. Dx, Dy, Dz), three rotational parameters (i.e. eX, eY, eZ) and one scalar factor m. In addition, change in ellipsoid semi-major axis Da and flattening Df are also necessary. Accordingly, mathematical relationships have been developed to transform the co-ordinates from one datum to other (say from Everest-1830 to WGS-84 or vice versa). However, in order to achieve results of conversion by avoiding lengthy manual calculations, help of computer programs is normally taken. For this purpose a number of Softwares have been developed by different organisations for converting the co-ordinates of the local system to WGS-84 system. Among the above, the "DATUM" Software developed by EUROCONTROL and the "MADTRAN" software developed by National Imagery and Mapping Agency (NIMA), (earlier known as Defense Mapping Agency, DMA), USA are most popular. It is also mentioned that although, NIMA has brought the latest version of Transformation Software in Feb. 2003, known as GEOTRANS (Geographic Translator Vers 2.2.3), replacing MADTRAN, however, during this study, only MADTRAN has been used for transformation. In fact, the transformation parameters between WGS-84 and the local co-ordinates system (such as Everest Co-ordinates System) vary from place to place and therefore, for each particular location a different set of formulae (transformation parameters) are required to be used. On the other hand, a ready-made software such as MADTRAN and DATUM mentioned above uses the standard and average values of these parameters. For example, MADTRAN uses the following transformation parameters for conversion of local co-ordinates to WGS-84. 
In this above table, NIMA has also provided the transformation parameters of Reference Ellipsoid Everest-1830 (or India-1830) (EA) and India-1956 (EC), which is a modified form of Everest-1830 for refining the parameters of Everest ellipsoid from time to time. Accordingly MADTRAN Software designed and developed by NIMA (Earlier US Defense Mapping Agency, DMA) uses the same for conversion of Everest system (Indian datum) to WGS-84. 
It may be mentioned that the difference of transformation parameters between WGS-84 and Local co-ordinates systems is quite small and it does not make any significant difference for non-precision activities and in respect of small-scale maps prepared in two systems. However, for best precise results, actual survey of the site by using GPS equipment and also by other sophisticated survey equipment is always recommended, so that the actual values of the transformation parameters are available. |