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Error Estimates for WGS-84 and Everest (India-1956) Transformation

Mr. B.K. Srivastava
General Manager (Cartography)
Mr. K. Ramalingam
Member (Planning)
Airports Authority of India, New Delhi, India
Introduction
WGS-84 coordinate System is being adopted universally as the standard form of Geographical Coordinates Representation System. This system has come into existence only towards the end of 20th Century, and prior to that the local coordinate system (Everest or Indian System) had been in use in India for more than 150 years. Thus, most of the maps, records and data are available in the form of Everest system only. Till such time all the records are transformed to WGS-84 and new maps are printed, the local system is also likely to continue along with WGS-84.
Thus, a need is felt to assess the extent of error involved in case of transforming the geographical coordinates from one system to other by using standard conversion softwares like MADTRAN, which uses the average values of transformation parameters. Similarly, it is also desirable to determine whether coordinates of one system could be used instead of other system without any transformation for non-precision activities in the field of aviation.
The paper deals about the study conducted to examine the above aspects of WGS–84 and Everest Coordinate Systems.
WGS-84 Co-ordinates System4
The position of any place, object or point can be represented by means of its geographical co-ordinates expressed in three-dimensional form of Latitude, Longitude, and height. The Latitude and Longitude are measured from the intersection of lines of prime meridian (passing through Greenwich) and the Equator. Similarly the height (or elevation) is normally measured from the mean sea level and is generally referred as "Above Mean Sea Level" or AMSL (amsl).
However, it is a known fact that the surface of earth is not flat but it is approximately of spheroid (or ellipsoid) shape having an assumed centre of its own. Thus with a view to get the accurate results of the distance between two points say, Delhi and Mumbai, a spheroid (or ellipsoid) which best fits the shape of earth between Delhi and Mumbai should also be assumed.
In the similar manner, it can be further extended to represent all the areas of the country into a common spheroid, which best fits to the surface of earth existing in India. This spheroid can be defined in terms of its inherent characteristics such as the semi-major axis, semi-minor axis, eccentricity etc. on the basis of which it is possible to mathematically work out the distances and bearings of any two points by geometrically plotting these points on that spheroid. This spheroid provides the basis for mapping to that area.
Thus it is evident that the geographical position of a place or object when expressed in terms of X, Y, Z co-ordinates (known as Latitude, Longitude and Height of the place) are always based on a particular reference datum. These co-ordinates are called 'ground derived co-ordinates' or 'local co-ordinates' and the reference datum on which measurements are made is known as local datum.
In other words a geographical datum is a mathematical model representing the shape of the earth that is used as a reference or starting point for the determination or calculation of Latitude, Longitude and height.
Accordingly a mathematical spheroid roughly representing the shape of Indian sub-continent has been assumed by the Survey of India and all measurements are related to this spheroid. The reference datum fixed by "Survey of India" is located near Kalianpur in Madhya Pradesh. This is known as 'Everest-1830' (Everest is the name of first Surveyor General of India '(Late) Sir George Everest' 5 and the term '1830' represents the year in which the spheroid was defined). This datum is also sometimes called as 'Indian datum'. The Indian spheroid has been marginally modified on a number of occasions so that the parameters assumed for the spheroid have been refined slightly from time to time. For example, such changes were made in the year 1930, 1956 and so on. Thus sometimes the Everest spheroid or (Indian spheroid) is also referred as Indian-1880, Everest-1930 or Indian-1956 etc. (Even now some changes to the original definition are under consideration by Survey of India).
Obviously, the centre of the Everest spheroid does not coincide with the centre of the earth. However, this is the best fitting spheroid that works fairly well for our country. All the maps prepared by Survey of India and other agencies use 'Everest-1830 datum' for expressing geographical co-ordinates of places in India. Based on this, a number of sub-datums have also been established in India and all measurements are taken from the main datum and sub-datums. [Aerodrome Reference Points (or ARPs) established at various airports in India, which for all practical purposes, are assumed, as the centre of the airport, are also one of the sub-datums].
It is, however also true that the spheroid defined for India does not hold good for other countries such as England or USA or Australia, which have defined their own spheroids in the similar manner, and thus, have brought out a set of co-ordinates best fitting to their countries and best representing the shape of earth in the particular geographical region. Thus, each country has its own datum for measurement of ground derived geographical co-ordinate and height. The mathematical parameters of these datums differ with each other and normally their datum centres would not coincide with the centre of earth, unless and until their co-ordinates have been re-adjusted to a geo-centric spheroid, (Such as North American datum NAD-83, which is an earth centred datum) and may be in few more countries.
Due to that reason, a need was felt for defining a new set of co-ordinates having a common origin and a common spheroid. This has now been done and is known as World Geodetic System of 1984 or WGS-84. This particular datum is a geocentric geodetic datum, established through space geodetic observations, which is earth-centred, earth-fixed (ECEF). Global Positioning System (GPS) and other similar modern aids needed for Global Navigation Satellite System (GNSS) are using the new co-ordinates system i.e. WGS-84 System, which does not change from place to place or from country to country.
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