Simplified Flat Coordinate Model for Northern Parts of Arabian Gulf

Abstract

      The method of coordinate conversion is still considered important and laborious due to the shift from the spatial ellipsoidal (geographic) to the flat planned system. The most common method uses a contiguous UTM system as one of the most reliable systems in the conversion process; however, this system faces a problem in large areas that contain more than one zone. The goal of this research is to create a simple and low computational cost model to represent a non-contiguous semi-UTM geographic coordinates for confined regions of the globe. The considered region taken in this study is the northern parts of Arabian Gulf (including parts of Iraq, Kuwait, Iran, and Saudi Arabia). The determined mathematical model was based on using two dimensional Taylor sequence. The most accurate representation met in this study was based on the 6^th two dimensional polynomial. The estimation of equations’ coefficients was done using the least square criterion for the overall error of estimating coordinate values of either (latitude, longitude) or (Easting, Northing). The two basic determinations were applied for the forward and the backward; in the first step, the conversion of coordinates was calculated from the ellipsoidal coordinates (i.e., Longitude, Latitude) to UTM (WGS84) coordinates (i.e., Easting, Northing) and vice versa.

The attained results indicated that the mathematical model used is successful for achieving the conversion process. With the use of the 6^th order 2D-polynomial equations, a very small error of less than 1 m was achieved in the Easting and Northing coordinates.