Abstract
The process of converting coordinates is, still, considered an important and difficult issue due to the way of conversion from geographic ellipsoidal system to the projected flat system. The most common method uses contiguous UTM system as one of the most accurate systems in the conversion process, but the users of thesystem face problems related to contiguity, especially at the large areas that lie within more than one zone. The aim of the present research is to solve the problem related to the multiple zones coverage found in the Iraqi territory using a mathematical model based on the use of Taylor series. The most accurate conversion equation used in this paper was based on the 4th order polynomial of two variables. The calculation of equations’ coefficients was performed using least square criterion for the coordinate’s values, i.e., either latitude, longitude) or East (E), North (N) coordinates. The two basic determinations, for the forward and backward, wereapplied. In the first stages, the conversion of the coordinates from Longitude/ Latitude to East/ North was determined. Then, the second conversion stage was determined, i.e., the coordinates conversion from East, North to Longitude, Latitude). For each phase, a spatial accuracy assessment was conducted. The resultsshowed that the adopted mathematical model was successful to accomplish the conversion process. A very small error average of about 3 cm at east and less than 5 cm at north was reached using the 4th order polynomial equations.
Highlights
The Universal Transverse Mercator (UTM) is a projection coordinate system
The datasets represent grid points of the coordinates of longitude, latitude covering the Iraqi territory and some adjacent areas; so that the distance between each two points in the grid is 0.5 degrees. These coordinates are converted to X, Y coordinates using UTM system conversion software in the conversion process, but we will determine this program on zone 38 and calculate X, Y coordinates values, as shown in Table-1 and Figure-3
When the second test of the normalization method was used, the rate of error was gradually reduced to the lowest ratio, using the fourth-order polynomials equation. This resulted in the success of the conversion process and produced results that were near to idealism, as described in the following: Using the second-order polynomial equation, the result of the error average values was approximately 120 meters at X east and about 50 meters at Y north
Summary
The Universal Transverse Mercator (UTM) is a projection coordinate system. The position of a point in the rectangular coordinate system is defined by its distance from the x and y axes. To avoid dealing with negative numbers, the central meridian of each zone is defined to coincide with 500000 meters East. A point that has an easting of 400000 meters is about 100 km west of the central meridian [5]. For most such points, the true distance would be slightly more than 100 km, as measured on the surface of the Earth, due to the distortion of the projection. UTM eastings range from about 167000 meters to 833000 meters at the equator [6, 7, 8]
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