Modern Development for the Improvement of Accuracy of Nigerian Coordinate Transformation Process Using the Adapted NTv2 Model: The Critical Issues of the Mathematical Algorithm

Abstract

Changing coordinates using appropriate mathematical models from one reference system to another may be influenced if the operation requires the change of datum. A set of transformation parameters has been adopted for Nigeria. However, the critical concern usually associated with the problem of transformation of coordinates is the issue of recoverability of the original values of transformed coordinates. The recursive effect of variables associated with spatial problems can be aptly modelled with an appropriate algorithm that set out a process to achieve a definite output. Consequently, the main thrust of this paper is to highlight the critical elements of the mathematical algorithm associated with the National Transformation Version 2 (NTv2) model adapted for the Nigerian Datum Transformation process. The adapted NTv2 model adopts the bi-linear interpolation approach and the covariance function obtained were used to generate transformation elements in latitude (Δφ p) and longitude (Δλ p) and corresponding accuracies at the lattice nodes. The mathematical algorithm of this adapted NTv2 model underscores the likely attainment of better and significant values and statistical indicator of the improved accuracy as the average shift values for latitude and longitude for any transformed points in Nigeria. This capability makes the mathematical algorithm to be adaptable and fit for the purpose of the transformation process. The improvement in the positional accuracy is directly attributable to the application of the NTv2 model which provides a flexible and robust system of modelling any inherent systematic error in the national network.

Comparative Analysis of the Molodensky and Kotsakis Ellipsoidal Heights Transformation between Geocentric and Non-Geocentric Datums Models

“…The 5-parameters Molodensky model used for the transformation of ellipsoidal heights between geocentric and non-geocentric reference frames is [3,4,5,7,8].…”

“…The local, as well as non-geocentric datum ellipsoidal heights can be obtained from the conversion of ellipsoidal heights computed on the global, as well as geocentric (WGS84) ellipsoid. The conversion can be achieved through the application of the 5-parameters Molodensky's model [3,4,5] and the 8-parameters Kotsakis model [6] for ellipsoidal heights transformation between the geocentric and non-geocentric Datums, as well as reference frames. The Molodensky model involves the use of the 3 translation datum shift parameters, change in semi-major axis and difference in flattening between the two reference frames, as well as ellipsoids while the Kotsakis model comprises 3 translation and 2 rotation datum shift parameters, change in scale, change in semi-major axis and difference in flattening between the two reference ellipsoids.…”