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

Abstract

The non-availability of ellipsoidal heights of local geodetic Datums has made it necessary for the application of ellipsoidal heights transformation models to the available global ellipsoidal heights to obtain their respective theoretical heights in local Datums. It is required to know the accuracy, as well as reliability of any model of interest before its application. For that reason, this study comparatively analyses the Molodensky and Kotsakis models for the transformation of ellipsoidal heights between geocentric and non-geocentric Datums to determine the reliability of the Kotsakis model. The Global Navigation Satellite System (GNSS) data of the used stations were processed in World Geodetic System 1984 (WGS84) datum to obtain their global geographic coordinates and ellipsoidal heights. The coordinates, ellipsoidal heights and the transformation parameters between WGS84 and Minna Datums were applied to the Molodensky and Kotsakis models to compute the Clarke 1880 theoretical heights of the stations. The Molodensky model was used as a reference to which the Kotsakis model ellipsoidal heights were compared to obtain the Kotsakis model ellipsoidal heights discrepancies, as well as residuals. The residuals were used to compute the Root Mean Square Error (RMSE) of the Kotsakis model. The computed RMSE, as well as reliability of the model is 1.244 m. The study concluded that the low reliability, as well as accuracy of the Kotsakis model might be as a result of the two rotation datum shift parameters in it as they are the main differences between the two models.