Analysis of Methods for Ellipsoidal Height Estimation – The Case of a Local Geodetic Reference Network

Abstract

Ghana’s local geodetic reference network is based on the War Office 1926 ellipsoid with data in latitude, longitude and orthometric height  without the existence of ellipsoidal height. This situation makes it difficult to apply the standard forward transformation equation for direct conversion of curvilinear geodetic coordinates to its associated cartesian coordinates (X, Y, Z) in the Ghana local geodetic reference network. In order to overcome such a challenge, researchers resort to various techniques to obtain the ellipsoidal height for a local geodetic network. Therefore, this paper evaluates, compares, and discusses different methods for estimating ellipsoidal height for a local geodetic network. The investigated methods are the Abridged Molodensky transformation model, Earth Gravitational Model, and the Orthometric Height approach. To evaluate these methods, their estimated local ellipsoidal height values were implemented in the seven-parameter similarity transformation model of Bursa-Wolf. The performance of each of the methods was assessed based on statistical indicators of Mean Square Error (MSE), Mean Absolute Error (MAE), Horizontal Position Error (HE) and Standard Deviation (SD). The statistical findings revealed that, the Abridged Molodensky model produced more reliable transformation results compared with the other methods. It can be concluded that for Ghana’s local geodetic network, the most practicable method for estimating ellipsoidal height is the Abridged Molodensky transformation model. 

Keywords: Abridged Molodensky Model, Earth Gravitational Model, Orthometric Height, Geodetic Network