A Least Squares Collocation Method of Geoid and Datum Determination for Nigeria
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The geodetic datum in Nigerian is ill-defined, hence a redefinition is necessary. Such a redefinition should utilize the best available method to achieve the best solution that would meet various needs of geodetic datum. In this work, we undertake a feasibility study of the geoid and datum determination for Nigeria by the method of least squares collocation. We wish to ascertain whether the method is appropriate for Nigerian (local) geoid and datum determination, and if so, on what definite factors a good determination, would depend. We have arrived at the following conclusions based on simulated observations at a maximum number of 300 points: 1. Least squares collocation is appropriate for the geoid and datum determination for Nigeria. The method is seen as a better approach in handling the linear functionals of the anomalous gravity field than the classical least squares adjustment method. 2. Accurate geoid and datum determination depends on the covariance model, type, number and the distribution of the observations. For datum determination alone, a good estimate is also dependent on the datum-geometry. 3. Datum determination in low latitude regions to which Nigeria belongs can be more accurately accomplished using geoidal undulations alone than using any other combinations of the gravity dependent observations. However, only the datum shift parameters have been determined with reasonable accuracy by this method. 4. Based on the adopted covariance model (Tscheming and Rapp model), a mean accuracy estimate of the parameters which is better than the a priori standard error of the observed signals (undulations) is achieved. A minimum gain of 53% in the accuracies of the predicted signals (undulations) is also achieved. 5. Astrogeodetic deflections of the vertical alone are not suitable for the direct application to a datum determination; they should first be used in astro-geodetic levelling to compute geoidal undulations, which would later be applied in least squares collocation for the determination of the parameters.