Enhanced geoid modelling in local geodetic networks: Comparative analysis of Least Squares Collocation techniques

The geoid is an equipotential surface of the Earth’s gravity field that closely approximates mean sea level in a least-squares sense. Meanwhile, this study aims to enhance local geoid modeling by comparing the Stationary (SLSC) and Non-Stationary Least Squares Collocation (NSLSC) techniques in Akure South and Gombe, Nigeria. Performance evaluation of the techniques, including comparison of SLSC and NSLSC approaches using three (Gaussian, Exponential, and Matern) covariance models and statistical (MANOVA) analysis, was carried out. In the Akure study area, Matern covariance model, though requiring longer processing time, has proved to be the best-fit (optimum) model for the application of SLSC and NSLSC techniques with standard deviations of 1.711825 m and 1.711782 m respectively. Also, using the GGM dataset for both approaches, the standard deviations for both approaches yielded 1.538476 m and 1.538454 m respectively. Furthermore, using the DEM dataset for both approaches, the standard deviations for both approaches yielded 0.943200 m and 0.943198 m respectively. However, in the Gombe study area, using terrestrial datasets, the Gaussian function proved to be the best-fit (optimum) model yielding the standard deviations of 0.352219 m and 0.352564 m for SLSC and NSLSC techniques, respectively. The results obtained from the GGM datasets yielded standard deviations of 0.340943 m and 0.338443 m for the SLSC and NSLSC techniques, respectively, while the DEM datasets produced standard deviations of 0.352285 m and 0.352496 m for the two techniques, respectively. The findings suggest that NSLSC is better suited for geoid determination in mountainous terrains like Akure South due to its flexibility, while SLSC is computationally more efficient for gently rolling terrains such as Gombe.