Comparison of Two Corrector Surface Models of Orthometric Heights from GPS/Levelling Observations and Global Gravity Model

Abstract

The advent of space-based measurement systems such as the Global Positioning System (GPS) offers a new alternative in orthometric height determination over conventional spirit levelling. The ellipsoidal height (h) obtained from GPS observations can be transformed into orthometric height if the geoid undulation (N) is known from a national gravimetric geoid model. However, the lack of a national geoid model in Nigeria hinders the use of the method. This study compares two corrector surface models of orthometric heights from GPS/levelling observations and the Global Gravity Model. Model A (7-parameter) and Model B (8-parameter) are based on the general 7-parameter similarity datum shift transformation.  A network of twenty-one (21) GPS/levelling benchmarks within the study area were used and their geoidal heights were computed using GeoidEval utility software with reference to Global Gravitational Model (EGM08). Least squares adjustment was used to compute the coefficients of the models. Root mean square error (RMSE) was used to assess the accuracy of the models with model A having RMSE=0.171m and model B having RMSE=0.169m. Model B with the lowest RMSE is hence the better of the two models. The t-test and hypothesis test conducted at a 95% confidence level, however, revealed that the two models did not differ significantly. The study shows that the use of corrective surface to combine the gravity field model EGM08 and GPS/levelling significantly improves the determination of heights as observed from GPS in the study area.