Improved determination of heights using a conversion surface by combining gravimetric quasi-geoid/geoid and GPS-levelling height differences

摘要

The quasi-geoid/geoid can be determined from the Global Positioning System (GPS) ellipsoidal height and the normal/orthometric heights derived from levelling (GPS-levelling). In this study a gravimetric quasigeoid and GPS-levelling height differences are combined to develop a new surface, suitable for “levelling” by GPS. This new surface provides better conversion of GPS ellipsoidal heights to the national normal heights. Different combining procedures, a four-parameter solution, linear and cubic splines interpolations, as well as the least-squares collocation method were investigated and compared over entire Norway. More than 1700 GPS-levelling stations were used in this study. The combined surface provides significant accuracy improvement for the normal height transformation of GPS height data, as demonstrated by the post-fitting residuals. The best solution, based on the least-squares collocation, provided a conversion surface for the transformation of GPS heights into normal height in Norway with an accuracy of about 5 cm.