Fitting gravimetric guasigeoid model to GPS/levelling data in Poland

Abstract

Considerable investigations were conducted in Poland on the determination of precise gravimetric quasigeoid model using terrestrial and marine gravity data, geopotential models and height data. Quality of the model was evaluated using precise GPS/levelling data. Precise gravimetric quasigeoid model makes possible to transform ellipsoidal heights to normal heights, what is required for using GPS heighting in surveying practice. To determine transformation parameters, the gravimetric quasigeoid model needs to be fitted to GPS/levelling heights in the area of interest. In order to eliminate datum shift, residual long-wavelength gravity errors, as well as possible systematic errors in levelling, the residual height anomalies at GPS/levelling sites were modelled by a smooth function consisting of a trend function and a residual. The parameters of the model were determined using least-squares collocation. In practice, a trend was modelled by a plane function, and the residuals were modelled by Hirvonen’s covariance function. For Poland the a priori error of 37 mm and the correlation length of 70 km were used. Obtained results show that the fit of gravimetric geoid to vertical datum, measured by the standard deviation of residuals at the GPS/levelling control traverse sites, is at the level of ±1.5 cm.