Comparison of Techniques for the Computation of a Height Reference Surface from Gravity and GPS-Levelling Data

Abstract

Three different techniques for quasigeoid modelling from gravity and GPS-levelling data are compared: (i) a penalized least-squares technique using spherical radial basis functions provides a gravimetric quasigeoid solution; the combination with GPS-levelling data is formulated as the solution of a Cauchy boundary-value problem for the Laplace operator. This solution when added to gravimetric solution yields the final quasigeoid; (ii) a direct least-squares solution using gravimetric and GPS-levelling data as observations and point masses as parameterization of the disturbing potential. The inconsistency between GPS-levelling data and gravimetric data is treated assigning high weights to GPS-levelling data in the least-squares adjustment; (iii) a least-squares collocation technique for computing a gravimetric quasigeoid. The combination with GPS-levelling data is realized using a low-degree polynomial corrector surface estimated from the differences between gravimetric height anomalies and height anomalies from GPS-levelling data. The three methods are compared using real data for an area in Germany. The results reveal a very similar performance of these methods if gravity data and GPS-levelling data are combined, whereas gravimetric quasi-geoid solutions differ significantly