On the combined adjustment of a gravimetrically determined geoid and GPS levelling stations

Summary A new basic geodetic network using the GPS technique is now being set up in France. There will be altogether 1000 benchmarks connected to the French levelling network. Obviously, the GPS levelling points are not dense enough to produce a national levelling reference surface. A gravimetrically determined geoid has therefore been proposed to be used for the interpolation between the GPS levelling points. However, because of long-wavelength errors, we consider that a gravimetric geoid does not have sufficient accuracy. A regression by fitting the gravimetrically determined geoid to the GPS levelling points is generally proposed. Unfortunately, this country-wide geoid fitting work cannot eliminate local deformations in the geoid, which happen in areas where there are errors or shortages of gravity or DTM data. This paper proposes and discusses a combined adjustment method. The principle is to divide up the geoid into small pieces and then to adjust them to the GPS levelling points locally with constraint conditions for the common points of the adjacent pieces. In order to benefit from the advantages of the high resolution and high relative accuracy of the gravimetric geoid, as well as the high absolute accuracy of the GPS levelling points, we establish respectively a relative observation equation for the difference of the gravimetric geoid undulation and an absolute observation equation for the GPS levelling points. Finally, we adjust the observation equations as a whole. Several global and local systematic errors are also taken into account and some special cases, such as adjustment in groups and blunder detection, are also discussed.