Improvement of the geoid in local areas by satellite-to-satellite tracking

Summary The concept of satellite-to-satellite tracking measuring the relative velocity of two orbiting satellites spaced some hundreds kilometers on a close orbit, provides now possibilities for the investigation of the Earth’s gravity field. In the paper only medium and short wave length effects affecting the measured relative velocity have been considered. Collocation is used in such an analysis of local geoid improvement, because this method allows to combine heterogeneous data in a consistent way. Covariance functions relevant for the particular case of a circular equatorial orbit are given. Two kinds of observation equations have been formulated. The choice of observation equation with regard to satellites configuration is discussed. It is found that it is sufficient to have a limited number of satellite-to-satellite observations in a 7^o×7^o area around the estimation point with distances between profiles of about 1^o.5 and between the two satellites forming the pair of 200+350 km; the altitude of satellite-to-satellite observations should be as low as possible. The accuracy of the geoid determination strongly depends on the degree and order of the reference field used. An accuracy of about ±1 m can be achieved with an assumed reference field of (40,40). The influence of measuring errors is discussed and it is shown that only satellite-to-satellite observations with accuracy better then 0.1 mm/sec will give an improvement of the geoid. Finally, some results on the combination of low-low satellite-to-satellite tracking and terrestrial gravity data are given. The proposed method seems to be especially interesting for unsurveyed areas. Furthermore, it has the practical advantage that only a local coverage data is needed.