Geoid Heights, Geoid Height Differences, and Mean Gravity Anomalies from 'Low-Low' Satellite-to-Satellite Tracking - An Error Analysis

摘要

The mathematical model for a simultaneous estimation of improved orbital parameters and an approximation of the earth's gravity field from range rate observations in an SST 'low-low' experiment is described. In a somewhat simplified model an error analysis for the estimation of geoid heights, geoid height differences 1 deg x 1 deg mean gravity anomalies is performed employing the least squares collocation method. Investigated is the dependence of the estimated parameters upon the measurement precision, the spatial configuration of the two satellites, the intersatellite distance, and the experiment altitude. In an optimal situation - assuming a range rate precision of + or - ten to the minus 6th power/ms, an intersatellite distance of 250 km, and an experiment altitude of 200 km - the estimated a posteriori std. dev. are + or - 0.9 m for point geoid heights, + or - 0.7 m for geoid height differences (point separation 150 km), and + or - 6 to 7 mgal for 1 deg x 1 deg mean gravity anomalies. These numbers compare very well with the results obtained from GEOS-3 altimetry for the seasurface topography. Unmodelled short-wavelength uncertainties in the orbit have thereby to be controlled down to 1 cm in radial direction, whereas the requirements for the control of long-wavelength error effects are moderate. (Author)