RECOVERY OF 1 DEGREEE-MEAN ANOMALIES IN A LOCAL REGION FROM A LOW-LOW SATELLITE TO SATELLITE TRACKING MISSION (COLLOCATION, LEAST SQUARES ADJUSTMENT, FOURIER SERIES, GEOPOTENTIAL RESEARCH MISSION)

A simulation study was used to estimate the accuracy of 1(DEGREES)-mean anomalies which could be recovered from the Geopotential Research Mission (GRM) data. The earth's gravity field was defined by a set of potential coefficients of Rapp (1981) to degree 180. Line of sight accelerations were used as measurements in the recovery. The line of sight acceleration can be expressed in terms of potential coefficients, which makes data generation at a regular grid interval very efficient. An altitude of 160 kilometers above a spherical earth and a separation of 200 kilometers were used in the data simulation. Three methods were used in the recovery: the least squares collocation method; a numerical integration procedure proposed by Rummel (1982) or the Rummel procedure; and the least squares adjustment. In the least squares adjustment, a Fourier series of fictitious surface densities was used to represent a local gravity field; the Fourier coefficients were the unknowns. The Fourier coefficients were then used to compute a gravity anomaly in a very simple way. Three techniques of least squares adjustment were employed: the method of observation equations; the method of observation equations with weighted parameters; and the singular value decomposition method. After 1(DEGREES)-mean anomalies in a selected area were recovered by these estimation methods, they were compared with the true values (directly computed from the 180-field) to obtain the accuracy estimate. The result of the Rummel procedure was unacceptable because the fundamental assumption of the procedure, an isotropic functional relationship between the measurement and the unknown, was not fulfilled in the low-low satellite to satellite tracking problem. The results of the least squares collocation and the least squares adjustment indicated that an accuracy of 2.5 milligals for 1(DEGREES)-mean anomalies was possible in an area of the smooth gravity field. The accuracy of the recovery over the rough gravity field was about 30 milligals.