Gravity Parameter Estimation from Large Data Sets Using Stabilized Integral Formulas and a Numerical Integration Based on Discrete Point Data

摘要

A gravity parameter estimation technique is proposed that allows the processing of arbitrarily large and (at least locally) densely spaced, homogeneous sets of observations. The method is characterized by two independent features: First, for a problem at hand the least-squares collocation estimator is replaced by its corresponding global limit where it becomes a stable integral formula. This way the large (infinite dimensional) system of linear equations can be solved analytically. Moreover, since the integral formulas represents an optimal estimator a reliable error measure can be linked to it. Second, the integral formula is approximated by numerical integration, but directly based on the discrete point observations instead of the commonly used mean block values. The required area weights attached to each observation are derived from a numerical triangulation spread over all data points. In a first and preliminary test some 1 deg x 1 deg mean gravity anomalies were computed from GEOS-3 altimetry. (Author)