Improving gravity field determination in ill-conditioned inverse problems

Abstract

It is well known that the determination of the Earth's gravity field from satellite observational data in ill-conditioned inverse problems can provide inaccurate results. A usual practice to overcome the effects of this ill-conditioning is the addition of a priori covariance information (on the nominal solution) into the solution process. This technique will bias the estimates toward the nominal solution and tend to stabilize the calculations. A problem with this method however, is that the recovery of the gravitational and nongravitational parameters depends too strongly on the a priori statistics used instead of the observational data. It has been shown recently that the estimates in unobservable (singular) orbit determination problems can be improved in such situations by scaling optimally the a priori covariance through the use of “ridge-type” estimation methods. The work presented here concentrates on the improvement in the accuracy of gravitational field recovery using ridge-type estimation methods in observable (full-rank) but ill-conditioned inverse problems without the use of a priori statistics. These types of problems are more representative of real-world situations. The results of such a gravity field determination simulation are presented, the accuracy of which is compared to the accuracy of the gravity field obtained by standard minimum variance estimation methods.