Improvements in Mars Gravity Field Determination Using Ridge-Type Estimation Methods

Abstract

The use of ridge-type estimation methods in determining the proper weighting of the a priori covariance appears to improve the accur acy of the Mars50c gravity field model derived from Viking and Mariner 9 Doppler tracking data. These advanced parameter estimation techniques were applied to the calculation of GM and a (50 × 50) field of harmonic coefficients, representing the gravitational potential of Mars. Calculation of the gravity field coefficients involves solving a large, ill-conditioned system of linear equations, whose solution leads to erroneous estimates if not augmented by appropriate a priori information. In calculating Mars50c, an a priori covariance was used in order to provide a set of constraints on the gravity field solution. This study involved the use of ridge-type estimation methods to optimally weight a set of a priori constraints based upon Kaula’s Rule in order to obtain more accurate estimates. The computed gravity field, denoted AUMGM9, was compared to Mars50c on the basis of total variance of the solution and residual sum of squares. Analysis of the results show that through the use of ridge-type estimation methods, AUMGM9 provides more accurate gravity field coefficients than does Mars50c.