Knowledge Bank

The variational equations, proposed by Obenson and proposed by Rapp, which are used to generate observation equation coefficients in the direct combination of satellite and gravimetric data are critically reviewed. Each procedure is tested with respect to accuracy as a function of step size, integration procedure, and orbit time. The two procedures are combined into a single program that combines the best features of the original proposals. The study concludes that if an orbit arc of less than 15 hours is being considered, Rapp's method with a fixed fourth-order predictor and a fifth order corrector gives the best results. If orbit arcs greater than 15 hours are being used, the combine solution composed of a fixed fourth order predictor and fifth order corrector for anomaly integration and Obenson's method for element integration gives the best results.