Inclusion of second order information in the variational equations and batch least squares estimator
This thesis proposes a second order form of the batch least squares estimator for potential use in improving the gravity field estimation process for the GRACE-FO mission. The second order variational equations -- which introduce a State Transition Tensor that is verified with a combination of the complex step and finite differencing methods -- are incorporated into the approximation of the spacecraft state under several different combinations of force models to address nonlinearity in the orbit problem. When compared to the linear first order approximation in a sensitivity analysis, the second order form achieves results significantly closer to the simulated true trajectory in cases where the true and nominal trajectories share the same force model, and nearly equivalent solutions when their force models differ. The variational equations are then folded into the observation matrix for the batch least squares estimator, and two iterative algorithms are presented for the first and second order least squares estimators. Both estimators converge to approximately the same estimate for the nominal initial conditions, with faster convergence of the second order form when the the same force model is considered, and faster or equivalent convergence when the dynamics models differ.