Effect of nonlinearities on orbit covariance propagation

Abstract

This thesis will examine the effect of nonlinearities on the propagation of orbit uncertainties in order to gain insight into the accurateness of the estimation of covariance with time. Many real-world applications rely on a first-order approximation of nonlinear equations of motion for propagation of orbit uncertainty. The nonlinear effects that are ignored during the linearization process can greatly influence the accuracy of the solution. A comparative analysis of linear and nonlinear orbit uncertainty propagation is presented in order to attempt to determine when linearized uncertainty becomes non-Gaussian. An examination of performance metrics is then accomplished to compare linearly propagated uncertainty to uncertainty propagated using a second-order approximation. An attempt is then made to develop a performance metric that determines when propagated uncertainty is no longer Gaussian. The results show it is difficult to determine a clear method of defining when the linear approximated uncertainty is no longer Gaussian, but there are metrics that can be implemented given a user-defined threshold of performance.