Nonlinear Semi-Analytic Methods for Trajectory Estimation

Nonlinear semi-analytic filtering methods to sequentially estimate spacecraft states and their associated uncertainties are presented. We first discuss the state transition tensors that characterize the localized nonlinear behavior of the trajectory statistics and illustrate the importance of higher-order effects on orbit uncertainty propagation. We then present a semi-analytic filtering method by implementing the state transition tensors to sequentially update the filter information with contributions from eachmeasurement, which requires no integration once the tensors are computed. A sun–Earth halo orbit about the L1 point is considered as an example with realistic orbit uncertainties, and the results are compared with the extended Kalman filter and unscented Kalman filter.