A nonlinear semi-analytic flltering method to sequentially estimate spacecraft states and their associated uncertainties is presented. We flrst discuss the state transition tensors that characterize the localized nonlinear behavior of the spacecraft trajectory and illustrate the importance of higher order efiects on orbit uncertainty propagation. We then present the semi-analytic flltering method by implementing the state transition tensors to sequentially update the information with contributions from each measurement, 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 fllter and unscented Kalman fllter.