Abstract: A method estimates a state of a spacecraft in a planet-moon environment by executing iteratively a particle filter. The particle filter comprising integrates individually states of each particle of the particle filter according to a probability-evolution equation using a model of the state of the spacecraft represented as a planar circular restricted three-body problem and determines a prior probability of each particle as a previous posterior probability of a corresponding particle during a previous iteration. A joint probability distribution of the state of the spacecraft is determines using the states of each particle and the prior probabilities of each particle and the states and the prior probabilities of each particle are updated according to the joint probability distribution of the state of the spacecraft and a measurement of the state of the spacecraft to produce posterior probabilities of each particle.

Abstract: A motion of an object is controlled from a geostationary transit orbit (GTO) of an earth to an orbit of a moon. A first trajectory of the motion of the object is determined from an intermediate orbit of an earth to a neighborhood of a stable manifold of a first Lagrange point (L1). A second trajectory of the motion of the object is determined from the GTO to the intermediate orbit. A third trajectory of the motion of the object is determined from the neighborhood to the stable manifold to an L1 orbit, and a fourth trajectory of the motion of the object is determined from the L1 orbit to the orbit of the moon. A trajectory from the GTO to the orbit of the moon is determined based on a combination of the first, the second, the third, and the fourth trajectories.