Station-Keeping for Periodic Orbit Manifolds in Cislunar Space via a Polynomial Approach

This paper presents an integrated framework for cislunar station-keeping, combining orbit tracking and state estimation. A novel nonlinear model predictive control (NMPC) scheme is developed to maintain a spacecraft within a periodic orbit family near a libration point. Rather than tracking a single predefined orbit, the proposed optimizer uses a reduced-order multivariate polynomial regression model to dynamically select the most fuel-efficient reference orbit within the family and compute the necessary thruster burns. To estimate the spacecraft’s relative states, this NMPC is paired with a new double high-order filter based on differential algebra. The filter processes relative line-of-sight and range measurements and uses polynomial representations to compute high-order moments for improved state estimates. All uncertainties are modeled as nonadditive Gaussian noise with known covariance. The circular restricted three-body problem is used to represent the system dynamics for both guidance and state estimation algorithms. Numerical simulations show that the proposed NMPC significantly reduces fuel consumption compared to conventional methods. The proposed filter achieves superior convergence speed and steady-state accuracy. Monte Carlo analysis confirms the reliability of the integrated framework across various initial conditions.