Robust 6-DOF State Estimation for Spacecraft Proximity Operations Using Zonotopic Set Membership Based Kalman Filtering

This paper introduces a hybrid estimation and control framework that combines zonotopic set-membership filtering with the Extended Kalman Filter (EKF) for robust six-degree-of freedom (6-DOF) state estimation and guidance in spacecraft rendezvous and proximity operations. The proposed approach simultaneously addresses translational and rotational dynamics in the presence of stochastic noise and unknown-but-bounded (UBB) disturbances. A nonlinear system model is linearized via Taylor series expansion, where the Lagrange remainder and UBB uncertainties are bounded using zonotopes. These bounds are incorporated within a Kalman filtering framework, and the Kalman gain is optimized to minimize the mean-squared estimation error. The resulting Zonotopic Set-Membership Kalman Filter (ZSM-KF) accounts for stochastic, UBB, and linearization errors in a unified manner, overcoming key limitations of conventional EKF methods. The estimated states from the hybrid filter are integrated into a time-varying Model Predictive Control (MPC) scheme to enable feedback-based, constraint aware guidance. Simulation results with full 6-DOF spacecraft dynamics demonstrate enhanced robustness, estimation accuracy, and control performance compared to standard EKF-based approaches.