Nonlinear Prediction in Marker-Based Spacecraft Pose Estimation with Polynomial Transition Maps

Spacecraft relative state estimation is of paramount importance in the problem of rendezvous with an uncooperative target; indeed, an accurate prediction of its relative position and attitude is crucial for safe proximity operations, especially considering autonomous guidance, navigation, and control. Therefore, a key point for the success of these missions is the development of efficient algorithms capable of limiting the computational burden without any reduction in performance. This paper addresses the issue proposing and analyzing nonlinear filters based on differential algebra. High-order numerical extended Kalman filter and unscented Kalman filter are developed in the differential algebra framework, and their performance is assessed and compared in terms of accuracy, robustness, and computational time, highlighting advantages and drawbacks. The European Space Agency e.deorbit mission, involving Envisat, is considered as the reference case, and the analysis is carried out through numerous numerical simulations, taking into account different measurement acquisition frequencies and levels of uncertainties.