Set-membership estimations for relative trajectory between two satellites

Estimating the relative pose (position and attitude) between two satellites is a challenging problem. Most of the existing methods tackling this problem rely on stochastic approaches, as, for example, the well-known Extended Kalman Filter (EKF). However, the use of such methods has some limits: they are based on a knowledge of the density function of sensor noises, that are hard to be obtained in practice, and do not give any guarantee on the state estimation set. In this paper, two alternative methods, based on set-membership approaches, are proposed. Such methods do not need any statistical property and provide sets guaranteed to contain the true state. This paper focuses on zonotopic and ellipsoidal state estimation to compute bounds of the satellites relative state. Simulations are provided in order to illustrate the benefits of the methods.