Relative position and attitude estimation of satellites in formation flying using Kalman filters and particle filter

Abstract

In this thesis, the Kalman Filter (EKF, UKF), and the Particle Filter algorithms have been designed to estimate the relative position of two satellites taking account of the effect of $J_2$ geopotential disturbing force, atmospheric drag, and the eccentricity in the reference orbit, having the relative range and speed between two satellites and attitude information of the chief satellite as measurements. Then, the quaternion-based EKF has also been designed to estimate the relative attitude making use of the relative position vectors, which are obtained by the pseudo-ranges generated by the transmitters and receivers fixed on the two satellites, and the direction cosine matrix(DCM). An overview of the relative orbit dynamics of two satellites with and without the effects of the $J_2$ disturbing force, atmospheric drag and eccentricity in the reference orbit is presented, followed by the relative attitude kinematics. Numerical simulations are performed under several circumstances for both the relative position estimation and the relative attitude estimation with the aforementioned measurements to verify not only the validity and feasibility of the measurements used for estimators but also the performances of the EKF, UKF, and PF algorithms.