Relative State Estimation of Satellite Formation Flying Using Kalman Filter

In this paper, an approach is proposed for relative state estimation for satellites in formation flying. To estimate the relative states of two satellites, the Kalman Filter algorithms (EKF, UKF) are adopted with the relative range and range rate between two satellites and attitude of a satellite as measurement variables. In case that the initial state and measurements errors are moderate, both EKF and UKF perform well. As those errors increase, however, the EKF degrades unlike the UKF. Numerical simulations are performed under two circumstances. The first one presented both chief and deputy satellites are orbiting a circular reference orbit around a perfectly spherical Earth model with no disturbing acceleration, in which the elementary relative orbital dynamics are taken into account. In reality however, the Earth is not a perfect sphere, but rather an oblate spheroid. Both satellites are under the effect of 2 J geopotential disturbance, which causes the relative distance between two satellites to increase gradually. The near-Earth orbit decays as a result of atmospheric drag. In order to remove the modeling error, the second scenario incorporates the effect of 2 J geopotential disturbing force, atmospheric drag, and the eccentricity.