Federated Unscented Kalman Filter Design for Multiple Satellites Formation Flying in LEO

Abstract

The main focus of this paper is to design a more accurate optimal/suboptimal fault tolerant state estimator for relative dynamic model representing formation flying of two satellites in low earth orbit (LEO). First of all a mathematical model describing the relative dynamic motion of two satellites in formation is derived and next state estimation based on Kalman filter is emphasized. The measurement system comprises of a RADAR sensor installed on the leader satellite which measures the relative position, azimuth and elevation angle of the follower satellite with respect to reference satellite and carrier phase differential GPS (CDGPS) sensor measuring relative position directly. We have adopted nonlinear system and measurement models and used more advanced nonlinear filtering method called Unscented Kalman filter (UKF) in this paper in pursue of better state estimator in a nonlinear environment. Also we are using more than one sensor to measure same state hence this becomes a multisensor data fusion problem. We implement a federated UKF and apply fault detection and isolation (FDI) algorithms to get a fault tolerant filter. A comparison of Unscented Kalman filter and extended Kalman filter has been made to show superior performance of UKF.