Unscented Kalman Filter for Spacecraft Attitude Estimation and Calibration Using Magnetometer Measurements

This paper develops an unscented Kalman filter (UKF) in an attempt to solve the spacecraft attitude estimation and calibration problem based only magnetometer measurements. Three-component Rodrigues parameters are used to describe attitude vector, which avoids the singularity of the covariance matrix when using unit quaternion in attitude determination. In addition, in order to reduce computational costs of estimators, a better-behaved sigma point selection strategy of unscented transformation (UT) for UKF, spherical simplex sigma, is investigated. The UKF estimator is tested through numeric simulation of a fully actuated rigid body with only magnetometer. For comparison, an extended Kalman filter (EKF) estimator is also developed and is used to gauge the performance of UKF estimator. The results presented in this paper clearly demonstrate the UKF is superior to EKF in coping with the nonlinearity of attitude dynamics in the presence of model uncertainties.