Implementation of an Unscented Kalman Filter for Attitude Determination of a Satellite with a Rotating Antenna.

As part of the development of ESA’s Earth Explorer 11 mission, the Politecnico di Torino has contributed to the design of WIVERN (WInd VElocity Radar Nephoscope), a future Earth observation mission aiming at characterizing global winds, clouds and precipitation by employing a fast-rotating, conically scanning Doppler radar antenna. In this work the primary focus is on the line-of-sigh (LOS) Doppler relative velocity measurement errors, induced by the spacecraft Attitude Determination and Control System (ADCS). The estimation of the misalignment of the antenna pointing is critical, as errors in its determination directly affect the accuracy of the observed wind, as even small angles lead to relative velocity errors along the boresight due to the high orbital speed of the satellite. This study expands on previous work carried out at Politecnico di Torino, where during the past years a numerical simulator of the Attitude and Orbit Control System (AOCS) of the WIVERN multibody spacecraft was developed. Currently, the implemented determination system adopts a full suite of sensors (star trackers, gyroscope and encoder) and an Extended Kalman Filter (EKF) as the observer algorithm, delivering overall satisfactory results. However, for nonlinear estimation problems and highly complex systems, the EKF may not provide optimal performance, motivating the exploration of more advanced filtering techniques. In this study, an Unscented Kalman Filter (UKF) is proposed for the WIVERN satellite attitude determination, exploring different solutions in its implementation. Initially, a standard UKF with a linear measurement model is considered. Subsequently, alternative approaches are investigated to further improve accuracy. Different simulations in nominal conditions (i.e. with system parameters at expected without perturbations) and Monte Carlo analysis were performed, demonstrating that the attitude determination system can satisfy the maximum Absolute Knowledge Error (AKE) requirements of 100 µrad per axis and 1 m/s for the main body attitude and LOS velocity, respectively. Furthermore, the performances of the UKF and EKF were compared under similar conditions, to better assess the differences between the two solutions. In particular, the critical issues related to antenna unbalance were studied through simulations of worst cases and Monte Carlo campaigns, confirming that the implemented UKF presents acceptable performances and robustness.