Extended Kalman filtering for pico-satellites attitude determination

The extended Kalman filter (EKF) algorithm has been applied widely in orbital guidance and navigations problems for miniand micro-satellites. This paper evaluates the performance and computational complexity of EKF for smaller satellites. The impact of some limitations, including low power and computing capabilities on the implementation of EKF in smaller satellites is also addressed. The filter formulation is based on a kinematics model propagated with three-axis rate integrating gyros, where the attitude is parameterized using quaternions. A multiplicative quaternion-error approach is used to define the attitude error, which ensures that quaternion normalization is maintained. The results indicate that the EKF is sensitive to initial conditions. Using TRIAD algorithm to determine initial conditions, the filter converges after 50 minutes with an average error of 1.5°, but may diverge for extreme cases. The time and space complexities of EKF have also been estimated to be O(n³) and O(n²), respectively.