Quaternion Invariant Extended Kalman Filtering for Spacecraft Attitude Estimation

The spacecraft attitude estimation is addressed in the framework of invariant Kalman filtering, which rests on invariance of the system dynamics and output map with respect to appropriate coordinate transformations. The available measurements are assumed to be the angular velocity from three-axis gyroscopes and vector measurements from attitude sensors. Two continuous-discrete quaternion filters are developed from output state errors defined in the inertial frame and the spacecraft body frame, respectively. The former is termed the right-invariant extended Kalman filter and the latter is termed the left-invariant extended Kalman filter. These two filters both respect the norm constraint of the attitude quaternion but stem from different invariance properties of the system dynamics. It is shown that the left-invariant extended Kalman filter bears much resemblance to, and thus can be viewed as, a minor variant of the conventional quaternion multiplicative extended Kalman filter. The right-invariant extended Kalman filter possesses less dependence on the estimated trajectory and, as a result, better robustness than the left-invariant extended Kalman filter and multiplicative extended Kalman filter. Extensive Monte Carlo simulations of spacecraft attitude determination implementations demonstrate the advantageous performance of the right-invariant extended Kalman filter as compared to the left-invariant extended Kalman filter, multiplicative extended Kalman filter, and some of their improved variants.