SE(3) based Extended Kalman Filter for Spacecraft Attitude Estimation
This work addresses attitude estimation for spacecraft, offering an incremental improvement by re-deriving an existing filter with a new mathematical framework.
The paper tackled spacecraft attitude estimation by formulating attitude and gyroscope bias as elements of SE(3) to derive an extended Kalman filter, termed SE(3)-EKF, which is shown to be equivalent to the geometric extended Kalman filter (GEKF), providing a new perspective on this method.
In this paper, the spacecraft attitude estimation problem has been investigated making use of the concept of matrix Lie group. Through formulation of the attitude and gyroscope bias as elements of SE(3), the corresponding extended Kalman filter, termed as SE(3)-EKF, has been derived. It is shown that the resulting SE(3)-EKF is just the newly-derived geometric extended Kalman filter (GEKF) for spacecraft attitude estimation. This provides a new perspective on the GEKF besides the common frame errors definition. Moreover, the SE(3)-EKF with reference frame attitude error is also derived and the resulting algorithm bears much resemblance to the right invariant EKF.