  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.
