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In this paper, the spacecraft attitude estimation problem has beeninvestigated making use of the concept of matrix Lie group. Through formulationof the attitude and gyroscope bias as elements of SE(3), the correspondingextended Kalman filter, termed as SE(3)-EKF, has been derived. It is shown thatthe resulting SE(3)-EKF is just the newly-derived geometric extended Kalmanfilter (GEKF) for spacecraft attitude estimation. This provides a newperspective on the GEKF besides the common frame errors definition. Moreover,the SE(3)-EKF with reference frame attitude error is also derived and theresulting algorithm bears much resemblance to the right invariant EKF.

SE(3) based Extended Kalman Filter for Spacecraft Attitude Estimation