  In this paper, the well-known multiplicative extended Kalman filter (MEKF) is
re-investigated for attitude estimation using vector observations. From the Lie
group theory, it is shown that the attitude estimation model is group affine
and its error state model should be trajectory-independent. Moreover, with such
trajectory-independent error state model, the linear Kalman filter is still
effective for large initialization errors. However, the measurement model of
the traditional MEKF is dependent on the attitude prediction, which is
therefore trajectory-dependent. This is also the main reason why the
performance of traditional MEKF is degraded for large initialization errors.
Through substitution of the attitude prediction related term with the vector
observation in body frame, a trajectory-independent measurement model is
derived for MEKF. Meanwhile, the MEKFs with reference attitude error definition
and with global state formulating on special Euclidean group have also been
studied, with main focus on derivation of the trajectory-independent
measurement models. Extensive Monte Carlo simulations and field test of
attitude estimation implementations demonstrate that the performance of MEKFs
can be much improved with trajectory-independent measurement models.
