  We derive symmetry preserving invariant extended Kalman filters (IEKF) on
matrix Lie groups. These Kalman filters have an advantage over conventional
extended Kalman filters as the error dynamics for such filters are independent
of the group configuration which, in turn, provides a uniform estimate of the
region of convergence. The proposed IEKF differs from existing techniques in
literature on the account that it is derived using minimal tools from
differential geometry that simplifies its representation and derivation to a
large extent. The filter error dynamics is defined on the Lie algebra directly
instead of identifying the Lie algebra with an Euclidean space or defining the
error dynamics in local coordinates using exponential map, and the associated
differential Riccati equations are described on the corresponding space of
linear operators using tensor algebra. The proposed filter is implemented for
the attitude dynamics of the rigid body, which is a benchmark problem in
control, and its performance is compared against a conventional extended Kalman
filter (EKF). Numerical experiments support that the IEKF is computationally
less intensive and gives better performance than the EKF.
