Abstract—This paper considers the problem of
obtaining minimum-energy state estimates for a
system defined on the rotation group, SO(3). The
signals of the system are modeled as purely deterministic
signals. We derive a non-linear observer
(“filter”) posed directly on SO(3) that respects the
geometry of the group and achieves a performance
that is close to optimal in the sense of minimizing
an integral cost that is measuring the state energy.
The performance of the proposed filter is demonstrated
in simulations involving large initialization,
process and measurement errors where the results
are compared against a quaternion implementation
of an Extended Kalman Filter (EKF). Our results
indicate that the proposed filter achieves better
robustness against a range of noise levels and
initialization errors
