  Dynamic state estimation, as opposed to kinematic state estimation, seeks to
estimate not only the orientation of a rigid body but also its angular
velocity, through Euler's equations of rotational motion. This paper
demonstrates that the dynamic state estimation problem can be reformulated as
estimating a probability distribution on a Lie group defined on phase space
(the product space of rotation and angular momentum). The propagation equations
are derived non-parametrically for the mean and covariance of the distribution.
It is also shown that the equations can be approximately solved by ignoring the
third and higher moments of the probability distribution. Numerical experiments
show that the distribution constructed from the propagated mean and covariance
fits the sample data better than an extended Kalman filter.
