  This paper proposes a simple, accurate and computationally efficient method
to apply the ordinary unscented Kalman filter developed in Euclidean space to
systems whose dynamics evolve on manifolds.We use the mathematical theory
called stable embedding to make a variant of unscented Kalman filter that keeps
state estimates in closeproximity to the manifold while exhibiting excellent
estimation performance. We confirm the performance of our devised filter by
applying it to the satellite system model and comparing the performance with
other unscented Kalman filters devised specifically for systems on manifolds.
Our devised filter has a low estimation error, keeps the state estimates in
close proximity to the manifold as expected, and consumes a minor amount of
computation time. Also our devised filter is simple and easy to use because our
filter directly employs the off-the-shelf standard unscented Kalman filter
devised in Euclidean space without any particular manifold-structure-preserving
discretization method or coordinate transformation.
