  This paper considers the problem of optimal filtering for partially observed
signals taking values on the rotation group. More precisely, one or more
components are considered not to be available in the measurement of the
attitude of a 3D rigid body. In such cases, the observed signal takes its
values on a Stiefel manifold. It is demonstrated how to filter the observed
signal through the anti-development built from observations. A particle filter
implementation is proposed to perform the estimation of the signal partially
observed and corrupted by noise. The sampling issue is also addressed and
interpolation methods are introduced. Illustration of the proposed technique on
synthetic data demonstrates the ability of the approach to estimate the angular
velocity of a partially observed 3D system partially observed.
