Solving the so-called geodesic endpoint problem, i.e., finding a that connects two given points on manifold, is at basis of virtually all data processing operations, including averaging, clustering, interpolation and optimization. On Stiefel manifold orthonormal frames, this problem computationally involved. A remedy to use quasi-geodesics as replacement for Riemannian geodesics. Quasi-geodesic...

The Stiefel manifold Vp,d is the space of all d×p orthonormal matrices, and includes the d−1 hypersphere and the space of all orthogonal matrices as special cases. It is often desirable to parametrically or nonparametrically estimate the distribution of variables taking values on this manifold. Unfortunately, the intractable normalizing constant in the likelihood makes Bayesian inference challe...

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-d...