Riemannian subspace tracking algorithms on Grassmann manifolds

Based on the differential geometry of the Grassmann manifold, we propose a new class of Newton-type algorithms for adaptively computing the principal and minor subspaces of a time-varying family of symmetric matrices. Using local parameterization of the Grassmann manifold, simple expressions for the subspace tracking schemes are derived. Key benefits of the algorithms are (a) the reduced computational complexity due to efficient parametrizations of the Grassmannian and (b) their guaranteed accuracy during all iterates. Numerical simulations illustrate the feasibility of the approach.