Geometric Filtering for Subspace Tracking

Anuj Srivastava, Eric Klassen

We address the problem of tracking principal subspaces using ideas from nonlinear filtering. The subspaces are represented by their complex projection-matrices, and time-varying subspaces correspond to trajectories on the Grassmann manifold. Under a Bayesian approach, we impose a smooth prior on the velocities associated with the subspace motion. This prior combined with any standard likelhood function forms a posterior density on the Grassmannian, for filtering and estimation. Using a sequential Monte Carlo method, a recursive nonlinear tracking algorithm is derived and some implementation results are presented.