Particle Filtering On The Complex Stiefel Manifold With Application To Subspace Tracking

In this paper, we extend previous particle filtering methods whose states were constrained to the (real) Stiefel manifold to the complex case. The method is then applied to a Bayesian formulation of the subspace tracking problem. To implement the proposed particle filter, we modify a previous MCMC algorithm so as to simulate from densities defined on the complex manifold. Also, to compute subspace estimates from particle approximations, we extend existing averaging methods to complex Grassmannians. As we verify via numerical simulations, the proposed method is advantageous over traditional SVD-based subspace tracking algorithms for scenarios with low signal-to-noise ratio.