Bayesian Filtering on the Stiefel Manifold

The Stiefel manifold comprises sets of orthonormal vectors in Euclidean space, and as such arises in a variety of contemporary statistical signal processing contexts. Here we consider the problem of estimating the state of a hidden Markov process evolving on this manifold, given noisy observations in the embedding Euclidean space. We describe an approach using sequential Monte Carlo methods, and provide simulation examples for several cases of interest. We also compare our framework to a recently proposed deterministic algorithm for mode tracking in a related context, and demonstrate superior tracking performance over a range of synthetic examples, albeit at a potentially higher computational cost.