Subspace Tracking with Dynamical Models on the Grassmannian

Alex Saad-Falcon, Brighton Ancelin, Justin Romberg

Abstract: Tracking signals in dynamic environments presents difficulties in both analysis and implementation. In this work, we expand on a class of subspace tracking algorithms which utilize the Grassmann manifold - the set of linear subspaces of a high-dimensional vector space. We design regularized least squares algorithms based on common manifold operations and intuitive dynamical models. We demonstrate the efficacy of the approach for a narrowband beamforming scenario, where the dynamics of multiple signals of interest are captured by motion on the Grassmannian.