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arXiv · 2402.10352

Subspace Tracking with Dynamical Models on the Grassmannian

Alex Saad-Falcon·Brighton Ancelin·Justin Romberg
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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.

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Alex Saad-Falcon, Brighton Ancelin, Justin Romberg. 2024-02-15. Subspace Tracking with Dynamical Models on the Grassmannian. https://arxiv.org/abs/2402.10352

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