  Dynamic subspace estimation, or subspace tracking, is a fundamental problem
in statistical signal processing and machine learning. This paper considers a
geodesic model for time-varying subspaces. The natural objective function for
this model is non-convex. We propose a novel algorithm for minimizing this
objective and estimating the parameters of the model from data with
Grassmannian-constrained optimization. We show that with this algorithm, the
objective is monotonically non-increasing. We demonstrate the performance of
this model and our algorithm on synthetic data, video data, and dynamic fMRI
data.
