The differential geometry of asymptotically efficient subspace estimation

Subspace estimation is often a prelude to parameter estimation. The underlying parameterization constrains the set of subspaces of interest and the singular value decomposition, which is the maximum likelihood (ML) estimator when rank is the only limitation, is not the ML subspace estimator for the parameter constrained problem. Using the Stiefel manifold formulation of the standard problem we establish intrinsic Cramer-Rao bounds for the constrained subspace estimation problem. In addition we establish an asymptotic ML formulation for the constrained problem which has a closed-form solution for the important special case of damped exponential signals on uniformly spaced sensor arrays.