We consider the problem of subspace estimation in a Bayesian setting. Since we are operating in the Grassmann manifold, the usual approach which consists of minimizing the mean square error (MSE) between the true subspace U and its estimateÛ may not be adequate as the MSE is not the natural metric in the Grassmann manifold. As an alternative, we propose to carry out subspace estimation by minimizing the mean square distance (MSD) between U and its estimate, where the considered distance is a natural metric in the Grassmann manifold, viz. the distance between the projection matrices. We show that the resulting estimator is no longer the posterior mean of U
In REF , the authors formulate the optimal subspace estimator which minimizes the mean square (subspace) distance.
Minimum mean square distance estimation of a subspace
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Computer Science Mathematics