Subspace tracking via rigid body dynamics

The problem of estimating or tracking the time-varying principal components of a data covariance is considered. We assert that the incorporation of some notion of subspace motion or dynamics will make possible the application of subspace-based direction-finding or beamforming algorithms in scenarios which otherwise would be considered data-starved. An ordinary differential equation for simple uniform motion in the space of projection matrices is developed. This dynamical model is then used along with the artificial assumption of subspace sphericalization in a Gaussian data model, from which the cost function for maximum-likelihood estimation of subspace motion parameters is derived. Approaches to computing these subspace parameters in the one-dimensional case are proposed