Tryphon Georgiou — Page 2

arXiv2014

Stochastic bridges of linear systems

We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed to have known states at the boundary. Thus, the movement of the particles can be modeled as an Ornstein-Uhlenbeck process conditioned on position and velocity measurements at the two end-points. It is shown that optimal stochastic control provides a stochastic differential equation (SDE) that generates such a bridge as a degenerate diffusion process. Generalizations to higher order linear diffusions are considered.

eess.SY↗

arXiv2011

Geometric methods for estimation of structured covariances

We consider problems of estimation of structured covariance matrices, and in particular of matrices with a Toeplitz structure. We follow a geometric viewpoint that is based on some suitable notion of distance. To this end, we overview and compare several alternatives metrics and divergence measures. We advocate a specific one which represents the Wasserstein distance between the corresponding Gaussians distributions and show that it coincides with the so-called Bures/Hellinger distance between covariance matrices as well. Most importantly, besides the physically appealing interpretation, computation of the metric requires solving a linear matrix inequality (LMI). As a consequence, computations scale nicely for problems involving large covariance matrices, and linear prior constraints on the covariance structure are easy to handle. We compare this transportation/Bures/Hellinger metric with the maximum likelihood and the Burg methods as to their performance with regard to estimation of power spectra with spectral lines on a representative case study from the literature.

math.OC↗