An Optimization Approach to the Spectral Estimation Problem for Stationary Random Vector Fields

Time: 15:00-16:00, 08/05/2019
Location: Room 210, building 336, south campus of Sun Yat-sen University
Speaker: Bin Zhu, Doctor
Hoster: Yao Lu, Professor

Short bio: Bin Zhu was born in Changshu, Jiangsu Province, China in 1991. He received the B.Eng. degree from Xi’an Jiao Tong University, Xi’an, China in 2012 and the M.Eng. degree from Shanghai Jiao Tong University, Shanghai, China in 2015, both in control science and engineering. He is now a postdoctoral researcher at the Department of Information Engineering, University of Padova, Padova, Italy. His current research interests include spectral estimation, rational covariance extension, and ARMA modeling.

Abstract: Spectral estimation for random signals is an important problem in modeling, identification, and signal processing. A modern approach called “THREE”, was originally built upon the idea of covariance extension, where one aims to find a spectral density function that satisfies a finite number of linear integral equations. This is an inverse problem that in general admits infinitely many solutions. In order to select the solutions that are of system-theoretic interest, optimization with entropy-like functionals is advocated in the literature.

In this talk, we will present an extension of the “THREE” spectral estimation technique to handle stationary random vector fields, namely vector-valued processes that are indexed in a multidimensional integer lattice. The multidimensional Itakura-Saito distance is employed in our optimization problem where the moment equations are viewed as constraints. In order to avoid technicalities that may happen on the boundary of the feasible set, we deal with the discrete version of the problem where the multidimensional integrals are approximated by Riemann sums. The solution spectrum is also discrete, which occurs naturally when the underlying random field is periodic. We show that a solution to the discrete problem exists and is unique. Moreover, the solution depends smoothly on the problem data. Therefore, we have a well-posed problem whose solution can be tuned in a smooth manner.

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