# Bin Zhu: An Empirical Bayes Approach to Frequency Estimation

Abstract: In this talk, we show that the classical problem of frequency estimation can be formulated and solved efficiently in an empirical Bayesian framework by assigning a uniform a priori probability distribution to the unknown frequency. We discover that the covariance matrix of the signal model is the discrete-time counterpart of the operator whose eigenfunctions are the famous prolate spheroidal wave functions, introduced by Slepian and coworkers in the 1960's and widely studied in the signal processing literature although motivated by a different class of problems. The special structure of the covariance matrix is exploited to design an estimator for the hyperparameters of the prior distribution which is essentially linear, based on subspace identification. This is in contrast to standard parametric estimation methods which are based on iterative optimization algorithms of local nature. Simulations show that the approach is quite promising and seems to compare very favorably with classical methods from the literature.

Short Bio: Bin Zhu was born in Changshu, Jiangsu Province, China in 1991. He received the B.Eng.~degree from Xi'an Jiaotong 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. In 2019, he obtained a Ph.D. degree in information engineering from University of Padova, Padova, Italy, and now he is a postdoctoral researcher in the same university. His current research interest includes spectral estimation by rational covariance extension and Bayesian frequency estimation.

**Time: **
Fri 2019-10-11 11.00 - 12.00

**Location: **
F11

**Participating: **
Bin Zhu, postdoc from University of Padova