A New Family of High-Resolution Multivariate Spectral Estimators

Abstract

In this paper, we extend the Beta divergence family to multivariate power spectral densities. Similarly to the scalar case, we show that it smoothly connects the multivariate Kullback-Leibler divergence with the multivariate Itakura-Saito distance. We successively study a spectrum approximation problem, based on the Beta divergence family, which is related to a multivariate extension of the THREE spectral estimation technique. It is then possible to characterize a family of solutions to the problem. An upper bound on the complexity of these solutions will also be provided. Finally, we will show that the most suitable solution of this family depends on the specific features required from the estimation problem

Fusion of Sensors Data in Automotive Radar Systems: A Spectral Estimation Approach

“…as the domain of the real-valued window function w(·), and discard those covariance estimates (21) with indices k outside the set Λ. The resulting spectrum estimator iŝ…”

“…This means that the steps to get the covariance estimates in (21) given the data array y(t), t ∈ Z 3 N are the following three:…”

Empirical Bayesian learning in AR graphical models

“…As a consequence, the estimator proposed by is strictly connected with the generalized moment problems in the sense of Byrnes-Georgiou-Lindquist which have been extensively studied by many researchers, e.g. Byrnes et al (2000); Ferrante et al (2012); Karlsson & Georgiou (2013); Zorzi ( , 2014aZorzi ( , 2014b. Since then, many other extensions has been proposed: Maanan et al (2017) proposed a two stage approach to estimate sparse AR graphical models; Alpago et al (2018) proposed a regularized estimator for sparse graphical models of reciprocal processes; Chandrasekaran et al (2010), Zorzi & Sepulchre (2016), Maanan et al (2018), Liégeois et al (2015) and Ciccone et al (2018) proposed regularized estimators for the so called latent-variable graphical models.…”

Maximum likelihood gradient identification for multivariate equation‐error moving average systems using the multi‐innovation theory

“…17,18 In this field, Wang and Ding proposed two recursive identification algorithms for the multivariate systems with ARMA noise and analyzed their performance. 20 Recently, Zorzi presented a new family of high-resolution multivariate spectral estimators 21 and a multivariate spectral estimation algorithm based on the concept of optimal prediction. 20 Recently, Zorzi presented a new family of high-resolution multivariate spectral estimators 21 and a multivariate spectral estimation algorithm based on the concept of optimal prediction.…”

“…19 Based on the auxiliary model identification idea, a filtering-based auxiliary model recursive generalized least squares method is derived for the multivariate output-error systems with autoregressive noise. 20 Recently, Zorzi presented a new family of high-resolution multivariate spectral estimators 21 and a multivariate spectral estimation algorithm based on the concept of optimal prediction. 22 This paper addresses the identification problems of the multivariate equation-error moving average systems.…”