Generalized least squares innovation representation
type: Item
instance of: scholarly article
title: Generalized least squares innovation representation
zbMATH Open document ID: 0653.93061
DOI: 10.1016/0898-1221(88)90157-5
publication date: 1988-01-01T00:00:00Z
review text: The paper gives a unified approach to the stochastic realization problem of finite dimensional discrete-time stochastic systems. If y(t)\(\in R\) m is a discrete weakly stationary stochastic process, then using different bases in the spaces of its future - generated by y(0), y(1),... and its past - generated by y(-1), y(-2),... - we can define different algorithms for the matrices in its innovation representation. The essence of these algorithms is: (i) compose a Hankel matrix based on the covariances of some random variables generating the future and the past, respectively; (ii) factor the elements of this Hankel-matrix using the Ho-Kalman algorithm; (iii) using some Riccati equations to obtain the required matrices. Using the unnormalized forward and backward innovations of y(t) as bases in the future and the past we get Faurre's algorithm, using normalized innovations we get the Desai-Pal algorithm, using unnormalized innovations in the future space and normalized innovations in the past space we get the algorithm which is discussed in the paper and called GLS IR algorithm.
Mathematics Subject Classification ID: 93E12
Mathematics Subject Classification ID: 93B15
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 93E25
zbMATH DE Number: 4066764
zbMATH Keywords: generalized least squares algorithm
zbMATH Keywords: stochastic realization
zbMATH Keywords: finite dimensional discrete-time stochastic systems
zbMATH Keywords: innovation representation
zbMATH Keywords: Hankel matrix
zbMATH Keywords: Riccati equations
author: István Bencsik
author: György Michaletzky
MaRDI profile type: Publication
full work available at URL: 0898-1221(88)90157-5
OpenAlex ID: W1984578514
cites work: Markovian Representation of Stochastic Processes by Canonical Variables
cites work: All optimal Hankel-norm approximations of linear multivariable systems and theirL,∞-error bounds†
cites work: Q5638871
cites work: Identification of errors-in-variables models with Faurre type realization algorithms
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4066764