Stabilization of Subba Rao-Liporace models

Citation
M. Juntunen et al., Stabilization of Subba Rao-Liporace models, CIRC SYST S, 18(4), 1999, pp. 395-406
Citations number
22
Categorie Soggetti
Eletrical & Eletronics Engineeing
Journal title
CIRCUITS SYSTEMS AND SIGNAL PROCESSING
ISSN journal
0278081X → ACNP
Volume
18
Issue
4
Year of publication
1999
Pages
395 - 406
Database
ISI
SICI code
0278-081X(1999)18:4<395:SOSRM>2.0.ZU;2-L
Abstract
The stability of time-varying autoregressive (TVAR) models is an important issue in many applications such as time-varying spectral estimation, EEG si mulation and analysis, and time-varying linear prediction coding (TVLPC). F or stationary AR models there are methods that guarantee stability, but the for nonadaptive time-varying approaches there are no such methods. On the other hand, in some situations, such as in EEG analysis, the models that te mporarily exhibit roots with almost unit moduli are difficult to use. Thus we may need a tighter stability condition such as stability with margin 1 - rho. In this paper we propose a method for the estimation of TVAR models t hat guarantees stability with margin 1 - rho, that is, the moduli of the ro ots of the time-varying characteristic polynomial are less than or equal to some arbitrary positive number rho for every time instant. The model class is the Subba Rao-Liporace class, in which the time-varying coefficients ar e constrained to a subspace of the coefficient time evolutions. The method is based on sequential linearization of the associated nonlinear constraint s and the subsequent use of a Gauss-Newton-type algorithm. The method is al so applied to a simulated autoregressive process.