The geometry of positive real functions with applications to the rational covariance extension problem

Author

Byrnes, Christopher I. ; Lindquist, Anders ; Gusev, Sergei V. ; Matveev, Alexei S.

Author_Institution

Washington Univ., St. Louis, MO, USA

Volume

4

fYear

1994

fDate

14-16 Dec 1994

Firstpage

3883

Abstract

In this paper we provide a characterization of all positive rational extensions of a given partial covariance sequence. Indeed, motivated by its application to signal processing, speech processing and stochastic realization theory, this characterization is in terms of a complete bianalytic parameterization using familiar objects from systems theory. In particular, this proves a long-standing conjecture by Georgiou. The methodology is based on global analysis of the dynamics of certain fast algorithms for Kalman filtering

Keywords

computational geometry; covariance analysis; filtering theory; identification; signal processing; stochastic processes; system theory; transfer functions; Kalman filtering; identification; partial covariance sequence; positive rational extensions; positive real functions; signal processing; speech processing; stochastic process; stochastic realization theory; systems theory; Algorithm design and analysis; Filtering algorithms; Geometry; Interpolation; Kalman filters; Polynomials; Signal processing algorithms; Speech processing; Stochastic processes; Stochastic systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1994., Proceedings of the 33rd IEEE Conference on

Conference_Location

Lake Buena Vista, FL

Print_ISBN

0-7803-1968-0

Type

conf

DOI

10.1109/CDC.1994.411772

Filename

411772