The structure of state covariances and its relation to the power spectrum of the input

Author

Georgiou, Tryphon T.

Author_Institution

Dept. of Electr. & Comput. Eng., Minnesota Univ., Minneapolis, MN, USA

Volume

47

Issue

7

fYear

2002

fDate

7/1/2002 12:00:00 AM

Firstpage

1056

Lastpage

1066

Abstract

We study the relationship between power spectra of stationary stochastic inputs to a linear filter and the corresponding state covariances, and identify the structure of positive-semidefinite matrices that qualify as state covariances of the filter. This structure is best revealed by a rank condition pertaining to the solvability of a linear equation involving the state covariance and the system matrices. We then characterize all input power spectra consistent with any specific state covariance. The parametrization of input spectra is achieved through a relation to solutions of an analytic interpolation problem which is analogous, but not equivalent, to a matricial Nehari problem

Keywords

filtering theory; interpolation; matrix algebra; spectral analysis; stochastic processes; input power spectrum; linear equation; linear filter; matricial Nehari problem; positive-semidefinite matrices; rank condition; spectral analysis; state covariances; stationary stochastic inputs; Covariance matrix; Equations; Interpolation; Inverse problems; Nonlinear filters; Spectral analysis; Statistical analysis; Stochastic processes; Time measurement; Vectors;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2002.800643

Filename

1017546