Optimal linear-quadratic systems for detection and estimation

Author

Picinbono, Bernard ; Devaut, P.

Author_Institution

Lab. des Signaux et Syst., Gif-sur-Yvette, France

Volume

34

Issue

2

fYear

1988

fDate

3/1/1988 12:00:00 AM

Firstpage

304

Lastpage

311

Abstract

The problem of linear-quadratic systems for detection has long been solved by assuming the deflection criterion and Gaussian noise. It is shown here that the Gaussian assumption can be removed, and a complete solution is presented for an arbitrary probability distribution with finite fourth-order moments. The optimal solution can always be obtained by solving a linear system of equations. Some properties of the optimal systems are developed for particular examples of nonGaussian noise. It is shown that there is a strong relationship between linear-quadratic optimal detection and optimal estimation, which extends results known for the purely linear case

Keywords

estimation theory; probability; signal detection; arbitrary probability distribution; finite fourth-order moments; linear-quadratic systems; nonGaussian noise; optimal detection; optimal estimation; optimal solution; signal detection; Covariance matrix; Equations; Gaussian noise; Linear systems; Matched filters; Probability distribution; Signal detection; Symmetric matrices; System testing; Vectors;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.2638

Filename

2638