On the linear-exponential filtering problem for general Gaussian processes

Author

Kleptsyna, M.L. ; Le Breton, A. ; Vio, M.

Author_Institution

Lab. de Statistique et Processus, Univ. du Maine, Le Mans, France

fYear

2009

fDate

15-18 Dec. 2009

Firstpage

2646

Lastpage

2651

Abstract

The explicit solution of the filtering problem with exponential criteria for a general Gaussian signal is obtained through an approach which is based on a conditional Cameron-Martin type formula. This key formula is derived for conditional expectations of exponentials of some quadratic functionals of a general continuous Gaussian process. The formula involves conditional expectations and conditional covariances in some auxiliary optimal risk-neutral filtering problem.

Keywords

Gaussian processes; filtering theory; Cameron-Martin type formula; auxiliary optimal risk-neutral filtering problem; conditional covariances; general Gaussian processes; linear-exponential filtering problem; quadratic functionals; Computer aided software engineering; Filtering; Gaussian processes; Integral equations; Leg; Maximum likelihood detection; Nonlinear filters; Performance analysis; Riccati equations; Signal processing; Gaussian process; Riccati-Volterra equation; exponential criteria; filtering error; optimal filtering; risk-sensitive filtering;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on

Conference_Location

Shanghai

ISSN

0191-2216

Print_ISBN

978-1-4244-3871-6

Electronic_ISBN

0191-2216

Type

conf

DOI

10.1109/CDC.2009.5400249

Filename

5400249