Title :
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
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;
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
Print_ISBN :
978-1-4244-3871-6
Electronic_ISBN :
0191-2216
DOI :
10.1109/CDC.2009.5400249
