Signal detection in fractional Gaussian noise and an RKHS approach to robust detection and estimation

This thesis is divided into two parts. In the first part, the problem of signal detection in fractional Gaussian noise is considered. To facilitate the study of this problem, several results related to the reproducing kernel Hilbert space of fractional Brownian motion are presented. In particular, this reproducing kernel Hilbert space is characterized completely and an alternative characterization for the restriction of this class of functions to a compact interval (0,T) is given. Infinite-interval whitening filters for fractional Brownian motion are also developed. Application of these results to the signal detection problem yields necessary and sufficient conditions for a deterministic or stochastic signal to produce a nonsingular shift when embedded in additive fractional Gaussian noise. Also, a formula for the likelihood ratio corresponding to any deterministic nonsingular shift is developed. Finally, some results concerning detector performance in the presence of additive fractional Gaussian noise are presented.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Engineering, Electronics and Electrical

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Barton, Richard James

Contributors dc:contributor

• Poor, H.V.

• Engineering, Electronics and Electrical

Statement dc:rights

• Copyright 1989 Barton, Richard James

Language dc:language

eng

Identifier

AAI8916214
(UMI)AAI8916214

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23459