Signal detection in fractional Gaussian noise and an RKHS approach to robust detection and estimation
Barton, Richard James
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https://hdl.handle.net/2142/23459
Description
Title
Signal detection in fractional Gaussian noise and an RKHS approach to robust detection and estimation
Author(s)
Barton, Richard James
Issue Date
1989
Doctoral Committee Chair(s)
Poor, H.V.
Department of Study
Engineering, Electronics and Electrical
Discipline
Engineering, Electronics and Electrical
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
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.
In the second part of the thesis, the application of reproducing kernel Hilbert space theory to the problems of robust detection and estimation is investigated. It is shown that this approach provides a general and unified framework in which to analyze the problems of $L\sp2$ estimation, matched filtering, and quadratic detection in the presence of uncertainties regarding the second-order structure of the random processes involved. Minimax robust solutions to these problems are characterized completely, and some results concerning existence of robust solutions are presented.
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