{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23459"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23459","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Signal detection in fractional Gaussian noise and an RKHS approach to robust detection and estimation","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Barton, Richard James"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Engineering, Electronics and Electrical","degree_department":null,"school":null,"contributors":["Poor, H.V."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T14:14:57Z","date_published":"2011-05-07T14:14:57Z","updated_at":"2026-07-22T22:25:22Z","subjects":["Engineering, Electronics and Electrical"],"languages":["eng"],"rights":["Copyright 1989 Barton, Richard James"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI8916214","(UMI)AAI8916214"],"render_values":[{"text":"AAI8916214","href":null,"code":true},{"text":"(UMI)AAI8916214","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23459","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Poor, H.V."]},{"key":"dc:creator","label":"Author","values":["Barton, Richard James"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T14:14:57Z","10000-01-01","1989"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering, Electronics and Electrical"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engineering, Electronics and Electrical"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1989 Barton, Richard James"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI8916214","(UMI)AAI8916214","http://hdl.handle.net/2142/23459"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Made available in DSpace on 2011-05-07T14:14:57Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 8916214.pdf: 3845488 bytes, checksum: 2a37bf9952ae4cf84b4e57b2404184ec (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:04:37Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:30:53-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Signal detection in fractional Gaussian noise and an RKHS approach to robust detection and estimation"]}]}],"canonical_facts":{"dc:contributor":["Poor, H.V."],"dc:creator":["Barton, Richard James"],"dc:date":["2011-05-07T14:14:57Z","10000-01-01","1989"],"dc:description":["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.","Made available in DSpace on 2011-05-07T14:14:57Z (GMT). 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