Optimal estimation via nonanticipative rate distortion function and applications to time-varying Gauss-Markov processes

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Stavrou, Photios A.
dc.contributor.author Charalambous, Themistoklis
dc.contributor.author Charalambous, Charalambos D.
dc.contributor.author Loyka, Sergey
dc.date.accessioned 2018-12-21T10:29:53Z
dc.date.available 2018-12-21T10:29:53Z
dc.date.issued 2018-01-01
dc.identifier.citation Stavrou , P A , Charalambous , T , Charalambous , C D & Loyka , S 2018 , ' Optimal estimation via nonanticipative rate distortion function and applications to time-varying Gauss-Markov processes ' SIAM Journal on Control and Optimization , vol. 56 , no. 5 , pp. 3731-3765 . DOI: 10.1137/17M1116349 en
dc.identifier.issn 0363-0129
dc.identifier.issn 0095-7138
dc.identifier.other PURE UUID: 434989cb-35ad-4e31-be09-80487a38e8b8
dc.identifier.other PURE ITEMURL: https://research.aalto.fi/en/publications/optimal-estimation-via-nonanticipative-rate-distortion-function-and-applications-to-timevarying-gaussmarkov-processes(434989cb-35ad-4e31-be09-80487a38e8b8).html
dc.identifier.other PURE LINK: http://www.scopus.com/inward/record.url?scp=85056113103&partnerID=8YFLogxK
dc.identifier.other PURE FILEURL: https://research.aalto.fi/files/30346941/ELEC_Stavrou_etal_Optimal_Estimation_via_SIAMJCO_56_5_3731.pdf
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/35644
dc.description.abstract In this paper, we develop finite-time horizon causal filters for general processes taking values in Polish spaces using the nonanticipative rate distortion function (NRDF). Subsequently, we apply the NRDF to design optimal filters for time-varying vector-valued Gauss-Markov processes, subject to a mean-squared error (MSE) distortion. Unlike the classical Kalman filter design, the developed filters based on the NRDF are characterized parametrically by a dynamic reverse-waterfilling optimization problem obtained via Karush-Kuhn-Tucker conditions. We develop algorithms that provide, in general, tight upper bounds to the optimal solution to the dynamic reverse-waterfilling optimization problem subject to a total and per-letter MSE distortion constraint. Under certain conditions, these algorithms produce the optimal solutions. Further, we establish a universal lower bound on the total and per-letter MSE of any estimator of a Gaussian random process. Our theoretical framework is demonstrated via simple examples. en
dc.format.extent 35
dc.format.extent 3731-3765
dc.format.mimetype application/pdf
dc.language.iso en en
dc.relation.ispartofseries SIAM Journal on Control and Optimization en
dc.relation.ispartofseries Volume 56, issue 5 en
dc.rights openAccess en
dc.subject.other Control and Optimization en
dc.subject.other Applied Mathematics en
dc.subject.other 111 Mathematics en
dc.title Optimal estimation via nonanticipative rate distortion function and applications to time-varying Gauss-Markov processes en
dc.type A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä fi
dc.description.version Peer reviewed en
dc.contributor.department KTH Royal Institute of Technology
dc.contributor.department Department of Electrical Engineering and Automation
dc.contributor.department University of Cyprus
dc.contributor.department University of Ottawa
dc.subject.keyword Causal filters
dc.subject.keyword Dynamic reverse-waterfilling
dc.subject.keyword Mean-squared error distortion
dc.subject.keyword Nonanticipative rate distortion function
dc.subject.keyword Universal lower bound
dc.subject.keyword Control and Optimization
dc.subject.keyword Applied Mathematics
dc.subject.keyword 111 Mathematics
dc.identifier.urn URN:NBN:fi:aalto-201812216652
dc.identifier.doi 10.1137/17M1116349
dc.type.version acceptedVersion

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