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OPTIMAL ESTIMATION VIA NONANTICIPATIVE RATE DISTORTION FUNCTION AND APPLICATIONS TO TIME-VARYING GAUSS-MARKOV PROCESSES
KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
Aalto Univ, Dept Elect Engn & Automat, Sch Elect Engn, Espoo, Finland..
Univ Cyprus, Dept Elect & Comp Engn, Nicosia, Cyprus..
Univ Ottawa, Sch Elect Engn & Comp Sci, Ottawa, ON K1N 6N5, Canada..
2018 (English)In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 56, no 5, p. 3731-3765Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
SIAM PUBLICATIONS , 2018. Vol. 56, no 5, p. 3731-3765
Keywords [en]
causal filters, nonanticipative rate distortion function, mean-squared error distortion, dynamic reverse-waterfilling, universal lower bound
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-238938DOI: 10.1137/17M1116349ISI: 000448810200025Scopus ID: 2-s2.0-85056113103OAI: oai:DiVA.org:kth-238938DiVA, id: diva2:1263029
Note

QC 20181114

Available from: 2018-11-14 Created: 2018-11-14 Last updated: 2018-11-16Bibliographically approved

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