Filtering with fidelity for time-varying Gauss-Markov processes

Photios A. Stavrou, Themistoklis Charalambous, Charalambos D. Charalambous

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

12 Citations (Scopus)

Abstract

In this paper, we revisit the relation between Nonanticipative Rate Distortion (NRD) theory and real-time realizable filtering theory. Specifically, we give the closed form expression for the optimal nonstationary (time-varying) reproduction distribution of the Finite Time Horizon (FTH) Nonanticipative Rate Distortion Function (NRDF) and we establish its connection to real-time realizable filtering theory via a realization scheme utilizing time-varying fully observable multidimensional Gauss-Markov processes. As an application we provide the optimal filter with respect to a mean square error constraint. Unlike classical filtering theory, our filtering approach based on FTH NRDF is performed with waterfilling. We also derive a universal lower bound to the mean square error of any causal estimator to Gaussian processes based on the closed form expression of FTH NRDF. Our theoretical results are demonstrated via an illustrative example.

Original languageEnglish
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherIEEE
Pages5465-5470
Number of pages6
ISBN (Electronic)9781509018376
DOIs
Publication statusPublished - 27 Dec 2016
MoE publication typeA4 Article in a conference publication
EventIEEE Conference on Decision and Control - ARIA Resort & Casino, Las Vegas, United States
Duration: 12 Dec 201614 Dec 2016
Conference number: 55

Conference

ConferenceIEEE Conference on Decision and Control
Abbreviated titleCDC
CountryUnited States
CityLas Vegas
Period12/12/201614/12/2016

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    Stavrou, P. A., Charalambous, T., & Charalambous, C. D. (2016). Filtering with fidelity for time-varying Gauss-Markov processes. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 (pp. 5465-5470). [7799108] IEEE. https://doi.org/10.1109/CDC.2016.7799108