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

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

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)
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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.

Original languageEnglish
Pages (from-to)3731-3765
Number of pages35
JournalSIAM Journal on Control and Optimization
Volume56
Issue number5
DOIs
Publication statusPublished - 1 Jan 2018
MoE publication typeA1 Journal article-refereed

Keywords

  • Causal filters
  • Dynamic reverse-waterfilling
  • Mean-squared error distortion
  • Nonanticipative rate distortion function
  • Universal lower bound

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