Optimal Estimation via Nonanticipative Rate Distortion Function and Applications to Time-Varying Gauss-Markov Processes

In this paper, we develop finite-time horizon causal filters using the nonanticipative rate distortion theory. We apply the developed theory to design optimal filters for time-varying multidimensional Gauss-Markov processes, subject to a mean square error fidelity constraint. We show that such filte...

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Bibliographic Details
Main Authors Stavrou, Photios A, Charalambous, Themistoklis, Charalambous, Charalambos D, Loyka, Sergey
Format Journal Article
LanguageEnglish
Published 14.03.2016
Subjects
Computer Science - Information Theory
Mathematics - Dynamical Systems
Mathematics - Information Theory
Mathematics - Optimization and Control
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DOI10.48550/arxiv.1603.04172

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Summary:In this paper, we develop finite-time horizon causal filters using the nonanticipative rate distortion theory. We apply the developed theory to design optimal filters for time-varying multidimensional Gauss-Markov processes, subject to a mean square error fidelity constraint. We show that such filters are equivalent to the design of an optimal \encoder, channel, decoder\, which ensures that the error satisfies a fidelity constraint. Moreover, we derive a universal lower bound on the mean square error of any estimator of time-varying multidimensional Gauss-Markov processes in terms of conditional mutual information. Unlike classical Kalman filters, the filter developed is characterized by a reverse-waterfilling algorithm, which ensures that the fidelity constraint is satisfied. The theoretical results are demonstrated via illustrative examples.
DOI:10.48550/arxiv.1603.04172