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Optimal estimation via nonanticipative rate distortion function and applications to time-varying Gauss-Markov processes
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en
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35
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SIAM Journal on Control and Optimization, Volume 56, issue 5, pp. 3731-3765
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.
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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. https://doi.org/10.1137/17M1116349