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

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Stavrou, Photios A. Charalambous, Themistoklis Loyka, Sergey Charalambous, Charalambos D.
Copyright Year	2018
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.
Starting Page	3731
Ending Page	3765
Page Count	35
File Format	PDF
ISSN	03630129
DOI	10.1137/17M1116349
e-ISSN	10957138
Issue Number	5
Volume Number	56
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2018-10-16
Access Restriction	Subscribed
Subject Keyword	causal filters Stochastic systems, general Rate-distortion theory nonanticipative rate distortion function Iterative methods for linear systems Norms of matrices, numerical range, applications of functional analysis to matrix theory dynamic reverse-waterfilling universal lower bound Convex programming mean-squared error distortion
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics

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