Zero-delay rate-distortion optimization for partially observable Gauss-Markov processes

In this paper, we consider rate-distortion tradeoff problems for time-varying, multi-dimensional, partially observable Gauss-Markov processes subject to the zero-delay constraint. As a distortion metric, we consider the mean square error between the hidden state process and the reconstructed process...

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Bibliographic Details
Published in2015 54th IEEE Conference on Decision and Control (CDC) pp. 5725 - 5730
Main Author Tanaka, Takashi
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.2015
Subjects
Channel estimation
Distortion
Kernel
Measurement
Optimization
Rate-distortion
Yttrium
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DOI10.1109/CDC.2015.7403118

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Summary:In this paper, we consider rate-distortion tradeoff problems for time-varying, multi-dimensional, partially observable Gauss-Markov processes subject to the zero-delay constraint. As a distortion metric, we consider the mean square error between the hidden state process and the reconstructed process. It is shown that an optimal test channel can be realized by a cascade connection of a pre-Kalman filter estimating the hidden state of the Gauss-Markov process, an additive white Gaussian noise channel, and a post-Kalman filter estimating the internal state of the pre-Kalman filter. An optimal test channel can be constructed by semidefinite programming (SDP). We also show that for stationary sources, there exists a time-invariant optimal test channel, which can also be found by SDP.
DOI:10.1109/CDC.2015.7403118