Remote estimation of the Wiener process over a channel with random delay
Name
1701.06734.pdf
Description
Submitted version
Size
506.09 KB
Format
Adobe PDF
Checksum (MD5)
be0177040c7d405d0f41fd1346ac8dba
Author(s)
Sun, Yin
Polyanskiy, Yury
Uysal-Biyikoglu, Elif
Date Issued
August 2017
Journal
2017 IEEE International Symposium on Information Theory (ISIT)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Yin, Sun et al. "Remote estimation of the Wiener process over a channel with random delay." 2017 IEEE International Symposium on Information Theory (ISIT), June 2017, Aachen, Germany, Institute of Electrical and Electronics Engineers (IEEE), August 2017 © 2017 Institute of Electrical and Electronics Engineers (IEEE)
Version
Original manuscript
Abstract
In this paper, we consider a problem of sampling a Wiener process, with samples forwarded to a remote estimator via a channel that consists of a queue with random delay. The estimator reconstructs a real-time estimate of the signal from causally received samples. Motivated by recent research on age-of-information, we study the optimal sampling strategy that minimizes the mean square estimation error subject to a sampling frequency constraint. We prove that the optimal sampling strategy is a threshold policy, and find the optimal threshold. This threshold is determined by the sampling frequency constraint and how much the Wiener process varies during the channel delay. An interesting consequence is that even in the absence of the sampling frequency constraint, the optimal strategy is not zero-wait sampling in which a new sample is taken once the previous sample is delivered; rather, it is optimal to wait for a non-zero amount of time after the previous sample is delivered, and then take the next sample. Further, if the sampling times are independent of the observed Wiener process, the optimal sampling problem reduces to an age-of-information optimization problem that has been recently solved. Our comparisons show that the estimation error of the optimal sampling policy is much smaller than those of age-optimal sampling, zero-wait sampling, and classic uniform sampling.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/isit.2017.8006542
