Remote estimation of the Wiener process over a channel with random delay
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-...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Electrical and Electronics Engineers (IEEE)
2019
|
| Online Access: | https://hdl.handle.net/1721.1/121589 |
| _version_ | 1811082955658887168 |
|---|---|
| author | Sun, Yin Polyanskiy, Yury Uysal-Biyikoglu, Elif |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Sun, Yin Polyanskiy, Yury Uysal-Biyikoglu, Elif |
| author_sort | Sun, Yin |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T12:15:19Z |
| format | Article |
| id | mit-1721.1/121589 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:15:19Z |
| publishDate | 2019 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1215892022-09-28T00:50:38Z Remote estimation of the Wiener process over a channel with random delay Sun, Yin Polyanskiy, Yury Uysal-Biyikoglu, Elif Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 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. 2019-07-11T20:16:25Z 2019-07-11T20:16:25Z 2017-08 2019-07-01T17:36:41Z Article http://purl.org/eprint/type/ConferencePaper 9781509040964 2157-8117 https://hdl.handle.net/1721.1/121589 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) en http://dx.doi.org/10.1109/isit.2017.8006542 2017 IEEE International Symposium on Information Theory (ISIT) Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Sun, Yin Polyanskiy, Yury Uysal-Biyikoglu, Elif Remote estimation of the Wiener process over a channel with random delay |
| title | Remote estimation of the Wiener process over a channel with random delay |
| title_full | Remote estimation of the Wiener process over a channel with random delay |
| title_fullStr | Remote estimation of the Wiener process over a channel with random delay |
| title_full_unstemmed | Remote estimation of the Wiener process over a channel with random delay |
| title_short | Remote estimation of the Wiener process over a channel with random delay |
| title_sort | remote estimation of the wiener process over a channel with random delay |
| url | https://hdl.handle.net/1721.1/121589 |
| work_keys_str_mv | AT sunyin remoteestimationofthewienerprocessoverachannelwithrandomdelay AT polyanskiyyury remoteestimationofthewienerprocessoverachannelwithrandomdelay AT uysalbiyikogluelif remoteestimationofthewienerprocessoverachannelwithrandomdelay |