1 research outputs found
Sampling of the Wiener Process for Remote Estimation 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 over a channel that is modeled as a
queue. The estimator reconstructs an estimate of the real-time signal value
from causally received samples. We study the optimal online sampling strategy
that minimizes the mean square estimation error subject to a sampling rate
constraint. We prove that the optimal sampling strategy is a threshold policy,
and find the optimal threshold. This threshold is determined by how much the
Wiener process varies during the random service time and the maximum allowed
sampling rate. Further, if the sampling times are independent of the observed
Wiener process, the above sampling problem for minimizing the estimation error
is equivalent to a sampling problem for minimizing the age of information. This
reveals an interesting connection between the age of information and remote
estimation error. Our comparisons show that the estimation error achieved by
the optimal sampling policy can be much smaller than those of age-optimal
sampling, zero-wait sampling, and periodic sampling.Comment: Accepted by IEEE Transactions on Information Theor