Abstract
A sampling problem for remote monitoring and estimation of the multi-dimensional Wiener process through a channel with random delivery time under the constraint of maximum sampling frequency is considered. The authors study the optimal sampling policy that minimizes the mean square error. It is showed that the threshold policy is optimal and the near closed-form expressions of the optimal threshold and the corresponding mean square error are given. A bisection method is proposed to search the numerical solutions. The results provide a general framework for remote estimation and sampling, including the special cases that the dimension of Wiener source is one and that the delivery time of the channel tends to zero. Simulation results show that even though there is no constraint on the maximum sampling frequency, age-optimal policy, periodic sampling policy and zero-wait policy are far from optimal.
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