Optimal Estimation with Limited Measurements and Noisy Communication

This paper considers a sequential estimation and sensor scheduling problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process, and makes a decision as to whether or not to send this measurement to the estimator. The sensor and the estimator have the common objective of minimizing expected distortion in the estimation of the state of the process, over a finite time horizon, with the constraint that the sensor can transmit its observation only a limited number of times. As opposed to the prior work where communication between the sensor and the estimator was assumed to be perfect (noiseless), in this work an additive noise channel with fixed power constraint is considered; hence, the sensor has to encode its message before transmission. For some specific source and channel noise densities, we obtain the optimal encoding and estimation policies in conjunction with the optimal transmission schedule. The impact of the presence of a noisy channel is analyzed numerically based on dynamic programming. This analysis yields some rather surprising results such as a phase-transition phenomenon in the number of used transmission opportunities, which was not encountered in the noiseless communication setting.Comment: X. Gao, E. Akyol, and T. Basar. Optimal estimation with limited measurements and noisy communication. In 54th IEEE Conference on Decision and Control (CDC15), 2015, to appea

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

Optimal sensor scheduling and remote estimation over an additive noise channel

In the applications of wireless sensor networks, sensors are built to measure the state of the system of interest and send their measurements to a remote decision unit via wireless communication. Based on the messages received from the sensors, the decision unit estimates the state of the system and makes decisions. In this scenario, the quality of decision making strongly depends on the quality of state estimation. On the other hand, the sensors are constrained by limited power and cannot always communicate with the decision unit. As a consequence, a communication scheduling strategy and an estimation strategy should be designed for the sensors and the decision unit, respectively, such that the state estimation error is minimized under the communication constraints. In this thesis, we consider a sensor scheduling and remote estimation problem with one sensor and one estimator. The sensor makes a series of observations on the state of a source and then decides whether to transmit each one in the sequence to the estimator. The sensor is charged a cost for each transmission. The remote estimator generates real-time estimates on the state of the source based on the messages received from the sensor. The estimator is charged for estimation error. In contrast to prior work in the literature, we further assume that there is additive communication channel noise, which makes the problem more challenging. As a consequence of the presence of channel noise, the sensor needs to encode the message before transmitting it to the estimator. For some specific distributions of the underlying random variables, we obtain a person-by-person optimal solution to the problem of minimizing the expected value of the sum of communication cost and estimation cost over the time horizon, which is globally optimal in the asymptotic case. In a modified problem we show that our solution is locally optimal and a globally optimal solution exists