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This paper considers a sequential sensor scheduling and remote estimationproblem with one sensor and one estimator. The sensor makes sequentialobservations about the state of an underlying memoryless stochastic process andmakes a decision as to whether or not to send this measurement to theestimator. The sensor and the estimator have the common objective of minimizingexpected distortion in the estimation of the state of the process, over afinite time horizon. The sensor is either charged a cost for each transmissionor constrained on transmission times. As opposed to the prior work wherecommunication between the sensor and the estimator was assumed to be perfect(noiseless), in this work an additive noise channel with fixed power constraintis considered; hence, the sensor has to encode its message before transmission.Under some technical assumptions, we obtain the optimal encoding and estimationpolicies in conjunction with the optimal transmission schedule. The impact ofthe presence of a noisy channel is analyzed numerically based on dynamicprogramming. This analysis yields some rather surprising results such as aphase transition phenomenon in the number of used transmission opportunities,which was not encountered in the noiseless communication setting.

Optimal Communication Scheduling and Remote Estimation over an Additive Noise Channel