Communication scheduling and remote estimation with additive noise channels

Communication scheduling and remote estimation scenarios arise in the context of wireless sensor networks, which involve monitoring and controlling the state of a dynamical system from remote locations. This entails joint design of transmission and estimation policies, where a sensor (or a group of sensors) observes the state of the system over a given horizon, but has to be selective in what (and when) it transmits due to energy constraints. The estimator, on the other hand, needs to generate real-time estimates of the state regardless of whether there is a transmission from the sensor or not. Hence, a communication scheduling strategy for the sensor and an estimation strategy for the estimator should be jointly designed to minimize the estimation error subject to the energy constraints. Prior works on this topic assumed that the communication channel between the sensor and the estimator is noiseless, which may not be that realistic even though it was an important first step. In this thesis, we study communication scheduling and remote estimation problems with additive noise channels. In particular, we consider a series of four problems as follows. In the first problem, the sensor has two options, namely, not transmitting its observation, or transmitting its observation over an additive noise channel subject to some communication cost. Because of the presence of channel noise, if the sensor decides to transmit its observation over the noisy channel, it needs to encode the message. Furthermore, the estimator needs to decode the noise-corrupted message. Hence, a pair of encoding and decoding strategies should also be jointly designed along with the communication scheduling strategy. In the second problem, the sensor has three options, where two of the options are the same as those in the first problem, and the third one is that the sensor can transmit its observation via a noiseless but more costly channel. The third problem is a variant of the first one, where the encoder has a constraint on its average total power consumption over the time horizon, instead of a constraint on the stage-wise encoding power, which is assumed in the first problem. In the fourth problem, the communication channel noise is generated by an adversary with the objective of maximizing the estimation error. Hence, a game problem instead of an optimization problem is formulated and studied. Under some technical assumptions, we obtain the optimal solutions for the first three problems, and a feedback Stackelberg solution for the fourth problem. We present numerical results illustrating the performances of the proposed solutions. We also discuss possible directions for future research based on the results presented in this thesis