This thesis investigates the transmission power control issues of a wireless sensor for remote state estimation under energy constraints. Two types of sensor models are considered: battery-powered sensors and energy harvesting sensors. For the battery-powered sensors, we consider two categories of transmission strategies, namely, offline power schedules without using the process state information and online power schedules which depend on the real-time state. In the offline scenario, we propose an optimal periodic transmission power schedule using a Markov chain model. We also derive an explicit expression for the estimation error covariance. In the online scenario, we design the power schedule from a different perspective: how to adapt the transmission power to the measurements of the...[ Read more ]

This thesis investigates the transmission power control issues of a wireless sensor for remote state estimation under energy constraints. Two types of sensor models are considered: battery-powered sensors and energy harvesting sensors. For the battery-powered sensors, we consider two categories of transmission strategies, namely, offline power schedules without using the process state information and online power schedules which depend on the real-time state. In the offline scenario, we propose an optimal periodic transmission power schedule using a Markov chain model. We also derive an explicit expression for the estimation error covariance. In the online scenario, we design the power schedule from a different perspective: how to adapt the transmission power to the measurements of the plant state and how to exploit information contained in the lost packets. Two online transmission power schedules based on the relative importance of the local estimate at each time are proposed. The first one is based on the magnitude of the local innovation and the second one extends the idea by utilizing a quadratic function of the innovation. We prove that the proposed online power schedules preserve the Gaussian distribution of the local estimate innovation, which enables us to obtain a closed-form expression of the expected state estimation error covariance. Comparisons with alternative offline schedules are provided which demonstrate significant performance improvement by the proposed online schedules. For the second type of sensors, which have energy harvesting capabilities, optimal power control strategies are also studied. To tackle the randomness of the energy arrivals, we formulate the power control problem as an infinite time-horizon Markov decision process (MDP). To deal with the computation complexity associated with this multi-dimensional MDP, a continuous-time approach and perturbation analysis is used and a closed-form approximate value function is derived. Based on the approximation, we obtain a closed-form optimal power control solution which has a threshold-based structure. Some concluding remarks and future work directions are discussed.