Improved results on transmission power control for remote state estimation

We consider a sensor transmission power control problem for remote state estimation. In this problem, a sensor sends its local estimate to a remote estimator over a wireless packet-dropping communication channel. The transmission power is determined by a recently proposed algorithm which uses the innovative information contained in the measurement. In the current paper, we focus on parameter optimization arising from the selection of design parameters for this power controller. The existing work obtained a suboptimal solution to the parameter optimization problem, while by using a vector rearrangement inequality argument and the vector majorization, we now show that there exists an optimal solution within a subset of the whole feasible set. By leveraging this property, we obtain an optimal solution via solving a convex optimization problem.