On the Optimal Solutions of the Infinite-Horizon Linear Sensor Scheduling Problem

Abstract

This paper studies the infinite-horizon sensor scheduling problem for linear\nGaussian processes with linear measurement functions. Several important\nproperties of the optimal infinite-horizon schedules are derived. In\nparticular, it is proved that under some mild conditions, both the optimal\ninfinite-horizon average-per-stage cost and the corresponding optimal sensor\nschedules are independent of the covariance matrix of the initial state. It is\nalso proved that the optimal estimation cost can be approximated arbitrarily\nclosely by a periodic schedule with a finite period. Moreover, it is shown that\nthe sequence of the average-per-stage costs of the optimal schedule must\nconverge. These theoretical results provide valuable insights into the design\nand analysis of various infinite-horizon sensor scheduling algorithms.\n