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