  We consider the design of an optimal collision-free sensor schedule for a
number of sensors which monitor different linear dynamical systems
correspondingly. At each time, only one of all the sensors can send its local
estimate to the remote estimator. A preliminary work for the two-sensor
scheduling case has been studied in the literature. The generalization into
multiple-sensor scheduling case is shown to be nontrivial. We first find a
necessary condition of the optimal solution provided that the spectral radii of
any two system matrices are not equal, which can significantly reduce the
feasible optimal solution space without loss of performance. By modelling a
finite-state Markov decision process (MDP) problem, we can numerically search
an asymptotic periodic schedule which is proven to be optimal. From a practical
viewpoint, the computational complexity is formidable for some special system
models, e.g., the spectral radii of some certain system matrices are far from
others'. Some simple but effective suboptimal schedules for any systems are
proposed. We also find a lower bound of the optimal cost, which enables us to
quantify the performance gap between any suboptimal schedule and the optimal
one.
