On optimal energy-efficient transmission scheduling for remote state estimation

The problem of sensor scheduling under resource constraints in remote state estimation systems has been extensively studied in the past. While many sophisticated scheduling policies have been proposed, practically most wireless sensors operate in the simple strictly periodic pattern for sampling and packet transmission. In this paper, from an energy-efficiency perspective that jointly considers remote estimation accuracy and sensor energy consumption, we provide a rigorous explanation that a strictly periodic sensor scheduling policy can arbitrarily approximate the optimal energy-efficient policy. From this foundation, we explicitly characterize the optimal periodic scheduling, underscoring that: 1) There exists a unique strictly periodic scheduling policy which is optimal among all periodic policies; 2) An exact expression of the optimal period of the strictly periodic policy is derived, which is solely dependent on the packet dropout rate of the communication channel and the spectral radius of the system matrix. Numerical results validate our theoretical findings.