On Optimal Energy-Efficient Transmission Scheduling for Remote State Estimation

This study finds and proves that strictly periodic scheduling is optimal in terms of energy efficiency within the context of remote state estimation. We model a problem where the sensor transmits local state estimates over an independent and identically distributed packet dropping channel to a remote estimator. From the angle of energy efficiency, we discover and explain that periodic scheduling can arbitrarily approach optimal scheduling in infinite horizon. Building upon this, we have derived explicit conclusions regarding the optimal periodic scheduling, underscoring that: 1) Under the condition of maximum energy efficiency, the optimal scheduling policy is to enforce a strict periodic scheduling; 2) A concrete expression for the identified strict scheduling period based on the system parameters has been established. The study culminates with a series of numerical simulations that showcase the efficacy of our theoretical findings.