Resource allocation and scheduling for energy efficient tracking

We examine the problem of tracking the states of a collection of systems over a finite horizon in a power limited scenario. Specifically, each system has a sensor which can track a property of interest and has a fixed budget with which to make measurements and communicate to a fusion center. The state at each system varies independently according to a Markov model and the transitions between different states occur according known transition matrices. Different systems can have vastly different state evolution statistics. At each time step, the fusion center can request an update from any number of the systems, subject to the constraint that the corresponding sensor has not exhausted its budget to do so. These measurement updates are expensive and hence resource limited. After the fusion center receives all updates, it must estimate the state at each system with minimum error. We give an optimal policy for the fusion center to request updates from each sensor and also provide an optimal policy for the fusion center to allocate the measurement budget to each sensor before deployment, given the transition matrices corresponding to each system.