Observation driven sensor scheduling

Consider a remote sensing system consisting of two sensors, a scheduler and a non-collocated fusion center. Each sensor observes a distinct component of a bivariate Gaussian source. The fusion center and the sensors are separated by a noiseless channel that can support the transmission of only one of the measurements at a time. The scheduler must decide which of the measurements will be revealed to the fusion center based on both of the observations. Finally, the fusion center forms an estimate of the entire source based on the observation chosen by the scheduler. Our goal is to design scheduling and estimation policies that jointly minimize a mean squared error criterion. We establish the person-by-person optimality between a scheduling policy where the observation with the largest magnitude is transmitted and its corresponding conditional expectation estimation policy in two scenarios: when the state is distributed according to a bivariate Gaussian density with independent components; and according to a symmetrically correlated Gaussian density with unit variances.