Zero-error target tracking with limited communication

We study the problem of target tracking in a sensor network environment. In particular, we consider a target that moves according to a Markov chain, and a tracker that queries sets of sensors to obtain tracking information. We are interested in finding the minimum number of queries per time step such that a target is trackable under three different requirements. First we investigate the case where the tracker is required to know the exact location of the target at each time step. We then relax this requirement and explore the case where the tracker may lose track of the target at a given time step, but it is able to catch-up at a later time, regaining up-to-date information about the target's track. Finally, we consider the case where tracking information is only known after a delay of d time steps. We provide necessary and sufficient conditions on the number of queries per time step to track in the above three cases. These conditions are stated in terms of the entropy rate of the target's Markov chain.