State estimation with a remote sensor under limited communication rate

This paper deals with the problem of estimating the state of a discrete-time linear Gaussian stochastic dynamical system subject to a limitation on the communication rate from the remote sensor unit. More specifically, the attention is devoted to a 2-node network consisting of: (1) a remote node S which collects measurements of the given system, computes optimal state estimates at the full measurement rate and transmits them at a reduced communication rate; (2) a local node F that, based on received estimates, provides an estimate of the system state at the full rate. A measurement-independent strategy for deciding when transmitting estimates from S to F will be considered. Sufficient conditions for the boundedness of the state covariance at node F will be given. Further, it will be shown that the optimal communication strategy for a given rate is characterized by an upper bound on the time between consecutive transmissions.