Controlled Sensing for Communication-Efficient Filtering and Smoothing in POMDPs

The trade-off between communication resources and estimation accuracy is widely considered in sensor networks. In this paper we consider the problem of estimating the trajectory of an event-triggered hidden Markov model, where the controller decides at each time step whether or not the sensor should sample and transmit a measurement to the estimator. Adopting a Shannon information-theoretic point of view, we quantify the required communication resources by the entropy of the transmitted observation sequence, with a special symbol to denote non-transmission. Furthermore we evaluate the trajectory uncertainty by the conditional entropy of the state sequence given the received observations. Simultaneous minimization of the communication resources and state uncertainty is formulated and solved within a partially observable Markov decision process framework, yielding a threshold policy for triggering transmissions.