Optimal stationary self-triggered sampling for estimation

In this paper, we study optimal stationary sampling for transmission of measurements of a stochastic process from a source encoder to a source decoder through a costly communication channel. We measure information transferred over a time interval by the change in the decoder's entropy regarding the state of the process given the transmitted measurements. In our setting, the encoder employs a sampler to control the information flow in the channel. The problem is casted as a discounted infinite horizon optimization problem that takes into account the transferred information and the paid price. We derive the optimal stationary sampling policy, and propose two computational methods with convergence guarantees by using techniques from approximate dynamic programing. In addition, we introduce two triggering mechanisms based on the value of information and on the covariance threshold that can generate the optimal policy. Finally, we present some numerical and simulation results.