An analogue of Shannon information theory for networked control systems: State estimation via a noisy discrete channel

The paper addresses a state estimation problem involving bit-rate communication capacity constraints. A discrete-time partially observed linear system is studied. Unlike the classic theory, the sensor signals are transmitted to the estimator over a noisy digital communication channel. A recursive coder-decoder state estimation scheme is proposed and investigated. It is shown that the classic Shannon´s noisy channel capacity constitutes the border separating the cases where the reliable state estimation is and, respectively, is not possible with arbitrarily high probability.