Optimal filtering for NCSs with amplify-and-forward relays

This paper is concerned with the optimal Markov jump estimator for wireless networked control system with amplify-and-forward (AF) relay. An AF relay is located in the transmission link between the sensor and the remote estimator to regulate the data transmission. A set of random variables obeying Markov distribution is adopted to model the transmission power of the sensor and relay. By utilising the reorganization Markov chain method, the observation equation with two independent jump processes is transformed into an equivalent one with single jump process. Then, the optimal Markov jump estimator is derived by using the complete square method and the stochastic approximation theory. Further, an optimal stationary Markov jump estimator is developed under the assumption of ergodicity of the associated Markov chain. It is shown that there exists a unique stabilizing solution for the corresponding coupled algebraic Riccati equation, which coincides with the limit of the solution to the corresponding coupled difference Riccati equation for the proposed Markov jump estimator.