Recursive Remote State Estimation for Stochastic Complex Networks with Degraded Measurements and Amplify-and-Forward Relays

This paper is concerned with the remote state estimation problem for stochastic complex networks under the effects of degraded measurements and amplify-and-forward (AF) relays. Three sets of random variables are employed to describe the measurement degradation, the sensor transmission energy, and the relay transmission energy, respectively. The measurement from each node is transmitted to an AF relay and then forwarded to the remote estimator to facilitate the state estimation. A novel recursive estimator is constructed in the form of the extended Kalman filter. An upper bound of estimation error covariance is determined by solving Riccati-like difference equations based on the statistical information of the random variables, and such an upper bound is then minimized by choosing an appropriate estimator gain. Furthermore, sufficient conditions are established under which the estimation error is exponentially bounded in the sense of mean square. Finally, the effectiveness of the proposed estimation scheme is demonstrated by some numerical simulations.