Consensus Optimal Filter for Linear Systems Over Amplify-and-Forward Relay Networks: Handling Delayed and Degraded Channels

This paper investigates the optimal Kalman consensus filter (KCF) for a class of linear discrete-time system with different transmission delays and fading channels. In order to improve communication distance and quality, the amplifyand- forward (AaF) relay protocol is utilized to regulate the data transmissions over the sensor-to-estimator communication channels. The reorganisation observation technology is employed to convert the observation sequence with time delay into a delayfree observation sequence. An optimal distributed KCF with a given Kalman-like framework is proposed for each node based on the linear minimum mean squared error (LMMSE) method, in which the Kalman gains and consensus gains are derived by solving a set of difference Riccati equations based on Lyapunov equations. Further, the stability and convergence of the proposed KCF algorithm are explored, where the stationary filter gains are determined by solving a set of algebraic Riccati equations based on algebraic Lyapunov equations. The novelty of this article is that a novel consensus structure is applied to deal with estimation issues for linear systems subject to different transmission delays and fading channels over the AaF relay mechanism.