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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.
Liu et al. (Fri,) studied this question.