Consensus-based Distributed State Estimation over Amplify-and-Forward Relay Networks with Fading Channels

This paper is concerned with the distributed fusion filter for a class of complex systems subject to transmission delays and fading channels within a Kalman consensus framework. To enhance the communication quality and extend the transmission distance, a amplify-and-forward (AaF) relay is introduced in transmission link from the sensors to the remote estimators. Under the effects of relay nodes, a three-terminal relay model is adopted to describe the system, that is the signal transmission lines between the sensors and estimators consisting of the sensor-to-estimator, the sensor-to-relay and the relay-to-estimator channels. Moreover, a new equivalent delay-free measurement sequence is defined by the measurement reorganization technology to tackle measurement delays. Then, a consensus-based distributed estimator is designed in the linear unbiased minimum variance (LUMV) sense based on the new delay-free measurement equation, in which the optimal estimator gains are derived by solving a set of difference Riccati equations based on Lyapunov equations.