Nonfragile Distributed Fusion Filtering for Time-Varying Systems With Sensor Saturations: A Decode-and-Forward Relay-Aided Approach.

In this article, the problem of distributed fusion filtering (DFF) has been studied for discrete-time, time-varying systems affected by sensor saturations, packet losses, and stochastic gain perturbations. The transmission process between sensors and remote filters is carried out via relay channels subject to packet losses. To enhance communication quality and ensure transmission reliability, a decode-and-forward (DaF) relay-aided mechanism is introduced. Random perturbations in the local filter gains are incorporated to model potential implementation uncertainties and parameter fluctuations. The objective of this work is to design an appropriate distributed fusion filter that ensures specific performance constraints are satisfied for both local and global filtering error systems. For each sensor node, a sufficient condition, derived from stochastic analysis theory, is first established to guarantee the existence of a desired local $H_{\infty }$ filter. The associated filter gains are then computed by solving a set of coupled difference equations. Building on these local designs, a distributed fusion filter is constructed, and the corresponding fusion parameters are determined through the solution of a convex optimization problem. Finally, the effectiveness of the proposed fusion filtering framework is demonstrated through a numerical example.