Distributed Fusion Filtering for Nonlinear Time-Varying Systems Over Amplify-and-Forward Relay Networks: An $H_{\infty }$ Quantized Framework

Abstract

This paper is concerned with the distributed fusion filtering problem for a class of nonlinear time-varying systems subject to quantization effects within a finite-horizon <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> framework. To improve the communication quality, the amplify-and-forward (AaF) relay mechanism, which accounts for phenomenon of missing measurements, is utilized to schedule the data transmissions from the sensors to the remote filters. The dynamic quantization, as a result of the inherent limit of network bandwidth, is further considered in the communication process from the filters to the fusion center. The main objective of this paper is to propose a distributed fusion scheme that ensures both local and fusion <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance indices over a finite horizon. A sufficient condition is first established for guaranteeing a prescribed performance constraint on the local filtering error dynamics, and then the corresponding filter gains are calculated by solving a set of recursive matrix inequalities. Subsequently, with the help of the acquired local state estimates, the desired parameters of the fusion filters are designed in terms of the solution to a convex optimization problem. Finally, the effectiveness of the obtained theoretical results is testified by a numerical example.