Modified matrix-weighted fusion estimation for cyber–physical systems under FDI attacks

Abstract

In this paper, a multi-sensor fusion estimation problem is investigated for a nonlinear cyber–physical system, where insecure sensor measurements may be falsified by false data injection (FDI) attacks. To make the system capable of proactively defending against the attacks, a multi-channel transmission strategy with stochastic communication protocol (SCP) is established for each insecure sensor. Due to the sensitivity of Kullback–Leibler divergence (KLD) to outliers generated by FDI attacks, a KLD-based detector is designed without relying on past data. A novel method is proposed by modifying the cross covariance according to detection results and a modified matrix-weighted fusion (MMWF) algorithm is presented. The fusion estimation error is derived to be bounded under certain conditions. Finally, a uniformly accelerated linear motion example confirms the validity of the theoretical derivations.