Secure nonlinear fusion estimation for cyber–physical systems under FDI attacks

Abstract

This paper aims to study the problem of multi-sensor fusion estimation for nonlinear cyber–physical systems, where sensor measurements may be tampered with by false data injection (FDI) attacks. Under the assumption that several sensors remain secure, local reorganized subsystems including FDI attack signals and “un-attacked” sensor measurements are constructed by the augmentation method. Then, nonlinear local joint estimators are designed based on the bounded recursive optimization method to estimate the system state and FDI attack signals simultaneously. To improve the estimation performance for system states, a learning-based fusion criterion is proposed by introducing an estimation compensation term that is designed by learning an expected objective. Moreover, it is proved that the designed fusion estimator can be boundedly stable under certain conditions. Finally, an illustrative example is employed to show the effectiveness and advantages of the proposed methods.