A Rao-Blackwellised particle filter-based likelihood ratio approach to fault diagnosis for linear stochastic systems

This paper presents a Rao-Blackwellised particle filter (RBPF)-based likelihood ratio approach to fault detection and isolation (FDI) in linear stochastic systems. In this paper, the faults are modelled as unknown changes in system parameters and the Rao-Blackwellised particle filtering technique is used for deriving an FDI scheme. Essentially, a set of RBPFs are designed for estimation of the parameters associated with the faults to be detected, along with a Kalman filter designed with the nominal system model. The likelihood functions of the observations are then evaluated using the particles from these RBPFs and the state estimate from Kalman filter. FDI is then achieved via the likelihood ratio test. The simulation results on a fourth-order system are provided which demonstrates the effectiveness of the proposed method.