Abstract
This paper presents a new robust filter structure to solve the simultaneous state and fault estimation problem of linear stochastic discrete-time systems with unknown disturbance. The method is based on the assumption that the fault and the unknown disturbance affect both the system state and the output, and no prior knowledge about their dynamical evolution is available. By making use of an optimal three-stage Kalman filtering method, an augmented fault and unknown disturbance models, an augmented robust three-stage Kalman filter (ARThSKF) is developed. The unbiasedness conditions and minimum-variance property of the proposed filter are provided. An illustrative example is given to apply this filter and to compare it with the existing literature results.
Highlights
The joint fault and state estimation for linear stochastic systems with unknown disturbance is concerned in this paper
On the other hand, when the fault and the unknown disturbance affect both the state and the measurement equations, we propose an augmented robust three-stage Kalman filter Augmented Robust Three-Stage Kalman Filter (ARThSKF) to overcome this problem
We propose to apply the proposed filter ARThSKF to obtain a robust estimation of simultaneous actuator and sensor faults
Summary
The joint fault and state estimation for linear stochastic systems with unknown disturbance is concerned in this paper. Gillijns and Moor have treated the problem of estimating the state in the presence of unknown inputs which affect the system model They developed a recursive filter which is optimal in the sense of minimum-variance. This filter has been extended by the same authors for joint input and state estimation to linear discretetime systems with direct feedthrough where the state and the unknown input estimation are interconnected. On the other hand, when the fault and the unknown disturbance affect both the state and the measurement equations, we propose an augmented robust three-stage Kalman filter ARThSKF to overcome this problem This latter is obtained by a direct application of the RThSKF on the augmented fault and unknown disturbance models. An illustrative example of the proposed filter is presented
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