Robust Fault Diagnosis with a Two-stage Kalman Estimator

In the first part of this paper, we present a two-stage Kalman filter for state and bias filtering in dynamic stochastic systems affected by unknown inputs and constant biases. It is shown that the state estimate can be expressed as x k / k = x k / k + β k / k b k / k , where the biasfree estimate x k / k and the bias estimate bk/k are computed via two reduced-order filters and where the coupling term βk/k only depends on matrices which arise in the computation of x k / k and bk/k. In the second part, the generalised likelihood ratio (GLR) test is applied on the bias filter's innovation sequence for robust fault diagnosis.

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