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Recursive Five-Step Filter for State and Fault Estimation of Linear Descriptor Stochastic Systems with Unknown Disturbances

This study deals with state and fault estimation for linear descriptor systems. The main contribution lies in the synthesis of a novel filter to estimate both state and fault for linear discrete-time descriptor stochastic systems in an unbiased minimum variance sense and without making any assumption on the direct feedthrough matrix. In this study, an equivalent standard state-space system (ESSS) with fault and unknown disturbances is firstly obtained for the considered descriptor stochastic system, and then a recursive filter is designed based on the ESSS representation. Moreover, this study proposes a recursive filter design method to deal with the effect of the unknown disturbances. The relationship between the proposed filter and the existing results in the literature is addressed. Finally, an illustrative example is given to illustrate the effectiveness of the recursive five-step state and fault estimator.