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Kalman filtering without direct feed through from unknown inputs

Author(s): Jilai Liu, Shuwen Pan, Yanjun Li

The problem of joint input and state estimation is addressed in this paper for discrete-time stochastic systems without direct feedthrough from unknown inputs to outputs. Following the identical idea of previous study on discrete-time stochastic systems with direct feedthrough, the weighted least squares estimation for an extended state vector including unknown inputs and states is used to derive a Kalman filter with unknown inputs without directfeedthrough (KF-UI-WDF) approach. The information on unknown inputs is not needed for KF-UI-WDF and the necessary and sufficient conditions for the state and input detectability are presented. The estimators of KF-UI-WDF are proven minimum variance unbiased (MVU) ones.

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