నైరూప్య

Kalman filtering without direct feed through from unknown inputs

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.