title: Input and state estimation for linear systems with a rank-deficient direct feedthrough matrix.
abstract: The problem of joint input and state estimation for linear stochastic systems with a rank-deficient direct feedthrough matrix is discussed in this paper. Results from previous studies only solve the state estimation problem; globally optimal estimation of the unknown input is not provided. Based on linear minimum-variance unbiased estimation, a five-step recursive filter with global optimality is proposed to estimate both the unknown input and the state. The relationship between the proposed filter and the existing results is addressed. We show that the unbiased input estimation does not require any new information or additional constraints. Both the state and the unknown input can be estimated under the same unbiasedness condition. Global optimalities of both the state estimator and the unknown input estimator are proven in the minimum-variance unbiased sense.
authors.affiliation: National Laboratory of Industrial Control Technology, Department of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China. Electronic address: wanghaokun@163.com.
authors.forename: Haokun
authors.initials: H
authors.lastname: Wang
authors.affiliation: National Laboratory of Industrial Control Technology, Department of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China. Electronic address: jzhao@iipc.zju.edu.cn.
authors.forename: Jun
authors.initials: J
authors.lastname: Zhao
authors.affiliation: National Laboratory of Industrial Control Technology, Department of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China. Electronic address: xuzh@iipc.zju.edu.cn.
authors.forename: Zuhua
authors.initials: Z
authors.lastname: Xu
authors.affiliation: National Laboratory of Industrial Control Technology, Department of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China. Electronic address: zjshao@iipc.zju.edu.cn.
authors.forename: Zhijiang
authors.initials: Z
authors.lastname: Shao
keywords: Global optimality; Minimum-variance unbiased estimation; State estimation; Unknown input estimation