Optimal Linear Filtering for Stochastic Descriptor Systems with Unknown Inputs

Chien-Shu Hsieh


Descriptor Kalman filtering, Maximum likelihood estimation, Optimal filtering, Unknown inputs, Unbiased minimum-variance filter


This paper addresses the optimal unbiased minimum-variance state estimation for descriptor systems with unknown inputs that affect both the system state and the output with the descriptor Kalman filtering method. It is shown that the recently developed 5-block form of the extended descriptor Kalman filter (EDKF) can yield the optimal system state estimate subject to that a specific rank condition holds. However, the EDKF may suffer from computational complexity problem. To remedy this problem, based on the recently proposed gain-covariance matrix (GCM) concept, two computationally efficient algorithms of the EDKF, named as the least-squares data-fitting filter (LSDFF) and the descriptor recursive three-step filter (DRTSF), are proposed in the paper. The DRTSF serves as a useful filtering structure to develop an extension of the recently developed extended recursive three-step filter (ERTSF) for descriptor systems. A simulation example is given to illustrate the proposed results.

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