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State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors
Author(s) -
Zhang Xiao,
Ding Feng,
Yang Erfu
Publication year - 2019
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.3027
Subject(s) - extended kalman filter , bilinear interpolation , control theory (sociology) , covariance intersection , kalman filter , covariance , linearization , covariance matrix , estimator , invariant extended kalman filter , state (computer science) , mathematics , nonlinear system , taylor series , computer science , algorithm , statistics , artificial intelligence , control (management) , mathematical analysis , physics , quantum mechanics
Summary This paper considers the state estimation problem of bilinear systems in the presence of disturbances. The standard Kalman filter is recognized as the best state estimator for linear systems, but it is not applicable for bilinear systems. It is well known that the extended Kalman filter (EKF) is proposed based on the Taylor expansion to linearize the nonlinear model. In this paper, we show that the EKF method is not suitable for bilinear systems because the linearization method for bilinear systems cannot describe the behavior of the considered system. Therefore, this paper proposes a state filtering method for the single‐input–single‐output bilinear systems by minimizing the covariance matrix of the state estimation errors. Moreover, the state estimation algorithm is extended to multiple‐input–multiple‐output bilinear systems. The performance analysis indicates that the state estimates can track the true states. Finally, the numerical examples illustrate the specific performance of the proposed method.