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A New Approach To Optimal and Self‐Tuning Filtering, Smoothing and Prediction For Discrete‐Time Systems
Author(s) -
Zhang Huanshui,
Xie Lihua,
Soh Yeng Chai
Publication year - 2001
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1111/j.1934-6093.2001.tb00062.x
Subject(s) - estimator , kalman filter , mathematics , smoothing , control theory (sociology) , discrete time and continuous time , optimal estimation , covariance , spectral theorem , mathematical optimization , computer science , algorithm , artificial intelligence , statistics , mathematical analysis , control (management) , operator theory
A new approach to optimal and self‐tuning state estimation of linear discrete time‐invariant systems is presented, using projection theory and innovation analysis method in time domain. The optimal estimators are calculated by means of spectral factorization. The filter, predictor, and smoother are given in a unified form. Comparisons are made to the previously known techniques such as the Kalman filtering and the polynomial method initiated by Kucera. When the noise covariance matrices are not available, self‐tuning estimators are obtained through the identification of an ARMA innovation model. The self‐tuning estimator asymptotically converges to the optimal estimator.