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optimal linear estimator for discrete-time systems with random delays

控制理论与应用（英文版） 2012年第1期10卷 19-27页

作者： Chunyan HAN Huanshui ZHANG Gang FENG School of Control Science and Engineering University of Jinan Jinan Shandong 250022 China School of Control Science and Engineering Shandong University Jinan Shandong 250061 China Department of Manufacturing Engineering and Engineering Management City University of Hong Kong Hong Kong China

In this paper, optimal estimation for discrete-time linear time-varying systems with randomly state and measurement delays is considered. By introducing a set of binary random variables, the system is converted into the one with both multiplicative noises and constant delays. Then, an estimator which includes the cases of smoothing and filter- ing, is derived via the projection formula, and the solution is given in terms of a partial difference Riccati equation with boundary conditions. A predictor for such systems is also presented based on the proposed filter and smoother. The ob- tained estimators have the same dimension as the original state. Conditions for existence, uniqueness, and stability of the steady-state optimal estimators are studied for time-invariant cases. In this case, the obtained estimators are very easy to implement and all calculations can be performed off line, leading to a linear time-invariant estimator.

关键词： optimal estimator Random delay Projection formula Partial difference equations Asymptotic stability

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LIMITING BEHAVIOR OF RECURSIVE M-estimatorS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES

引用

Acta Mathematica Scientia 2010年第1期30卷 319-329页

作者：缪柏其吴月华刘东海 Department of Statistics and Finance University of Science and Technology of China Department of Mathematics and Statistics York UniversityTorontoOntarioCanada Department of Fire Command Chinese People's Armed Police Forces Academy

Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.

关键词： asymptotic efficiency asymptotic normality asymptotic relative efficiency least absolute deviation least squares M-estimation multivariate linear optimal estimator reeursive algorithm regression coefficients robust estimation regression model

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