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This paper focuses on estimation of an non-integral quadratic function (NIQF) and integral quadratic function (IQF) of a random signal in dynamic system described by a linear stochastic differential equation. The quadratic form of an unobservable signal indicates useful information of a signal for control. The optimal (in mean square sense) and suboptimal estimates of NIQF and IQF represent a function of the Kalman estimate and its error covariance. The proposed estimation algorithms have a closed-form estimation procedure. The obtained estimates are studied in detail, including derivation of the exact formulas and differential equations for mean square errors. The results we demonstrate on practical example of a power of signal , and comparison analysis between optimal and suboptimal estimators is presented.
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참고문헌 (10)
참고문헌 신청
A. Gelb / 1974 / Applied Optimal Estimation / MIT Press
A. H. Jazwinski / 1970 / Stochastic Processes and Filtering Theory / Academic Press
B. Gibbs / 2011 / Advanced Kalman Filtering, Least Squares and Modelling. A Practical Handbook / John Wiley & Sons
B. Holmquist / 1996 / Expectations of products of quadratic forms in normal variables / Stochastic Analysis and Applications 14 : 149 ~ 164
F. L. Lewis / 1986 / Optimal Estimation with an Introduction to Stochastic Control The-ory / Wiley & Sons
A. H. Jazwinski / 1970 / Stochastic Processes and Filtering Theory / Academic Press
B. Gibbs / 2011 / Advanced Kalman Filtering, Least Squares and Modelling. A Practical Handbook / John Wiley & Sons
B. Holmquist / 1996 / Expectations of products of quadratic forms in normal variables / Stochastic Analysis and Applications 14 : 149 ~ 164
F. L. Lewis / 1986 / Optimal Estimation with an Introduction to Stochastic Control The-ory / Wiley & Sons
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