Korean J. Math.  Vol 25, No 1 (2017)  pp.45-60
DOI: https://doi.org/10.11568/kjm.2017.25.1.45

Estimation of non-integral and integral quadratic functions in linear stochastic differential systems

IL Young Song, Vladimir Shin, Won Choi


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.


Stochastic system; State vector; Random process; White noise, Estimation, Integral and non-integral functionals, Quadratic form, Kalman filtering

Subject classification

93E11, 93E24, 94A12


This work was supported by the Incheon National University Research Grant in 2016-2017.

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