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Estimation of non-integral and integral quadratic functions in linear stochastic differential systems. (English) Zbl 1461.93510

Summary: 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.

MSC:

93E11 Filtering in stochastic control theory
93C15 Control/observation systems governed by ordinary differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93C05 Linear systems in control theory
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References:

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