Optimal and Suboptimal Estimation of Quadratic Functionals of the State Vector in Linear Stochastic Systems

Abstract

ABSTRACTThis paper focuses on estimation of a quadratic functional (QF) of a random signal in dynamic systems described by a linear stochastic differential equations. The QF represents a quadratic form of state variables, which can indicate useful information of a target system for control. The optimal (in mean square sense) and suboptimal estimators of a QF represent a function of the Kalman estimate and error covariance. The proposed estimation algorithms have a closed-form estimation procedure. The quadratic estimators are studied in detail, including derivation of the exact formulas for mean square errors. The obtained results we demonstrate on practical example, and comparison analysis between optimal and suboptimal estimators is presented.Research highlights▸ An optimal mean square estimator for an arbitrary QF in linear stochastic systems is derived.▸ The proposed estimator is a comprehensively investigated, including derivation of matrix equation for its mean square error.▸ Performance of the optimal and suboptimal estimators is illustrated on theoretical and practical examples for real QFs.