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State estimation for nonlinear conti...

Kulikov, Gennady Yu.

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State estimation for nonlinear continuous-discrete stochastic systems = numerical aspects and implementation issues /

Record Type:	Electronic resources : Monograph/item
Title/Author:	State estimation for nonlinear continuous-discrete stochastic systems/ by Gennady Yu. Kulikov, Maria V. Kulikova.
Reminder of title:	numerical aspects and implementation issues /
Author:	Kulikov, Gennady Yu.
other author:	Kulikova, M. V.
Published:	Cham :Springer International Publishing : : 2024.,
Description:	xxi, 798 p. :ill., digital ;24 cm.
[NT 15003449]:	Numerical Integration Methods for Ordinary Differential Equations -- Kalman Filtering for Linear Stochastic Modeling -- Extended Kalman Filtering for Nonlinear Stochastic Modeling -- Unscented Kalman Filtering for Nonlinear Stochastic Modeling -- Cubature Kalman Filtering for Nonlinear Stochastic Modeling -- Kalman-Like Filtering for Stiff Stochastic Modeling.
Contained By:	Springer Nature eBook
Subject:	Kalman filtering. -
Online resource:	https://doi.org/10.1007/978-3-031-61371-5
ISBN:	9783031613715

State estimation for nonlinear continuous-discrete stochastic systems = numerical aspects and implementation issues /
Kulikov, Gennady Yu.

State estimation for nonlinear continuous-discrete stochastic systemsnumerical aspects and implementation issues /[electronic resource] :by Gennady Yu. Kulikov, Maria V. Kulikova. - Cham :Springer International Publishing :2024. - xxi, 798 p. :ill., digital ;24 cm. - Studies in systems, decision and control,v. 5392198-4190 ;. - Studies in systems, decision and control ;v. 539..

Numerical Integration Methods for Ordinary Differential Equations -- Kalman Filtering for Linear Stochastic Modeling -- Extended Kalman Filtering for Nonlinear Stochastic Modeling -- Unscented Kalman Filtering for Nonlinear Stochastic Modeling -- Cubature Kalman Filtering for Nonlinear Stochastic Modeling -- Kalman-Like Filtering for Stiff Stochastic Modeling.

This book addresses the problem of accurate state estimation in nonlinear continuous-time stochastic models with additive noise and discrete measurements. Its main focus is on numerical aspects of computation of the expectation and covariance in Kalman-like filters rather than on statistical properties determining a model of the system state. Nevertheless, it provides the sound theoretical background and covers all contemporary state estimation techniques beginning at the celebrated Kalman filter, including its versions extended to nonlinear stochastic models, and till the most advanced universal Gaussian filters with deterministically sampled mean and covariance. In particular, the authors demonstrate that, when applying such filtering procedures to stochastic models with strong nonlinearities, the use of adaptive ordinary differential equation solvers with automatic local and global error control facilities allows the discretization error-and consequently the state estimation error-to be reduced considerably. For achieving that, the variable-stepsize methods with automatic error regulation and stepsize selection mechanisms are applied to treating moment differential equations arisen. The implemented discretization error reduction makes the self-adaptive nonlinear Gaussian filtering algorithms more suitable for application and leads to the novel notion of accurate state estimation. The book also discusses accurate state estimation in mathematical models with sparse measurements. Of special interest in this regard, it provides a means for treating stiff stochastic systems, which often encountered in applied science and engineering, being exemplified by the Van der Pol oscillator in electrical engineering and the Oregonator model of chemical kinetics. Square-root implementations of all Kalman-like filters considered and explored in this book for state estimation in Ill-conditioned continuous-discrete stochastic systems attract the authors' particular attention. This book covers both theoretical and applied aspects of numerical integration methods, including the concepts of approximation, convergence, stiffness as well as of local and global errors, suitably for applied scientists and engineers. Such methods serve as a basis for the development of accurate continuous-discrete extended, unscented, cubature and many other Kalman filtering algorithms, including the universal Gaussian methods with deterministically sampled expectation and covariance as well as their mixed-type versions.

ISBN: 9783031613715

Standard No.: 10.1007/978-3-031-61371-5doiSubjects--Topical Terms:

544465
Kalman filtering.

LC Class. No.: QA402.3

Dewey Class. No.: 519.2

State estimation for nonlinear continuous-discrete stochastic systems = numerical aspects and implementation issues /
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245 1 0 $a State estimation for nonlinear continuous-discrete stochastic systems $h [electronic resource] : $b numerical aspects and implementation issues / $c by Gennady Yu. Kulikov, Maria V. Kulikova.
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505 0 $a Numerical Integration Methods for Ordinary Differential Equations -- Kalman Filtering for Linear Stochastic Modeling -- Extended Kalman Filtering for Nonlinear Stochastic Modeling -- Unscented Kalman Filtering for Nonlinear Stochastic Modeling -- Cubature Kalman Filtering for Nonlinear Stochastic Modeling -- Kalman-Like Filtering for Stiff Stochastic Modeling.
520 $a This book addresses the problem of accurate state estimation in nonlinear continuous-time stochastic models with additive noise and discrete measurements. Its main focus is on numerical aspects of computation of the expectation and covariance in Kalman-like filters rather than on statistical properties determining a model of the system state. Nevertheless, it provides the sound theoretical background and covers all contemporary state estimation techniques beginning at the celebrated Kalman filter, including its versions extended to nonlinear stochastic models, and till the most advanced universal Gaussian filters with deterministically sampled mean and covariance. In particular, the authors demonstrate that, when applying such filtering procedures to stochastic models with strong nonlinearities, the use of adaptive ordinary differential equation solvers with automatic local and global error control facilities allows the discretization error-and consequently the state estimation error-to be reduced considerably. For achieving that, the variable-stepsize methods with automatic error regulation and stepsize selection mechanisms are applied to treating moment differential equations arisen. The implemented discretization error reduction makes the self-adaptive nonlinear Gaussian filtering algorithms more suitable for application and leads to the novel notion of accurate state estimation. The book also discusses accurate state estimation in mathematical models with sparse measurements. Of special interest in this regard, it provides a means for treating stiff stochastic systems, which often encountered in applied science and engineering, being exemplified by the Van der Pol oscillator in electrical engineering and the Oregonator model of chemical kinetics. Square-root implementations of all Kalman-like filters considered and explored in this book for state estimation in Ill-conditioned continuous-discrete stochastic systems attract the authors' particular attention. This book covers both theoretical and applied aspects of numerical integration methods, including the concepts of approximation, convergence, stiffness as well as of local and global errors, suitably for applied scientists and engineers. Such methods serve as a basis for the development of accurate continuous-discrete extended, unscented, cubature and many other Kalman filtering algorithms, including the universal Gaussian methods with deterministically sampled expectation and covariance as well as their mixed-type versions.
650 0 $a Kalman filtering. $3 544465
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650 1 4 $a Control and Systems Theory. $3 3381515
650 2 4 $a Systems Theory, Control. $3 893834
650 2 4 $a Digital and Analog Signal Processing. $3 3538815
700 1 $a Kulikova, M. V. $3 3724705
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856 4 0 $u https://doi.org/10.1007/978-3-031-61371-5
950 $a Mathematics and Statistics (SpringerNature-11649)