Numerically stable square-root solutions in the family of adaptive Gaussian filters based on the general moment calculation principle for state estimation in continuous-discrete nonlinear stochastic systems.
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| Title: | Numerically stable square-root solutions in the family of adaptive Gaussian filters based on the general moment calculation principle for state estimation in continuous-discrete nonlinear stochastic systems. |
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| Authors: | Kulikov, G.Yu.1 (AUTHOR) gennady.kulikov@tecnico.ulisboa.pt, Kulikova, M.V.1 (AUTHOR) maria.kulikova@ist.utl.pt |
| Source: | Mathematics & Computers in Simulation. Jul2026, Vol. 245, p655-684. 30p. |
| Subjects: | Square root, Kalman filtering, Adaptive filters, Numerical solutions to differential equations, Stochastic systems, Stochastic differential equations, Nonlinear estimation |
| Abstract: | This paper solves the problem of accurate and robust state estimation in continuous-discrete stochastic systems whose process models are simulated by stochastic differential equations but their measurement equations enjoy a discrete-time nonlinear fashion. We show that any Gaussian filter designed for estimating the aforementioned systems can be presented in the form of some universal algorithm with its corresponding and easily-specified parameterization. In other words, such well-known state estimation schemes as the extended, unscented, cubature and quadrature Kalman filters are trivially implemented by adjusting the mean and covariance approximation weights and nodes in the algorithms devised below. The main features of state estimators under exploration are their adaptivity and numerical stability. The first one is grounded on ordinary differential equations (ODEs) developed and substantiated for evolution of deterministic samples utilized in calculations of the expectation and covariance in the process model of interest. These are effectively computed by variable-stepsize ODE solvers with automatic discretization error control and stepsize selection, including the widely known and commonly used built-in Matlab ODE solvers, which are available for integrating ODEs nowadays. The second characteristic is provided by employing square-root versions of the Gaussian filters designed, which are based on hyperbolic Q R factorizations. Such square-root implementations are exceptionally robust to round-off and numerical integration error accumulations. Also, these preserve the symmetry and positivity of the covariances computed in exact arithmetic. Performances of our novel continuous-discrete square-root Gaussian filters are assessed and compared to their non-square-root counterparts in a simulated flight control scenario with ill-conditioned measurements. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics & Computers in Simulation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Numerically stable square-root solutions in the family of adaptive Gaussian filters based on the general moment calculation principle for state estimation in continuous-discrete nonlinear stochastic systems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kulikov%2C+G%2EYu%2E%22">Kulikov, G.Yu.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> gennady.kulikov@tecnico.ulisboa.pt</i><br /><searchLink fieldCode="AR" term="%22Kulikova%2C+M%2EV%2E%22">Kulikova, M.V.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> maria.kulikova@ist.utl.pt</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+%26+Computers+in+Simulation%22">Mathematics & Computers in Simulation</searchLink>. Jul2026, Vol. 245, p655-684. 30p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Square+root%22">Square root</searchLink><br /><searchLink fieldCode="DE" term="%22Kalman+filtering%22">Kalman filtering</searchLink><br /><searchLink fieldCode="DE" term="%22Adaptive+filters%22">Adaptive filters</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+differential+equations%22">Numerical solutions to differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+systems%22">Stochastic systems</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+differential+equations%22">Stochastic differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+estimation%22">Nonlinear estimation</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper solves the problem of accurate and robust state estimation in continuous-discrete stochastic systems whose process models are simulated by stochastic differential equations but their measurement equations enjoy a discrete-time nonlinear fashion. We show that any Gaussian filter designed for estimating the aforementioned systems can be presented in the form of some universal algorithm with its corresponding and easily-specified parameterization. In other words, such well-known state estimation schemes as the extended, unscented, cubature and quadrature Kalman filters are trivially implemented by adjusting the mean and covariance approximation weights and nodes in the algorithms devised below. The main features of state estimators under exploration are their adaptivity and numerical stability. The first one is grounded on ordinary differential equations (ODEs) developed and substantiated for evolution of deterministic samples utilized in calculations of the expectation and covariance in the process model of interest. These are effectively computed by variable-stepsize ODE solvers with automatic discretization error control and stepsize selection, including the widely known and commonly used built-in Matlab ODE solvers, which are available for integrating ODEs nowadays. The second characteristic is provided by employing square-root versions of the Gaussian filters designed, which are based on hyperbolic Q R factorizations. Such square-root implementations are exceptionally robust to round-off and numerical integration error accumulations. Also, these preserve the symmetry and positivity of the covariances computed in exact arithmetic. Performances of our novel continuous-discrete square-root Gaussian filters are assessed and compared to their non-square-root counterparts in a simulated flight control scenario with ill-conditioned measurements. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics & Computers in Simulation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.matcom.2026.02.023 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 30 StartPage: 655 Subjects: – SubjectFull: Square root Type: general – SubjectFull: Kalman filtering Type: general – SubjectFull: Adaptive filters Type: general – SubjectFull: Numerical solutions to differential equations Type: general – SubjectFull: Stochastic systems Type: general – SubjectFull: Stochastic differential equations Type: general – SubjectFull: Nonlinear estimation Type: general Titles: – TitleFull: Numerically stable square-root solutions in the family of adaptive Gaussian filters based on the general moment calculation principle for state estimation in continuous-discrete nonlinear stochastic systems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kulikov, G.Yu. – PersonEntity: Name: NameFull: Kulikova, M.V. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 03784754 Numbering: – Type: volume Value: 245 Titles: – TitleFull: Mathematics & Computers in Simulation Type: main |
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