Comparative Analysis of the Performances of a Nonlinear Observer and Nonlinear Kalman Filters in the Presence of Non‐Gaussian Disturbances.
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| Title: | Comparative Analysis of the Performances of a Nonlinear Observer and Nonlinear Kalman Filters in the Presence of Non‐Gaussian Disturbances. |
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| Authors: | Movahedi, Hamidreza1 (AUTHOR), Zemouche, Ali2 (AUTHOR), Rajamani, Rajesh1 (AUTHOR) rajamani@umn.edu |
| Source: | International Journal of Robust & Nonlinear Control. 5/10/2026, Vol. 36 Issue 7, p3896-3913. 18p. |
| Subjects: | Nonlinear estimation, Kalman filtering, Random noise theory, Lyapunov stability, Robust control |
| Abstract: | This paper focuses on state estimation for a fairly general class of systems, involving nonlinear functions and disturbances in both the process dynamics and output equations. A nonlinear observer that satisfies a H∞$$ {\boldsymbol{H}}_{\boldsymbol{\infty}} $$ disturbance attenuation constraint in addition to providing asymptotic stability in the absence of disturbances is developed using Lyapunov analysis. A weighted form of this observer is able to adjust the estimation performance for systems that have states with considerably different levels of magnitude. The observer is shown analytically to provide a guaranteed upper bound on the vector norm of the estimation error, and this upper bound is utilized to guarantee the stability of observers in disturbed systems that are designed to be stable over a finite domain. The performance of the nonlinear observer is compared with the performance of the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). Three different applications are utilized for the comparison, consisting of a magnetic position estimation problem, a state‐of‐charge battery application, and a vehicle tracking application. In the case of the disturbances being Gaussian noise, the UKF and the nonlinear observer provide approximately the same level of performance, and they both surpass the performance of the EKF. However, in the case of 2‐norm‐bounded non‐Gaussian noise, such as spikes/pulses, the nonlinear observer is shown to significantly outperform both the UKF and the EKF. Extensive experimental results and comparisons using a range of covariance choices demonstrate the superiority of the nonlinear observer, confirming that it is not just an artifact of specific tests. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Robust & Nonlinear Control is the property of Wiley-Blackwell 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 192765758 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Comparative Analysis of the Performances of a Nonlinear Observer and Nonlinear Kalman Filters in the Presence of Non‐Gaussian Disturbances. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Movahedi%2C+Hamidreza%22">Movahedi, Hamidreza</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zemouche%2C+Ali%22">Zemouche, Ali</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Rajamani%2C+Rajesh%22">Rajamani, Rajesh</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> rajamani@umn.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Robust+%26+Nonlinear+Control%22">International Journal of Robust & Nonlinear Control</searchLink>. 5/10/2026, Vol. 36 Issue 7, p3896-3913. 18p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Nonlinear+estimation%22">Nonlinear estimation</searchLink><br /><searchLink fieldCode="DE" term="%22Kalman+filtering%22">Kalman filtering</searchLink><br /><searchLink fieldCode="DE" term="%22Random+noise+theory%22">Random noise theory</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+stability%22">Lyapunov stability</searchLink><br /><searchLink fieldCode="DE" term="%22Robust+control%22">Robust control</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper focuses on state estimation for a fairly general class of systems, involving nonlinear functions and disturbances in both the process dynamics and output equations. A nonlinear observer that satisfies a H∞$$ {\boldsymbol{H}}_{\boldsymbol{\infty}} $$ disturbance attenuation constraint in addition to providing asymptotic stability in the absence of disturbances is developed using Lyapunov analysis. A weighted form of this observer is able to adjust the estimation performance for systems that have states with considerably different levels of magnitude. The observer is shown analytically to provide a guaranteed upper bound on the vector norm of the estimation error, and this upper bound is utilized to guarantee the stability of observers in disturbed systems that are designed to be stable over a finite domain. The performance of the nonlinear observer is compared with the performance of the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). Three different applications are utilized for the comparison, consisting of a magnetic position estimation problem, a state‐of‐charge battery application, and a vehicle tracking application. In the case of the disturbances being Gaussian noise, the UKF and the nonlinear observer provide approximately the same level of performance, and they both surpass the performance of the EKF. However, in the case of 2‐norm‐bounded non‐Gaussian noise, such as spikes/pulses, the nonlinear observer is shown to significantly outperform both the UKF and the EKF. Extensive experimental results and comparisons using a range of covariance choices demonstrate the superiority of the nonlinear observer, confirming that it is not just an artifact of specific tests. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Robust & Nonlinear Control is the property of Wiley-Blackwell 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: 10.1002/rnc.70386 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 18 StartPage: 3896 Subjects: – SubjectFull: Nonlinear estimation Type: general – SubjectFull: Kalman filtering Type: general – SubjectFull: Random noise theory Type: general – SubjectFull: Lyapunov stability Type: general – SubjectFull: Robust control Type: general Titles: – TitleFull: Comparative Analysis of the Performances of a Nonlinear Observer and Nonlinear Kalman Filters in the Presence of Non‐Gaussian Disturbances. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Movahedi, Hamidreza – PersonEntity: Name: NameFull: Zemouche, Ali – PersonEntity: Name: NameFull: Rajamani, Rajesh IsPartOfRelationships: – BibEntity: Dates: – D: 10 M: 05 Text: 5/10/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 10498923 Numbering: – Type: volume Value: 36 – Type: issue Value: 7 Titles: – TitleFull: International Journal of Robust & Nonlinear Control Type: main |
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