Ellipsoidal state estimation based on sum of squares for non-linear systems with unknown but bounded noise
- Author(s): Paolo Massioni 1 ; Nikolay N. Salnikov 2 ; Gérard Scorletti 3
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View affiliations
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Affiliations:
1:
Laboratoire Ampère CNRS, INSA Lyon , Université de Lyon , 69621 Villeurbanne CEDEX , France ;
2: Institute of Space Research of National Academy of Sciences of Ukraine and State Space Agency of Ukraine , Kiev , Ukraine ;
3: Laboratoire Ampère CNRS, Ecole Centrale Lyon , Université de Lyon , 69134 Ecully CEDEX , France
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Affiliations:
1:
Laboratoire Ampère CNRS, INSA Lyon , Université de Lyon , 69621 Villeurbanne CEDEX , France ;
- Source:
Volume 13, Issue 12,
13
August
2019,
p.
1955 – 1961
DOI: 10.1049/iet-cta.2018.5072 , Print ISSN 1751-8644, Online ISSN 1751-8652
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© The Institution of Engineering and Technology
Received
21/03/2018,
Accepted
07/06/2019,
Revised
13/05/2019,
Published
07/06/2019
This brief concerns the set-theoretic recursive state estimation of non-linear systems with polynomial dynamics, making use of ellipsoidal bounds. The sum of squares approach is used to construct an optimal ellipsoid containing the intersection of sets obtained with the use of non-linear system equations and measurement equations. The properties of the proposed filter are illustrated with two examples, one concerning the simultaneous estimation of parameters and state of a linear system, and the other on the Euler equations of the rigid body rotational motion.
Inspec keywords: linear systems; state estimation; recursive estimation; set theory; least squares approximations; polynomials
Other keywords: ellipsoidal bounds; polynomial dynamics; optimal ellipsoid; linear system; ellipsoidal state estimation; nonlinear systems; set-theoretic recursive state estimation; unknown but bounded noise; nonlinear system equations
Subjects: Interpolation and function approximation (numerical analysis); Interpolation and function approximation (numerical analysis); Filtering methods in signal processing; Combinatorial mathematics; Simulation, modelling and identification; Algebra; Linear control systems
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