A new approximate algorithm for the Chebyshev center

The parameter or state estimation with bounded noises is getting increasingly important in many applications of practical systems with some uncertainties. The problem to estimate a deterministic parameter or state which is known to lie in an intersection of some ellipsoids can be formulated to find...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 49; no. 8; pp. 2483 - 2488
Main Authors: Wu, Duzhi, Zhou, Jie, Hu, Aiping
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.08.2013
Elsevier
Subjects:
Algorithms
Applied sciences
Approximation
Bounded noise
Chebyshev approximation
Chebyshev center
Computer science; control theory; systems
Control theory. Systems
Ellipsoidal estimation
Ellipsoids
Estimates
Estimation fusion
Exact sciences and technology
Intersections
Modelling and identification
Norms
Positive semidefinite relaxation
State estimation
Ellipsoidal estimation
Positive semidefinite relaxation
Bounded noise
Chebyshev center
Estimation fusion
Estimation error
Parameter estimation
Non convex programming
Error estimation
Chebyshev polynomial
Semi definite programming
L2 approximation
Robust control
Uncertain system
Minimax problem
Minimax method
Data fusion
System identification
Deterministic approach
Ellipsoid
State estimation
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Summary:The parameter or state estimation with bounded noises is getting increasingly important in many applications of practical systems with some uncertainties. The problem to estimate a deterministic parameter or state which is known to lie in an intersection of some ellipsoids can be formulated to find the Chebyshev center of the intersection set in the case of l2 norm of the estimation error. In this paper, an appropriate positive semidefinite relaxation of non-convex optimization problem is derived, and then a new algorithm for robust minimax estimation is provided. Some examples are given to compare the approximate estimate with the existing relaxed Chebyshev center.
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ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2013.04.029