Topic
Chebyshev center
About: Chebyshev center is a research topic. Over the lifetime, 121 publications have been published within this topic receiving 913 citations.
Papers published on a yearly basis
Papers
TL;DR: A fault-tolerant GCC fusion algorithm is proposed by introducing an adaptive parameter, which can obtain robust fusion and the degree of robustness varies with that of incoherency between estimates to be fused.
Abstract: The problem of distributed fusion for estimation when the cross-correlation of errors of local estimates is unavailable is addressed. We discuss a general estimation fusion approach for this problem-generalized convex combination (GCC) - and classify various GCC fusion approaches in three categories. We develop three GCC fusion algorithms for the problem under consideration. First, based on a set-theoretic formulation of the problem, we propose a relaxed Chebyshev center covariance intersection (RCC-CI) algorithm to fuse the local estimates. Second, based on an information-theoretic criterion, we develop a fast covariance intersection (IT-FCI) algorithm with weights in a closed form. The proposed RCC-CI and IT-FCI algorithms are characterized by both the local estimates and the mean-square error (MSE) matrices being taken into account. Third, to fuse incoherent local estimates, we propose a fault-tolerant GCC fusion algorithm by introducing an adaptive parameter, which can obtain robust fusion and the degree of robustness varies with that of incoherency between estimates to be fused.
148 citations
TL;DR: The conditional Chebyshev center problem is solved for the case when energy norm-bounded disturbances are considered and a closed-form solution is obtained by finding the unique real root of a polynomial equation in a semi-infinite interval.
Abstract: This paper deals with conditional central estimators in a set membership setting. The role and importance of these algorithms in identification and filtering is illustrated by showing that problems like worst case optimal identification and state filtering, in contexts in which disturbances are described through norm bounds, are reducible to the computation of conditional central algorithms. The conditional Chebyshev center problem is solved for the case when energy norm-bounded disturbances are considered. A closed-form solution is obtained by finding the unique real root of a polynomial equation in a semi-infinite interval.
90 citations
TL;DR: The structure of the complements of Chebyshev sets is studied, in particular considering the following question: How many connected components can the complement of a ChebysHEv set in a finite-dimensional normed or nonsymmetrically normed linear space have?
Abstract: A set is called a Chebyshev set if it contains a unique best approximation element. We study the structure of the complements of Chebyshev sets, in particular considering the following question: How many connected components can the complement of a Chebyshev set in a finite-dimensional normed or nonsymmetrically normed linear space have? We extend some results from [A. R. Alimov, East J. Approx, 2, No. 2, 215--232 (1996)]. A. L. Brown's characterization of four-dimensional normed linear spaces in which every Chebyshev set is convex is extended to the nonsymmetric setting. A characterization of finite-dimensional spaces that contain a strict sun whose complement has a given number of connected components is established.
43 citations
TL;DR: An optimal estimator is developed for the new performance metric, which quantifies the asymptotic decay rate for the probability of having an estimation error larger than $\delta$, which is the Chebyshev center of a union of ellipsoids.
Abstract: This article studies static state estimation in multisensor settings, with a caveat that an unknown subset of the sensors are compromised by an adversary, whose measurements can be manipulated arbitrarily. The attacker is able to compromise $q$ out of $m$ sensors. A new performance metric, which quantifies the asymptotic decay rate for the probability of having an estimation error larger than $\delta$ , is proposed. We develop an optimal estimator for the new performance metric with a fixed $\delta$ , which is the Chebyshev center of a union of ellipsoids. We further provide an estimator that is optimal for every $\delta$ , for the special case where the sensors are homogeneous. Numerical examples are given to elaborate the results.
40 citations
TL;DR: In this paper, an algorithm for finding the Chebyshev center of a finite point set in the Euclidean space Rn is proposed, where the current point is projected orthogonally onto the convex hull of a subset of a given point set.
Abstract: An algorithm for finding the Chebyshev center of a finite point set in the Euclidean spaceRn is proposed. The algorithm terminates after a finite number of iterations. In each iteration of the algorithm the current point is projected orthogonally onto the convex hull of a subset of the given point set.
38 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 5 |
| 2020 | 4 |
| 2019 | 6 |
| 2018 | 4 |
| 2017 | 4 |
| 2016 | 8 |