Applied Interval Analysis

Jaulin, Luc; Kieffer, Michel; Didrit, Olivier; Walter, Éric

doi:10.1007/978-1-4471-0249-6

Cited by 1,304 publications

(1,049 citation statements)

References 153 publications

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“…Most of the notions of interval analysis can be found in Jaulin et al [2001] in which an interval [x] is defined as a closed and connected subset of R: Since it is impossible to solve directly the Kalman filtering problem due to parameter uncertainties, our goal is to obtain an upper bound P + k such that:…”

Section: Problem Formulationmentioning

confidence: 99%

“…In order to reduce the effect of the dependency problem (Jaulin et al [2001]), the Equation (2) is rearranged as follows:…”

Section: Correction Stepmentioning

confidence: 99%

“…the solution set may not include all the classical Kalman filter solutions consistent with the bounded uncertainties represented in the system. In Xiong et al [2013], an improved interval Kalman filter (iIKF) has been proposed that solves the interval matrix inversion problem with the set inversion algorithm SIVIA (Set Inversion Via Interval Analysis) and constraint satisfaction problems (CSP) (see Jaulin et al [2001]). Nevertheless, this algorithm demands high computational time if there exist large uncertainties affecting the considered system (see Tran et al [2016]).…”

Section: Introductionmentioning

confidence: 99%

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Interval Kalman filter enhanced by positive definite upper bounds

et al. 2017

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A method based on the interval Kalman filter for discrete uncertain linear systems is presented. The system under consideration is subject to bounded parameter uncertainties not only in the state and observation matrices, but also in the covariance matrices of Gaussian noises. The gain matrix provided by the filter is optimized to give a minimal upper bound on the state estimation error covariance for all admissible uncertainties. The state estimation is then determined by using interval analysis in order to enclose the set of all possible solutions with respect to the classical Kalman filtering structure.

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Section: Problem Formulationmentioning

confidence: 99%

“…In order to reduce the effect of the dependency problem (Jaulin et al [2001]), the Equation (2) is rearranged as follows:…”

Section: Correction Stepmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Interval Kalman filter enhanced by positive definite upper bounds

et al. 2017

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“…BUGF (Believe Universal Generated Function) [12] and IUGF (Interval Universal Generated Function) [11] are two methods based on the UGF (Universal Generated Function) but they are applied on intervals and therefore are used in the case of interval-modeled imprecision, these two methods are efficient and give good results, the IUGF is also noted as more efficient than the BUGF in [12]. In our approach we propose to determine the availability of the system by using a new technique applied on intervals, that is the technique of contractors [4] which we introduce in section 3.…”

Section: Imprecise Markov Chainmentioning

confidence: 99%

“…"Intervalization with Gauss elimination" [4] is an important class of CSPs for which intervalization of finite subsolvers can be employed only if the system is formed of linear interval equations and if all elements on the diagonal of the matrix are different than zero. "Gauss-Seidel" contractor is an efficient way to contract intervals of a linear system but the matrix in this case must be reversible [4]. "Krawczyk and Newton contractors" are two contractors which are not always applicable and are much complicated than the other contractors [4].…”

Section: Types Of Contractorsmentioning

confidence: 99%