Rapid BLE Beacon Localization with Range-Only EKF-SLAM Using Beacon Interval Constraint

Abstract The “labeled interval calculus” is a formal system that performs quantitative inferences about sets of artifacts under sets of operating conditions. It refines and extends the idea of interval constraint propagation, and has been used as the basis of a program called a “mechanical design compiler,” which provides the user with a “high level language” in which design problems for systems to be built of cataloged components can be quickly and easily formulated. The compiler then selects optimal combinations of catalog numbers. Previous work has tested the calculus empirically, but only parts of the calculus have been proven mathematically. This paper presents a new version of the calculus and shows how to extend the earlier proofs to prove the entire system. It formalizes the effects of toleranced manufacturing processes through the concept of a “selectable subset” of the artifacts under consideration. It demonstrates the utility of distinguishing between statements which are true for all artifacts under consideration, and statements which are merely true for some artifact in each selectable subset.

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Interval constraint spreadsheets for financial planning

Proceedings First International Conference on Artificial Intelligence Applications on Wall Street ◽

10.1109/aiaws.1991.236585 ◽

2002 ◽

Cited By ~ 4

Author(s):

E. Hyvonen

Keyword(s):

Financial Planning ◽

Interval Constraint

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Methodology for the Assessment of Imprecise Multi-State System Availability

Mathematics ◽

10.3390/math10010150 ◽

2022 ◽

Vol 10 (1) ◽

pp. 150

Author(s):

Joanna Akrouche ◽

Mohamed Sallak ◽

Eric Châtelet ◽

Fahed Abdallah ◽

Hiba Hajj Chehade

Keyword(s):

Markov Chains ◽

Constraint Propagation ◽

State System ◽

Combined Approach ◽

System Availability ◽

Contraction Method ◽

Numerical Examples ◽

Complex Architectures ◽

Backward Propagation ◽

Interval Constraint

Most existing studies of a system’s availability in the presence of epistemic uncertainties assume that the system is binary. In this paper, a new methodology for the estimation of the availability of multi-state systems is developed, taking into consideration epistemic uncertainties. This paper formulates a combined approach, based on continuous Markov chains and interval contraction methods, to address the problem of computing the availability of multi-state systems with imprecise failure and repair rates. The interval constraint propagation method, which we refer to as the forward–backward propagation (FBP) contraction method, allows us to contract the probability intervals, keeping all the values that may be consistent with the set of constraints. This methodology is guaranteed, and several numerical examples of systems with complex architectures are studied.

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Safe Approximations for Distributionally Robust Joint Chance Constrained Program

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595915400047 ◽

2015 ◽

Vol 32 (01) ◽

pp. 1540004 ◽

Cited By ~ 1

Author(s):

Chenchen Wu ◽

Dachuan Xu ◽

Jiawei Zhang

Keyword(s):

Covariance Matrix ◽

Second Order ◽

Uncertain Parameters ◽

Cone Programming ◽

Second Order Cone Programming ◽

Numerical Tests ◽

Second Order Cone ◽

Distributionally Robust ◽

Interval Constraint

In this paper, we present a bilinear second-order cone programming safe approximation for the distributionally robust chance constrained program (DRCCP), assuming that the support of the uncertain parameters, and the first and second marginal moments of the probability with respect to the interval constraint imposed on the sum of the uncertain parameters are given. If we further know the covariance matrix, we can obtain a bilinear semi-definite programming safe approximation. Preliminary numerical tests indicate that the proposed models are competitive.

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