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Interval Computations and IntervalRelated Statistical Techniques: Tools for Estimating Uncertainty of the Results of Data Processing and Indirect Measurements
"... In many practical situations, we only know the upper bound ∆ on the (absolute value of the) measurement error ∆x, i.e., we only know that the measurement error is located on the interval [−∆, ∆]. The traditional engineering approach to such situations is to assume that ∆x is uniformly distributed on ..."
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In many practical situations, we only know the upper bound ∆ on the (absolute value of the) measurement error ∆x, i.e., we only know that the measurement error is located on the interval [−∆, ∆]. The traditional engineering approach to such situations is to assume that ∆x is uniformly distributed on [−∆, ∆], and to use the corresponding statistical techniques. In some situations, however, this approach underestimates the error of indirect measurements. It is therefore desirable to directly process this interval uncertainty. Such “interval computations” methods have been developed since the 1950s. In this chapter, we provide a brief overview of related algorithms, results, and remaining open problems.
Guaranteed Characterization of Capture Basins of Nonlinear StateSpace Systems
 In Informatics in Control, Automation and Robotics: Selected Papers from the International Conference on Informatics in Control, Automation and Robotics 2007
, 2008
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Interval Computations as an Important Part of Granular Computing: An Introduction
 in Handbook of Granular Computing, Chapter 1
, 2008
"... This chapter provides a general introduction to interval computations, especially to interval computations as an important part of granular computing. ..."
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Cited by 4 (1 self)
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This chapter provides a general introduction to interval computations, especially to interval computations as an important part of granular computing.
8. NUMERICAL TECHNIQUES An intervalbased target tracking approach for rangeonly multistatic radar
"... Abstract—This paper investigates the use of interval analysis to solve the problem of maneuvering target tracking, using rangeonly measures collected by a multistatic radar. The problem consists in one transmitter, and some receivers working together as a multistatic radar. The radar process is plag ..."
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Abstract—This paper investigates the use of interval analysis to solve the problem of maneuvering target tracking, using rangeonly measures collected by a multistatic radar. The problem consists in one transmitter, and some receivers working together as a multistatic radar. The radar process is plagued by several uncertainty sources that affect directly the receivers ’ measures. As a result, target tracking can be both imprecise and unreliable. This study presents the Tracking using an IntervalBased Approach (TIBA) that computes the set of all feasible configurations for the target which are consistent with the measures. The algorithm is compared to a conventional tracking method: particle filtering. solution is. However, Interval Analysis suffers from some criticisms, as the (relatively) slowness of their implementation, for instance. Hansen and Walster [7] refuted most of these and showed the advantages of the interval approaches as for example: the possibility to obtain the solution of certain problems that can not be solved by noninterval methods, the convergence of their algorithms and the reliability of their results. These facts have motivated the use of the interval methodology to solve the tracking problem. Index Terms—target tracking; manoeuvering target; multistatic radar; interval analysis; interval methods. I.
8. NUMERICAL TECHNIQUES An intervalbased target tracking approach for rangeonly multistatic radar
"... Abstract—This paper investigates the use of interval analysis to solve the problem of maneuvering target tracking, using rangeonly measures collected by a multistatic radar. The problem consists in one transmitter, and some receivers working together as a multistatic radar. The radar process is pla ..."
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Abstract—This paper investigates the use of interval analysis to solve the problem of maneuvering target tracking, using rangeonly measures collected by a multistatic radar. The problem consists in one transmitter, and some receivers working together as a multistatic radar. The radar process is plagued by several uncertainty sources that affect directly the receivers ’ measures. As a result, target tracking can be both imprecise and unreliable. This study presents the Tracking using an IntervalBased Approach (TIBA) that computes the set of all feasible configurations for the target which are consistent with the measures. The algorithm is compared to a conventional tracking method: particle filtering. Index Terms—target tracking; manoeuvering target; multistatic radar; interval analysis; interval methods. I.
1Department of Mathematical Sciences
"... Abstract It is known that there are feasible algorithms for minimizing convex functions, and that for general functions, global minimization is a difficult (NPhard) problem. It is reasonable to ask whether there exists a class of functions that is larger than the class of all convex functions for w ..."
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Abstract It is known that there are feasible algorithms for minimizing convex functions, and that for general functions, global minimization is a difficult (NPhard) problem. It is reasonable to ask whether there exists a class of functions that is larger than the class of all convex functions for which we can still solve the corresponding minimization problems feasibly. In this paper, we prove, in essence, that no such more general class exists. In other words, we prove that global optimization is always feasible only for convex objective functions. 1 Introduction It is well known that in general, global optimization is a difficulttosolve problem. In particular, it is known that even the problem of minimizing an objective
ABSTRACT HATTANGADY, SANDEEP K. Development of a Block Floating Point Interval ALU
"... for DSP and Control Applications. (Under the direction of Professor Willam W. ..."
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for DSP and Control Applications. (Under the direction of Professor Willam W.
Ordering events: more general sets
"... are usually not necessary Traditionally, an interval is used to describe incomplete knowledge aba)ut a moment of time "when an event oecured. In principle, more general.s ts are ~)metim~s needed to describe our knowledge. In this paper, we silow that if we are (rely interested in the ordering o ..."
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are usually not necessary Traditionally, an interval is used to describe incomplete knowledge aba)ut a moment of time "when an event oecured. In principle, more general.s ts are ~)metim~s needed to describe our knowledge. In this paper, we silow that if we are (rely interested in the ordering of events, then intervals are ufficient. This result pr(wides (me me)re justification for the use of the intervals. AA, ~ yl~op,~AOqnBaHmI C06bITnfl AOCTaTOqIIO TepBaaOB, 6oaee o6m e BHABI MHOJKeCTB,