The Possibilistic Kalman Filter: Definition and Comparison With the Available Methods

Ferrero, Alessandro; Jetti, Harsha Vardhana; Salicone, Simona

doi:10.1109/tim.2020.3010193

“…Other more specific applications are present in the more recent literature, like for instance the generalization of Bayes' theorem in the possibility domain [19,20] or the realization of a possibilistic Kalman filter [21,22], thus showing the versatility of the RFV approach. Obtained results when case studies B and C are considered: GUM approach (red lines), Monte Carlo approach (blue lines), RFV approach (cyan lines).…”

Section: Discussionmentioning

confidence: 99%

“…Other more specific applications are present in the more recent literature, like for instance the generalization of Bayes' theorem in the possibility domain [19,20] or the realization of a possibilistic Kalman filter [21,22], thus showing the versatility of the RFV approach.…”

Section: Figure 13mentioning

confidence: 99%

A General Mathematical Approach Based on the Possibility Theory for Handling Measurement Results and All Uncertainties

Salicone

¹

,

Jetti

²

2021

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The concept of measurement uncertainty was introduced in the 1990s by the “Guide to the expression of uncertainty in measurement”, known as GUM. The word uncertainty has a lexical meaning and reflects the lack of exact knowledge or lack of complete knowledge about the value of the measurand. Thanks to the suggestions in the GUM and following the mathematical probabilistic approaches therein proposed, an uncertainty value can be found and be associated to the measured value. In the last decades, however, other methods have been proposed in the literature, which try to encompass the definitions of the GUM, thus overcoming its limitations. Some of these methods are based on the possibility theory, such as the one known as the RFV method. The aim of this paper is to briefly recall the RFV method, starting from the very beginning and the initial motivations, and summarize in a unique paper the most relevant obtained results.

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“…given by [31] () =− =1 log 2 (12) And () and () represent nonspecificity and strife of possibility distribution [21], respectively, given by…”

Section: Klir's Uncertainty-preservation Transformationmentioning

confidence: 99%

“…As an alternative method to fuzzy sets for handling fuzzy uncertainty, possibility theory has in recent decades received extensive attention [1][2][3][4][5][6][7][8][9][10][11][12][44][45][46]. It was lately demonstrated that probability and possibility are customized for the measure of randomness and fuzziness, respectively [6].…”

Section: Introductionmentioning

confidence: 99%

Probability-Possibility Transformation under Perspective of Random-fuzzy Dual Interpretation of Unknown Uncertainty

Mei¹,

Li²,

Xu³

et al. 2022

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0

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Information-preservation is recognized as the only principle for probability-possibility transformation in this work and the normalized transformation is the right method. This is based on the viewpoint that the reason we can transfer probability and possibility is that we believe the uncertainty being handled can be information-equivalently described by both probability and possibility. That viewpoint is endorsed by the random-fuzzy dual interpretation of unknown uncertainty, which says that unknown uncertainty being estimated could be interpreted as either randomness or fuzziness, depending on the available prior information and the perspective of cognition and modeling. Information of uncertain variable is defined in this work as its distribution. The suggested information-preservation principle is different from Klir’s principle, which is in fact an entropy-preservation principle. Then we investigated the problem of information preservation and propagation in parallel probability-possibility systems. By parallel, we mean the two uncertainty systems have the same priori information. After uncertainty propagation the two parallel systems will generally bifurcate, which means information preservation only holds locally between the two parallel systems. This observation accords with our intuition since probability and possibility use different normalizations as well as different disjunctive operators, which makes them two different uncertainty systems appropriate for randomness and fuzziness, respectively.

show abstract

“…As an alternative method to fuzzy sets for handling fuzzy uncertainty, possibility theory has in recent decades received extensive attention [1][2][3][4][5][6][7][8][9][10][11][12][44][45][46]. It was lately demonstrated that probability and possibility are customized for the measure of randomness and fuzziness, respectively [6].…”

Section: Introductionmentioning

confidence: 99%

Probability-Possibility Transformation under Perspective of Random-fuzzy Dual Interpretation of Unknown Uncertainty

Mei¹,

Gan²,

Xu³

et al. 2021

Preprint

1

0

View full text Add to dashboard Cite

Information-preservation is recognized as the only principle for probability-possibility transformation in this work and the normalized transformation is the right method. This is based on the viewpoint that the reason we can transfer probability and possibility is that we believe the uncertainty being handled can be information-equivalently described by both probability and possibility. That viewpoint is endorsed by the random-fuzzy dual interpretation of unknown uncertainty, which says that unknown uncertainty being estimated could be interpreted as either randomness or fuzziness, depending on the available prior information and the perspective of cognition and modeling. Information of uncertain variable is defined in this work as its distribution. The suggested information-preservation principle is different from Klir’s principle, which is in fact an entropy-preservation principle. Then we investigated the problem of information preservation and propagation in parallel probability-possibility systems. By parallel, we mean the two uncertainty systems have the same priori information. After uncertainty propagation the two parallel systems will generally bifurcate, which means information preservation only holds locally between the two parallel systems. This observation accords with our intuition since probability and possibility use different normalizations as well as different disjunctive operators, which makes them two different uncertainty systems appropriate for randomness and fuzziness, respectively.

show abstract

The Possibilistic Kalman Filter: Definition and Comparison With the Available Methods

Cited by 12 publications

References 26 publications

A General Mathematical Approach Based on the Possibility Theory for Handling Measurement Results and All Uncertainties

A General Mathematical Approach Based on the Possibility Theory for Handling Measurement Results and All Uncertainties

Probability-Possibility Transformation under Perspective of Random-fuzzy Dual Interpretation of Unknown Uncertainty

Probability-Possibility Transformation under Perspective of Random-fuzzy Dual Interpretation of Unknown Uncertainty

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