Modeling and Processing Measurement Uncertainty Within the Theory of Evidence: Mathematics of Random–Fuzzy Variables

2007 ◽  
Vol 56 (3) ◽  
pp. 704-716 ◽  
Author(s):  
Alessandro Ferrero ◽  
Simona Salicone
Keyword(s):  
Measurement Uncertainty ◽  
Fuzzy Variables ◽  
Processing Measurement ◽  
Random Fuzzy Variables ◽  
Theory Of Evidence

Study on Random-Fuzzy Variables Method for ADC Measurement Uncertainty Evaluation

2014 ◽  
Vol 568-570 ◽  
pp. 76-81
Author(s):  
Wei Jiang ◽  
Qi Zhang
Keyword(s):  
Measurement Uncertainty ◽  
Random Effects ◽  
Uncertainty Propagation ◽  
Uncertainty Evaluation ◽  
Fuzzy Variables ◽  
Measurement Result ◽  
Random Fuzzy Variables ◽  
Theory Of Evidence ◽  
Power Measurements ◽  
Measurement Uncertainty Evaluation

The random-fuzzy variables (RFVs) method based on the theory of evidence is studied, for the need of ADC uncertainty evaluation and the limitations of existing approaches. The connotation of RFVs adopted for expression of measurement result together with its associated uncertainty is discussed, and the RFVs mathematics for uncertainty propagation is analyzed. RFVs can naturally separate the contributions to the measurement uncertainty of the systematic and random effects. Taking power measurements as an example, RFVs method is applied to the presentation and propagation of the measurement uncertainty of ADC, and the results are compared with those obtained by GUM, which shows the RFVs method can be effectively employed in evaluating uncertainty of ADC, and is capable of providing the interval of confidence for all possible levels of confidence, within which the measurement result is supposed to lie.

scholarly journals A Possibilistic Kalman Filter for the Reduction of the Final Measurement Uncertainty, in Presence of Unknown Systematic Errors

Metrology ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 39-51
Author(s):  
Harsha Vardhana Jetti ◽  
Simona Salicone
Keyword(s):  
Kalman Filter ◽  
Measurement Uncertainty ◽  
Systematic Error ◽  
Kalman Filters ◽  
Systematic Errors ◽  
The State ◽  
Fuzzy Variables ◽  
Final Measurement ◽  
Random Fuzzy Variables ◽  
System States

A Kalman filter is a concept that has been in existence for decades now and it is widely used in numerous areas. It provides a prediction of the system states as well as the uncertainty associated to it. The original Kalman filter can not propagate uncertainty in a correct way when the variables are not distributed normally or when there is a correlation in the measurements or when there is a systematic error in the measurements. For these reasons, there have been numerous variations of the original Kalman filter, most of them mathematically based (like the original one) on the theory of probability. Some of the variations indeed introduce some improvements, but without being completely successful. To deal with these problems, more recently, Kalman filters have also been defined using random-fuzzy variables (RFVs). These filters are capable of also propagating distributions that are not normal and propagating systematic contributions to uncertainty, thus providing the overall measurement uncertainty associated to the state predictions. In this paper, the authors make another step forward, by defining a possibilistic Kalman filter using random-fuzzy variables which not only considers and propagates both random and systematic contributions to uncertainty, but also reduces the overall uncertainty associated to the state predictions by compensating for the unknown residual systematic contributions.

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