Uncertainty Evaluation in Two-Dimensional Indirect Measurement by Evidence and Probability Theories

An improved method for 2-D uncertainty expression and propagation based on the theory of evidence and 2-D random-fuzzy variables (RFVs) is described. A previous 2-D RFV approach and two probability-based approaches are also introduced. The improved RFV approach exploits a new algorithm for the combination of random and systematic effects, trying to overcome a drawback of a 2-D RFV method already disclosed in a previous work. One of the two probability-based methods does not take into account any correlation among uncertainty sources and among different time instants of each source, whereas the other probability method exploits time correlation to take into account the repetitive nature of systematic uncertainty sources. All described methods are applied to the 2-D case of a vehicle position measurement on a plane. The obtained results are compared and show the compatibility of all approaches. The improved random-fuzzy method yields better uncertainty evaluation in case of narrow and elongated confidence regions than the previous method. The new 2-D RFV approach also exhibits a better behavior from a theoretical point of view. Main differences between the two probability-based methods are also presented.