Description and application of a new method for uncertainty evaluation in two-dimensional indirect measurement

It is described an improved method for two-dimensional uncertainty expression and propagation based on the theory of evidence, employing 2D random-fuzzy variables (RFVs) as the main tool. The improved approach exploits a new algorithm for the combination of random and systematic effects, trying to overcome a drawback of a 2D RFV method already disclosed in a previous work. Uncertainty evaluation in multi dimensional measurements is usually carried out using a probabilistic approach which relies on Monte Carlo simulations or on the GUM formula with covariance matrices for propagation, while a random-fuzzy approach for multi dimensional applications is almost completely new. The described improved method is applied to the 2D case of vehicle position measurement on a plane. The obtained results are compared with those obtained by the probabilistic approach with Monte Carlo simulations and by the previous 2D RFV method already disclosed. The results show that the confidence regions obtained by all three approaches are compatible and that the improved random-fuzzy method yields a better uncertainty evaluation in case of narrow and elongated confidence regions than the previous one. The new 2D RFV approach exhibits a better behavior also from a theoretical point of view.