Modeling distance uncertainties in two-dimensional space

Abstract

Distances are functions of spatial positions, therefore distance uncertainties should be resulted from transmission of spatial position uncertainties via the functional relationships accordingly. How to model the transmission precisely, a challenging problem in GIScience, has increasingly drawn attentions during the past several decades. Aiming at the limitations of presently available solutions to the problem, this article derived probability distribution functions and corresponding density functions of distance uncertainties in two-dimensional space related to one or two uncertain endpoints respectively, under the premise that real positions, corresponding with the observed position of an uncertain point, follow the kernel function within its error circle. The density functions were employed to explore the diffusing law of uncertainty information from point positions to distances, which opened up a new way for thoroughly solving problems of measuring distance uncertainties. It turns out that the proposed methods in this article are more efficient, robust than the corresponding Monte Carlo ones, which verifies their effectiveness and advantages.