Modeling directional uncertainties in 2D spaces

As an indispensible component in understanding spatial processes, direction has been concerned by researchers of related disciplines for a long time. Challenges still remain in modeling directional uncertainties due to randomness of positional information in the input data. By formulating involving cumulative distribution functions (CDFs) and corresponding probability density functions (PDFs), this paper modeled the directional uncertainty between an accurate point and an uncertain one as well as that between two uncertain points respectively in 2D spaces on the condition of that the real position corresponding to the observed one of an uncertain point follows either Poisson distribution or the kernel function decreasing from the center to periphery within its error circle. The established models accurately quantify the correlation of the directional uncertainty with r (the radius of the error circle of the uncertain point), L (the observed distance containing one or two uncertain points), and their ratio (r/L) for the four different situations respectively, which opens up a new way for related studies including spatial query, analysis and reasoning, etc. Experimental results indicate that the proposed methods in this article are more efficient, robust than the corresponding Monte Carlo simulation. Their effectiveness has also been demonstrated with practical cases.