Spatial operations on uncertain positional data

Abstract

Positional errors on spatial data affect spatial join accuracy in an unexpected and undesirable way. Furthermore, current probabilistic solutions barely achieve reasonable computational performance, unless they are employed in special cases such as when the errors follow a Circular Normal distribution. This paper presents a general framework for spatial operations that are robust to positional imprecision in geographic coordinates. The framework is designed to be i) generalist, ii) accurate, and iii) efficient. Two spatial operations are presented as case studies for the proposed framework. We developed some new procedures concerning spatial joins:
an adaptation of the Monte Carlo method to be used as a probabilistic filtering step and a probabilistic efficient alternative to Minimum Bounding Rectangles, which we call Confidence Rectangles. Empirical evidence suggests that our solution is Pareto efficient concerning these requirements, i.e., it is not outperformed by any competing solution. Moreover, the parameters of our solution corresponding to accuracy and efficiency may be adjusted to maximize the gain in one while relaxing the other according to the user's demand.