Visit Probability in Space–Time Prisms Based on Binomial Random Walk

Abstract

Space–time prisms are used to model the uncertainty of space–time locations of moving objects between (for instance, GPS-measured) sample points. However, not all space–time points in a prism are equally likely and we propose a simple, formal model for the so-called “visit probability” of space–time points within prisms. The proposed mathematical framework is based on a binomial random walk within one- and two-dimensional space–time prisms. Without making any assumptions on the random walks (we do not impose any distribution nor introduce any bias towards the second anchor point), we arrive at the conclusion that binomial random walk-based visit probability in space–time prisms corresponds to a hypergeometric distribution.