Approximating the Probabilities of Detecting and of Hitting Targets and the Probability Distribution of the Number of Trials Along the Visible Portions of Curves in the Plane Subject to a Poisson Shadowing Process

摘要

A target (deer) is moving along a path in the forest. The path is partly obscured from an observer (hunter) by trees which are randomly dispersed. In order to detect the target there should be a visible window along the path of length tau or larger. If a target is detected, the hunter starts shooting at it. Each shooting trial requires a visibility window of length tau. The hunter continues with the shooting trials until the target is hit or disappears in a shadowed portion of the path. The present paper provides a methodology for approximating the probability of detecting a target, and lower and upper bounds for the probability distribution of the total number of shooting trials along the visible portions of the path. Lower and upper bounds for the probability of hitting the target are provided too. These bounds and approximations are derived under the assumption that the obscuring elements constitute a Poisson random field. (Author)