On probabilistic search decisions under searcher motion constraints

Abstract

This article presents a sequential decision-theoretic formulation for conducting probabilistic search for a stationary target in a search region. A general recursion expression describing the evolution of the search decision (i.e., presence or absence of the target) is derived, which relates the temporal sequence of imperfect detections, both false positives and false negatives, to the spatial search conducted by a search agent. This relationship enables quantification of the decision performance - time till decision - for a given search strategy. Also, the role of searcher motion constraints, represented by a search graph, on the time till decision is characterized by the second smallest eigenvalue of the Laplacian of this graph. Numerical studies demonstrate this relationship. © 2009 Springer-Verlag.