Modeling and Analysis of Exhaustive Probabilistic Search

Abstract

This article explores a probabilistic formulation for exhaustive search of a bounded area by a single searcher for a single static target. The searcher maintains an aggregate belief of the target’s presence or absence in the search area, concluding with a positive or negative search decision on crossing of decision thresholds. The measure of search performance is defined as the expected time until a search decision is made as well as the probability of the search decision being correct. The searcher gathers observations using an imperfect detector, that is, one with false positive and negative errors, and integrates them in an iterative Bayesian manner. Analytic expressions for the Bayesian update recursion of the aggregate belief are given, with theoretical results describing the role of positive and negative detections, as well as sensitivity results for the effect of the detection errors on the aggregate belief evolution. Statistical studies via design of simulation experiments provide insights into the significant search parameters, including imperfect sensor characteristics, initial belief value, search decision threshold values, and the available prior probability information. Regression analysis yields statistical models to provide prescriptive guidance on the search performance as a function of these search parameters.