Search for a moving target under minimax estimation

Abstract

A target is assumed to choose its starting position in a search at an unknown position in a finite search space. No prior probability distribution for the target's initial location is assumed. During the search the target is assumed to move from position to position in the search space according to a Markov process. A search is defined to be the observation of a sequence of random variables. Representations for the minimax estimator for target location at any stage of the search, the least favorable prior distribution for the target, and the value of the estimation game are presented. An example is computed in which Bayes estimators are compared with minimax estimators for target location.