Discrete search stability for a hidden target on M-intervals with a known probabilistic distributed effort

Abstract

We consider a discrete search problem to detect a hidden target on one of the [Formula: see text]-intersected real lines at the origin. The target position is a vector of independent random variables with a known multivariate probability distribution that is symmetric around the origin. From the available information about the probability of the target, we can consider one bounded interval as a search space on each line. To maximize the detection probability, we divide each interval into a number of small subintervals. Some subintervals have low target probabilities; thus, we delete them and distribute their probabilities among the searched subintervals. The problem has a discrete version where each line contains a set of independent search subintervals. The search effort is bounded by a normal distribution. More than obtaining the maximum detection probability, we also need to get the minimum search effort to detect the target. After studying the stability of the minimum search effort, we present an illustrative example to show the effectiveness of our model.