On several properties of uniformly optimal search plans

TL;DR

This paper extends the known properties of uniformly optimal search plans from specific distributions to any continuous target distribution, aiding practical search missions.

Contribution

It generalizes the properties of uniformly optimal search plans beyond circular normal distributions to all continuous distributions.

Findings

Properties hold for any continuous target distribution

Provides guidance for real-world search missions

Enhances understanding of search plan optimality

Abstract

The uniformly optimal search plan is a cornerstone of the optimal search theory. It is well-known that when the target distribution is circular normal and the detection function is exponential, the uniformly search plan has several desirable properties. This article establishes that these properties hold for any continuous target distribution. The results provide useful information to the search team when they need to choose a non-circular normal target distribution in a real-world search mission.