# Calculating Probability of Detection in Search and Rescue

I wrote a couple of weeks ago about how to calculate a probability density distribution for a missing person search. This was the first element of the optimal search problem. The second element is to be able to calculate the probability of detection.

There have been numerous articles and methodologies proposed in the past. Most of these, unfortunately, have been wrong.

In order to calculate the probability of detection of a search resource you need several pieces of data.

Firstly the search resource’s track length must be calculated. In most cases this is simply a case of using a GPS track. However, with a foot search team, this must be multiplied by the number of searchers.

This figure is multiplied by the search resource’s “sweep width”. [I will explain more on sweep widths another time.]

This gives a Area Effectively Swept. This figure is divided by the Size of the Search Area to give the Search Coverage.

Once you know the Coverage you can use Koopman’s Exponential Detection Function to calculate POD.

Simple, eh?