Optimal search density for a stationary target among stationary false targets

This paper considers rational methods for the design of search densities when the intended target is stationary among stationary, Poisson-distributed false contacts. Attention is restricted to situations in which the searcher must immediately decide, based on sensed information, whether a contact is the intended target and, if the answer is yes, end the search and commit to the contact. Discrimination of false contact from target is modeled as reliable only with given probabilities. The paper seeks to allocate search effort to maximize the probability of finding the intended target in a fixed time. Modeling space and time as discrete, it applies the Kuhn-Tucker theorem to obtain a set of necessary conditions for an optimum. For the particular case of a discrete space and time approximation of search for a normally distributed target in R² and a uniform density of false contacts, the paper develops a computer algorithm that converges to a solution of the necessary conditions. Numerical results are presented.