Optimal search strategy for a three-dimensional randomly located target

In this paper, we formulate a new search model that finds a three‐dimensional randomly located target in a known zone by a single searcher. The searcher wishes to find the target's position, that is given by the value of the three independent trivariate random variables (X, Y, Z) and they have joint symmetric probability density function f(x, y, z). The purpose is to obtain an optimal search strategy that minimises the expected value of the time required to detect the target, assuming trivariate standard normal distributed estimates of its position. An illustrative example is given to demonstrate the applicability of this technique.