On the Optimal Deployment of Direction Finders

Abstract

The military uses direction finders to locate enemy forces by detecting the positions of transmitters that emit radio frequencies. This paper studies the deployment of direction finders with the objective of maximizing the effectiveness with which transmitter positions can be estimated in an area of interest. We present three methods to prescribe deployment. The first method uses Stansfield's probability density function to compute objective function coefficients numerically. The second and the third employ surrogate measures of effectiveness as objective functions. The second method, like the first, involves complete enumeration; the third formulates the problem as an integer program and solves it with an efficient network-based label-setting algorithm. We perform computational tests to evaluate the relative speed and position-estimation effectiveness of each method. Note to Practitioners-The problem that motivated this paper is that of triangulating the position of a radio transmitter on a battlefield. It is important to determine enemy positions, perhaps from the emissions of a communication device, to plan offensive, and perhaps defensive actions. Triangulation is also important to rescue operations, for example, locating downed aircraft and stranded ships. We employ several methodologies in this study, including simulation, numerical integration, and complete enumeration but synthesize our primary methodology using a surrogate measure of detection effectiveness and dynamic programming to solve a specially structured, constrained shortest path problem. Our method is well suited for battlefield application and our research continues to enhance our model, taking into consideration obstructions that might interfere with radio transmissions as well as uncertainty.