On the Optimal Deployment of Direction Finders

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.