Optimal Deployment of Direction-finding Systems

A direction-finding system with multiple direction finders (DFs) is a military intelligence system designed to detect the positions of transmitters of radio frequencies. This dissertation studies three decision problems associated with the direction-finding system.

The first part of this dissertation is to prescribe DF deployment to maximize the effectiveness with which transmitter positions are estimated in an area of interest (AOI). Three methods are presented to prescribe DF 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 enumerations; the third formulates the problem as an integer program and solves it with an efficient network-based label-setting algorithm. Our results show that the third method, which involved use of a surrogate measure as an objective function and an exact label-setting algorithm, is most effective.

The second part of this dissertation is to minimize the number of DFs to cover an AOI effectively, considering obstacles between DFs and transmitters. We formulate this problem as a partial set multicover problem in which at least -fraction of the likely transmitter positions must be covered, each by at least direction finders. We present greedy heuristics with random selection rules for the partial set multicover problem, estimating statistical bounds on unknown optimal values. Our results show that the greedy heuristic with column selection rule, which gives priority for selecting a column that advances more rows to k-coverage, performs best on the partial set multicover problems. Results also show that the heuristic with random row and column selection rules is the best of the heuristics with respect to statistical bounds.

The third part of this dissertation deals with the problem of deploying direction finders with the goal of maximizing the effectiveness with which transmitter positions can be estimated in an AOI while hedging against enemy threats. We present four formulations, considering the probability that a direction finder deployed at a location will survive enemy threats over the planning horizon (i.e., not be rendered inoperative by an attack). We formulate the first two as network flow problems and present an efficient label-setting algorithm. The third and the fourth use the well-known Conditional Value at Risk (CVaR) risk measure to deal with the risk of being rendered inoperative by the enemy. Computational results show that risk-averse decision models tend to deploy some or all DFs in locations that are not close to the enemy to reduce risk. Results also show that a direction-finding system with 5 DFs provides improved survivability under enemy threats.