Locating Direction Finders Optimally under Risk of Detection
Abstract
The military uses direction finders (DFs) to determine the locale of enemy forces by estimating the positions of their transmitters, which emit radio frequencies. This paper considers the problem of locating DFs with the goal of maximizing the accuracy with which transmitter positions can be estimated in a target area while managing the expected number of DFs that will not be detected by the enemy. Once detected, a DF is subject to jamming or attack by the enemy. This paper presents six models, each appropriate for a different battlefield situation. It casts three models as network flow problems and presents an efficient label-setting algorithm to solve them. The remaining formulations represent novel applications of the Conditional Value at Risk (CVaR) to deal with the probability of DF detection. Computational tests compare model solutions.References
U.S. Army,Field Manual 34-4-9, Direction finding operations, Headquarters, Department of the Army: Washington, 1991.
U.S. Army,Field Manual 101-5-1, Operational terms and graphics, Headquarters, Department of the Army: Washington, 1997.
P. Artzner, F. Delbaen, J.M. Eber and D. Heath, Coherent measures of risk, Mathematical Finance 9.3: 203-228, 1999.
M. Desrochers and F.A. Soumis, A generalized permanent labeling algorithm for the shortest path problem with time windows, INFOR 26: 193-214, 1988.
I. Dumitrescu and N. Boland, Algorithms for the weight constrained shortest path problem, International Transactions in Operational Research 8.1: 15-29, 2001.
H.D. Kennedy and R.B. Woolsey, Direction-Finding Antennas and Systems, in Antenna Engineering Handbook, 3rd Edition, edited by R.C. Johnson, Ed, New York: McGraw-Hill, Chapter 39, 1993.
H.H. Jenkins, Small-aperture radio direction-finding, Artech house, Norwood, 1991
S.H. Kim and W.E. Wilhelm, On the optimal deployment of direction finders, IEEE Transactions on Automation Science and Engineering 11(2), 2014.
P. Krokhmal, R. Murphey, P. Pardolas, and S. Uryasev, Robust decision making: Addressing uncertainties in distributions, Cooperative Control:Models, Applications, and Algorithms:165-185, 2003.
H.J. Lee, Y.D. Kim, and S.B. Lee, A simulation-based heuristic algorithm for disposition of direction finders, Computers and Industrial Engineering 55(1): 134-149. 2008.
L. Jingwen and S.A. Quek, Locating a target from directional data, Naval Research Logistics 45(4): 353-364, 1998.
R.T. Rockafellar and S. Uryasev, Optimization of conditional value-at-risk, Journal of risk 2: 21-42, 2000.
R.G. Stansfield, Statistical theory of DF fixing. Electrical Engineers-Part IIIA: Radiocommunication, Journal of the Institution of 94(15): 762-770, 1947.
I. Toumazis, C. Kwon, and R. Batta, Value-at-Risk and Conditional Value-at-Risk Minimization for Hazardous Materials Routing, Handbook of OR/MS Models in Hazardous Materials Transportation. Springer. New York, 2013.
S. Uryasev, Conditional value-at-risk: Optimization algorithms and applications, Computational Intelligence for Financial Engineering, Proceedings of the IEEE/IAFE/INFORMS 2000 Conference on. IEEE, 2000.
X. Zhu and W.E. Wilhelm, A three-stage approach for the resource-constrained shortest path as a sub-problem in column generation, Computers and Operations Research 39(2): 164-178, 2012.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
