Aircraft routing under the risk of detection

  1. Michael Zabarankin1,*,
  2. Stan Uryasev2,
  3. Robert Murphey3

Article first published online: 8 JUN 2006

DOI: 10.1002/nav.20165

Issue

Naval Research Logistics (NRL)

Naval Research Logistics (NRL)

Volume 53, Issue 8, pages 728–747, December 2006

Additional Information

How to Cite

Zabarankin, M., Uryasev, S. and Murphey, R. (2006), Aircraft routing under the risk of detection. Naval Research Logistics (NRL), 53: 728–747. doi: 10.1002/nav.20165

Author Information

  1. 1

    Department of Mathematical Sciences, Stevens Institute of Technology, Castle Point on Hudson, Hoboken, New Jersey 07030

  2. 2

    ISE Department, University of Florida, P.O. Box 116595, 303 Weil Hall, Gainesville, Florida 32611-6595

  3. 3

    Air Force Research Lab, Munitions Directorate, Eglin Air Force Base

*Department of Mathematical Sciences, Stevens Institute of Technology, Castle Point on Hudson, Hoboken, New Jersey 07030

Publication History

  1. Issue published online: 19 OCT 2006
  2. Article first published online: 8 JUN 2006
  3. Manuscript Accepted: 21 APR 2006
  4. Manuscript Revised: 14 APR 2006
  5. Manuscript Received: 10 APR 2005

Funded by

  • Air Force. Grant Number: F49620-01-1-0338

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Keywords:

  • trajectory optimization;
  • optimal path planning;
  • risk minimization;
  • risk of detection;
  • analytical solution;
  • network optimization;
  • network optimization algorithm;
  • Calculus of Variations;
  • aircraft;
  • radar cross-section

Abstract

The deterministic problem for finding an aircraft's optimal risk trajectory in a threat environment has been formulated. The threat is associated with the risk of aircraft detection by radars or similar sensors. The model considers an aircraft's trajectory in three-dimensional (3-D) space and represents the aircraft by a symmetrical ellipsoid with the axis of symmetry directing the trajectory. Analytical and discrete optimization approaches for routing an aircraft with variable radar cross-section (RCS) subject to a constraint on the trajectory length have been developed. Through techniques of Calculus of Variations, the analytical approach reduces the original risk optimization problem to a vectorial nonlinear differential equation. In the case of a single detecting installation, a solution to this equation is expressed by a quadrature. A network optimization approach reduces the original problem to the Constrained Shortest Path Problem (CSPP) for a 3-D network. The CSPP has been solved for various ellipsoid shapes and different length constraints in cases with several radars. The impact of ellipsoid shape on the geometry of an optimal trajectory as well as the impact of variable RCS on the performance of a network optimization algorithm have been analyzed and illustrated by several numerical examples. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

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