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Aircraft routing under the risk of detection

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  • Michael Zabarankin
  • Stan Uryasev
  • Robert Murphey

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

Suggested Citation

  • Michael Zabarankin & Stan Uryasev & Robert Murphey, 2006. "Aircraft routing under the risk of detection," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(8), pages 728-747, December.
    • Handle: RePEc:wly:navres:v:53:y:2006:i:8:p:728-747
    DOI: 10.1002/nav.20165
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    References listed on IDEAS

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    3. Refael Hassin, 1992. "Approximation Schemes for the Restricted Shortest Path Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 36-42, February.
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    Cited by:

    1. Hailong Huang & Andrey V. Savkin & Wei Ni, 2020. "Energy-Efficient 3D Navigation of a Solar-Powered UAV for Secure Communication in the Presence of Eavesdroppers and No-Fly Zones," Energies, MDPI, vol. 13(6), pages 1-12, March.

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