A robust optimal search tactic for targets with mirror symmetry


  1. Nguyen, B.
  2. Bourque, A.
  3. Hill, A.
Corporate Authors
Defence R&D Canada - Centre for Operational Research and Analysis, Ottawa ON (CAN)
In this paper, we propose a globally optimal strategy to detect a target in a mine hunting operation or in a search & rescue mission. We assume that the target exhibits mirror symmetry, i.e., that the left hand side of a target is the mirror image of the right hand side of the same target. In addition, it is assumed that the cross section is maximal at the interface between the left hand side and the right hand side and decreases monotonically as we move away from the interface. The optimal strategy consists of choosing n aspect angles to inspect a target to ensure that the probability of detection is maximal. This is generally an NP-hard problem in the sense that to find the optimal angles in n dimensions normally consumes a lot of computational power. Fortunately, in this problem, we are use a novel combination of variational calculus, symmetry principles, number theory and algebra to determine analytically the globally optimal angles. What is more, we derive the underlying group symmetry of the solutions. The solutions will help the operators plan for an effective strategy in a mine hunting operation or in a search and rescue mission. Such a strategy is robust as most targets of interest possess approximate mirror symmetry along one or more axes. For example, a human body or a canoe or a mine when cut in half yield approximately such symmetry. This work could inform the way mine hunting operations and search and rescue missions are conducted by recognizing the importance o

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search and detection;search and rescue;mine hunting;symmetry;mirror symmetry;look;angles;multiple looks;global optimization;variational calculus;number theory;group theory;algebra;roots
Report Number
DRDC-CORA-TM-2013-250 — Technical Memorandum
Date of publication
01 Apr 2013
Number of Pages
Electronic Document(PDF)

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