This talk describes an applications problem originating from Australia’s Defence Science and Technology Organization, in which a variety of modeling and optimization issues present themselves. For a flying military vehicle, in many scenarios avoiding detection is a key objective. Given a field of heterogeneous detectors such as radars in fixed positions, flying the least probability of detection path through the field of detectors is a fundamental strategy. Most previous optimization methods for this problem have sought to minimize cumulative radar exposure; in contrast, we consider a formulation that directly minimizes the probability of detection. We show how a variational dynamic programming method can be applied to this model to allow one to find a locally optimal path with low computational complexity, and then extend the idea in two directions. First, using homotopy methods, we consider how the vehicle can cope with adjustments to the detector field, resulting from introduction or removal of detectors, or changes of sensitivity. Then we consider the effect of taking Doppler measurements into account. This poses a challenge both in terms of modeling, and an increase in the dimension of the problem.

From the point of view of those seeking to detect the vehicle, the positioning of sensor assets is important. The talk considers how this can be done when the vehicle whose detection is desired optimizes its path. A relaxed version of the positioning problem can be formulated as a convex optimization problem and used to determine optimal or close-to-optimal detector positions.