Computation of most threatening radar trajectories areas and corridors based on fast-marching & Level Sets

We propose to use new shortest path computation methods based on Front propagation with Level Set approach for a radar application. This new radar function consists in computing most threatening trajectories & corridors in the radar coverage in order to adapt radar modes for detection optimization. This Radar problem may be declined as a variationnal problem solved by calculus of variations and front propagation based on an adaptation of Fermat´s principle of least time with an Hamilton-Jacobi formulation. A partial differential equation PDE drives the temporal evolution of contours of constant action (level lines of the manifold defined by the minimal potential surface given by the integration of a local function of the detection probability along every potential trajectories). The orthogonality between geodesics (shortest path) and curves of iso-action provides a simple numerical scheme for geodesics computation based on a steepest gradient descent algorithm (backtracking on the level-lines of iso-action). We underline the analogy of this radar problem with Feynman/Schwinger´s principle that states close connexion between variational principle and quantum theory. Finally, we have extended the problem to anisotropic constraint induced by Radar Cross Section.