Netted Multi-Function Radars Positioning and Modes Selection by Non-Holonomic Fast Marching Computation of Highest Threatening Trajectories & by CMA-ES Optimization

We aim to design a radar network which maximizes the detection probability of the worst threatening trajectory to reach a protected area. In game theory, we represent this problem as a non-cooperative zero-sum game: a first player chooses a setting for the network, and the other player chooses a trajectory from the admissible class of trajectories with full information over the network. The players’ objective is respectively to maximize and minimize the path cost which is the detection probability integrated along the trajectory in the network. In comparison with previous works, we added ambiguity maps depending on the distance and the radial speed, which are functions of internal parameters of the radars that can be optimized: PRI (Pulse Repetition Interval) and frequency. We also take into account RCS (Radar Cross Section) and a complex geometry with masks deduced from DEM (Digital Elevation Map) and Earth curvature. The computation of optimal trajectories is performed with a specialized variant of the Fast-Marching algorithm, devoted to computing curves that globally minimize an energy featuring both a data driven term and a second order curvature penalizing term. The profile of the cost function with regard to the direction of movement is non-convex, which is significant only with a curvature penalization: we chose the Dubins model, in which the curvature radius is bounded. We illustrate results on different Use-Cases.