Statistical Detection of Coordination in a Cognitive Radar Network through Inverse Multi-objective Optimization

Abstract: Consider a target being tracked by a cognitive radar network. If the target can intercept noisy radar emissions, how can it detect coordination in the radar network? By 'coordination' we mean that the radar emissions satisfy Pareto optimality with respect to multi-objective optimization over the objective functions of each radar and a constraint on total network power output. This paper provides a novel inverse multi-objective optimization approach for statistically detecting Pareto optimal ('coordinating') behavior, from a finite dataset of noisy radar emissions. Specifically, we develop necessary and sufficient conditions for radar network emissions to be consistent with multi-objective optimization (coordination), and we provide a statistical detector with theoretical guarantees for determining this consistency when radar emissions are observed in noise. We also provide numerical simulations which validate our approach. Note that while we make use of the specific framework of a radar network coordination problem, our results apply more generally to the field of inverse multi-objective optimization.