  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.
