Geometric barycenters of time/Doppler spectra for the recognition of non-stationary targets

We are interested in non-stationary targets, and represent their time/Doppler spectra in the form of curves tracing the evolution of the non-stationarity of the radar signal. We explain how to use this representation for Non Cooperative Target Recognition (NCTR) of helicopter signatures. The signature of reference used to recognize a specific type of helicopter is represented by the average curve over multiple simulations where we slightly vary certain parameters, such as the rotation speed of the blades, to model the hazards of real situations. The curves that we consider lie in the statistical manifold of centered stationary Gaussian distributions. In order to compare or average different signatures, the space of such curves is equipped with a metric and seen as a Riemannian manifold. We give algorithms to effectively compute distances and mean curves using this metric.