A Riemannian approach for training data selection in Space-Time Adaptive Processing applications

Heterogeneous situations are a serious problem for Space-Time Adaptive Processing (STAP) in an airborne radar context. Indeed, STAP detectors need secondary training data that have to be homogeneous with the tested data, otherwise the performances of these detectors are severely impacted when facing heterogeneous environments. Hence, training data have to be carefully selected and this is traditionally done in Euclidean geometry. We introduce a new criterion for data selection. We show that it can be viewed as an approximation of the metric distance in Riemannian geometry.