A new tool for multidimensional low-rank STAP filter: Cross HOSVDs

Space Time Adaptive Processing (STAP) is a two-dimensional adaptive filtering technique which uses jointly temporal and spatial dimensions to suppress disturbance. Disturbance contains both the clutter arriving from signal backscattering of the ground and the thermal noise. In practical cases, the STAP clutter can be considered to have a low rank structure, allowing to derive a low rank vector STAP filter, based on the projector onto the clutter subspace. In order to process new STAP applications (MIMO STAP, polarimetric STAP ...) and keeping the multidimensional structure, we propose in this paper a new low-rank tensor STAP filter based on a generalization of the Higher Order Singular Value Decomposition (HOSVD): the Cross-HOSVDs. This decomposition uses at the same time the simple (like polarimetric) and the combined information (for example spatio-temporal). We apply the filter on polarimetric STAP and compute the SNR Loss with Monte-Carlo simulations.