Information geometry for radar detection in heterogeneous environments
Résumé
Space-Time Adaptive Processing (STAP) performs two-dimensional space and time adaptive filtering where different space channels are combined at different times. In the context of radar signal processing, the aim of STAP is to remove ground clutter returns, in order to enhance slow moving target detection. Filters weights are adaptively estimated from training data in the neighborhood of the range cell of interest, called cell under test (CUT). The estimation of these weights is always deduced, more or less directly, from an estimation of the covariance matrices of the received signal, which is the key quantity in the process of adaptation. This STAP method is usually referred to as the sample matrix inversion (SMI). One main consideration goes into the choice of the training covariance matrices: how many and which matrices share the same statisticswith the matrix of the cell under test. On one hand, the statistics of the clutter often change rapidly and, on the other hand, we want to use as many matrices as possible to obtain a good estimate of the covariance matrix that minimizes the estimation loss. The traditional way to answer these questions is to use the Euclidean distance which relies on a power selection criterion. One can clearly see that this method, which works only on the signal power of the covariance matrix, does not take advantage of the structure of the covariance matrix. We propose in this paper a new criterion based on a physical point of view and look for the distance that fits to the minimization problem of the STAP filter.We show that this distance outperforms the classical Euclidian distance.We extend this distance to the Riemannian distance. When working on Hermitian positive-definite matrices, it is natural and desirable to work with the information geometry metric. We show that the distance associated with the information geometry metric performs very well in detecting clutter nonhomogeneity and we compare two processing using both the classical Euclidian and information geometry metric based on the Riemannian distance. These results lead to the hypothesis that information geometry may also be used for the computation of the mean of the selected covariance matrices, enabling better performance for target detection in heterogeneous environments.