Divergence measures and detection performance for dispersive targets in SAR

When electromagnetic waves impinge on objects with complex geometries and/or internal structure, we can observe scattering that is distributed in time rather than instantaneous. To detect and characterize such targets, we build the coordinate-delay synthetic aperture radar (cdSAR) images by adding a delay term to the standard SAR matched filter. In order to apply this approach to the case of extended targets where the image intensity and phase are subject to strong and rapid variations (the phenomenon called speckle), we sample the cdSAR image at several coordinate-delay “points” in the vicinity of the scatterer location. The discrimination between the instantaneous and delayed targets is realized through auto correlation analysis of this sample. Because of the statistical properties of speckle, misclassification errors are inevitable. Hence, prediction of the error rate as a function of system and target parameters becomes an important problem. While Monte Carlo simulations can generate the ensembles of data for direct calculation of the error rate, this approach is computationally demanding because of its slow convergence. In order to simplify the prediction of the error rate, we employ statistical divergence measures, namely, the Hellinger distance and Kullback-Leibler divergence. These divergence measuresare calculated directly from the theoretical models of reflectivity of extended targets that we want to distinguish. We empirically establish a linear relation between the misclassification rate and the Hellinger distance for a certain class of simple target models. This relation allows us to make predictions of the error rate without performing the Monte Carlo simulations.