We numerically examine subsurface sensing via an ultra-wideband ground penetrating radar system. The target is assumed to reside under a randomly rough air-ground interface, and is illuminated by a pulsed plane wave. The underlying wave physics is addressed through application of the multiresolution time-domain (MRTD) algorithm. The scattered time-domain fields are parametrized as a random process and an optimal detection scheme is formulated, accounting for the clutter and target signature statistics. Detector performance is evaluated via receiver operating characteristics (ROCs), for variable sensor parameters (polarization and incident angle) and for several rough-surface statistical models.