Passive imaging of moving targets exploiting multiple scattering using sparse distributed apertures

We present a new passive imaging method for moving targets using a sparse array of receivers and illumination sources of opportunity operating in multiple-scattering environments. We assume that the receivers are spatially distributed in an arbitrary fashion and the illumination sources of opportunity are non-cooperative where the locations of the transmitters and transmitted waveforms are unknown. Our method is capable of exploiting the multiple scattering in the environment. We use a physics-based and statistical approach to develop a model under Born approximation that relates the measurements at a given receiver to measurements at other receivers in terms of a hypothetical target in position and velocity spaces, the Green function of the background environment, as well as the statistics of the target, clutter and noise. Next, we use this model to formulate the imaging problem as a test of binary hypotheses for unknown target position and velocity, and address it by maximizing the signal-to-noise ratio of the test statistic. We use the resulting test statistic to form an image in position and velocity spaces. We illustrate our imaging method and analyze its resolution using a first-order specular reflection-based model of the Green function suitable for urban environments throughout the paper. We present numerical experiments to verify our theory and to demonstrate the performance of our method using practical waveforms of opportunity. While our primary interest is in radar imaging, our method can also be applied to passive acoustic and geophysical imaging.