Passive Imaging of Moving Targets Using Sparse Distributed Apertures

We develop a new passive imaging method for moving targets in free space using measurements from a sparse array of receivers that rely on illumination sources of opportunity. Our imaging method consists of a novel passive measurement model for moving targets and an associated image formation method. The passive measurement model for moving targets relates measurements at a given receiver to measurements at other receivers in terms of Doppler and delay based on the physics of wave propagation as well as the statistics of noise. Next, we use this model to address the image formation as a generalized likelihood ratio test for an unknown target position and velocity. The image is formed by using the position- and velocity-resolved test-statistic that is obtained by maximizing the signal-to-noise ratio of the test-statistic. When the discriminant functional is constrained to be linear, the test-statistic can be viewed as the superposition of the filtered, scaled, and delayed correlations of the measurements obtained at different receivers. We analyze the spatial and velocity resolution of the four-dimensional point spread function of our imaging method in terms of the number of receivers and transmitters and the nature of the waveforms of opportunity. We present extensive numerical simulations to demonstrate the performance of our passive moving target imaging method for different numbers of receivers and different types of waveforms of opportunity available in the real world.