Generalized Correlation-Based Imaging for Satellites

We consider imaging of fast moving small objects in space, such as low earth orbit satellites or satellite debris. The imaging system consists of ground based, asynchronous sources of radiation and several passive receivers above the dense atmosphere. We use the cross correlation of the received signals to reduce distortions from ambient medium fluctuations. Imaging with correlations also has the advantage of not requiring any knowledge about the probing pulse and depends weakly on the emitter positions. We account for the target's orbital velocity by introducing the necessary Doppler compensation. We show that over limited imaging regions, a constant Doppler factor can be used, resulting in an efficient data structure for the correlations of the recorded signals. We then investigate and analyze different imaging methods using the cross-correlation data structure. Specifically, we show that using a generalized two-point migration of the cross-correlation data, the top eigenvector of the migrated data matrix provides superior image resolution compared to the usual single-point migration scheme. We carry out a theoretical analysis that illustrates the role of the two-point migration methods as well as that of the inverse aperture in improving resolution. Extensive numerical simulations support the theoretical results and assess the scope of the imaging methodology.