Sparse reconstruction of equivalence classes of moving targets using single-channel synthetic aperture radar

Simultaneously estimating position and velocity of moving targets using only phase information from single-channel SAR data is impossible. This paper defines classes of equivalent target motion and solves the GMTI problem up to membership in an equivalence class using single-channel SAR phase data. We present a definitions for endo- and exo-clutter that is consistent with the equivalence classes, and show that most target motion can be detected, i.e. the set of endo-clutter targets is very small. We exploit the sparsity of moving targets in the scene to develop an algorithm to resolve target motion up to membership in an equivalence class, and demonstrate the effectiveness of the proposed technique using simulated data.