Theory of arbitrary rigid object motion autofocus for non‐uniform target rotation and translation

Moving targets in synthetic aperture radar (SAR) imagery often yield signatures that are smeared beyond recognition. One mitigation strategy is to attempt to refocus such smears as if the corresponding targets were stationary. This problem is especially difficult for cases in which the target executes time‐varying rotation rates for roll, pitch and yaw, as well as for simultaneous non‐linear target translational motion. The current analysis develops an arbitrary rigid object motion autofocus (AROMA) for performing automatic refocus of such targets having non‐uniform rotation and translation profiles. AROMA uses a maximum likelihood signal‐theoretic analysis of the physical rotation angles and translation distances arising from the unknown rigid object motions in order to generate refocused target imagery. The efficacy of this methodology is demonstrated via the injection of a simulated rotating and translating target comprised of multiple scattering centres into a cluttered background of measured Ku‐band SAR data. Furthermore, the application of AROMA to an input defocused smear corresponding to a ‘target‐of‐opportunity’ vehicle in measured Ka‐band SAR imagery yields significant improvement in the target focus, thus further validating the underlying theoretical analysis developed herein.