Cross-Range Scaling Algorithm for ISAR Images Using 2-D Fourier Transform and Polar Mapping

Abstract

This paper proposes a new method that solves the problem of inverse synthetic aperture radar image cross-range scaling by estimating the rotational velocity (RV) using the expansion-rotation-scale relationship between two range-Doppler (RD) images. This method is composed of three steps. The first step is preprocessing to construct 2-D Fourier transform images and initial polar-mapped images. In this step, two RD images are 2-D Fourier transformed to avoid the necessity of finding the rotation center; then, the transformed images are polar mapped with identical polar grids to convert rotation into translation in the theta-direction only. The second step is a coarse search that finds the angular shift that provides the maximum correlation between two polar images. The angular shift found is used as the initial relative rotation angle (RA), and the initial relative scaling factor (RSF) is calculated using the RV which is equal to the angular shift divided by the time delay between the images. The third step is the optimization of the relative RA using the Nelder-Mead approach, with the RSF updated using the relative RA derived during each iteration. In simulations using a Mig-25 aircraft, composed of ideal point scatterers, and the measured data from a Boeing 747-400, the targets were properly rescaled in the range-cross-range domain due to the accurate estimation of the RV.