Fast Implementation of Generalized Radon–Fourier Transform

The existing generalized Radon–Fourier transform (GRFT) algorithm can achieve coherent integration of high-order maneuvering targets by jointly searching in multiple dimensions, but it has high computational complexity. This article proposes a fast algorithm for the GRFT. We consider a maneuvering target with complex motions, where the jerk results in the third-order range migration (TRM) and the third-order Doppler migration (TDM). The echo data are segmented to allow the TRM, and the TDM of each segment is ignorable. In doing so, the jerk in each segment can be estimated by the second-order Radon–Fourier transform, which is used to compensate for the gain loss due to the ignoring of jerk. The final integration result can then be obtained by accumulating the results in all segments. Since the jerk does not need to be searched in the proposed algorithm, the computational complexity of the proposed algorithm is much lower than that of the standard GRFT.