This paper addresses the identification problem between the moving targets and deceptive false targets in the presence of the across-range unit (ARU) effect. Specifically, a typical self-defense jammer that generates multiple range-Doppler joint deception false targets within a short period is considered. Based on the radon-Fourier transform (RFT) results of two-dimensional radar echo, the disparity features between the physical and false targets in the output amplitude are first revealed. In this respect, a novel multi-stage RFT processing schema is designed to provide the amplitude characteristic for the under-determined targets. According to the constructed amplitude vector, the variance of the derived amplitude ratio vector is selected as the identification criterion for the proposed multi-stage RFT-based target identification (MSRFT-TI) algorithm. The performance of the proposed method in target identification is evaluated through numerical simulations for two different radar systems. The results indicate that the proposed MSRFT-TI algorithm is effective even in challenging scenarios with a small signal-to-noise ratio (SNR) and large jamming-to-signal ratio (JSR).