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Synthetic aperture radar (SAR) was originally exploited to image stationary scenes. However, it is important to derive target information of velocity for many applications. The fractional Fourier transform (FrFT) is a generalization of the classical Fourier transform and is well-known as a useful tool to estimate the chirp rate of linear frequency-modulated (LFM) signals. Motion compensation is critical to moving target imaging. It is difficult for us to obtain the actual motion parameters in real scenarios. Based on the moving target echo model in airborne along-track interferometric SAR (ATI-SAR) and expression of the ATI phase, a method is proposed to estimate the ship velocity by combining the ATI phase with FrFT. First, we use the FrFT to evaluate the chirp rate of the moving target echo. Then, we construct an equation to estimate the ship velocity using the chirp rate estimation, peak response time, and ATI phase. Finally, the simulation experiments are used to validate the effectiveness of the proposed method.

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