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Doppler rate is an important parameter in synthetic aperture radar (SAR) signal processing since it affects the SAR image focusing. This paper addresses the problem of Doppler rate estimation for spotlight SAR focused with the TWO-STEP algorithm and an improved shift-and-correlation (SAC) algorithm based on the Radon transform is proposed. Firstly, the original SAC algorithm is carried out to get the correlation peak line (CPL). Then the slope of the CPL is determined by the Radon transform and the CPL is corrected to be vertical using the obtained slope. Since there is no zero padding, aliasing will occur in the Doppler rate estimation and the ambiguity number is got from the CPL's slope. However, when the ambiguity number splits into two numbers the obtained ambiguity number may be wrong. This special case is analyzed in the paper and a trick is introduced to deal with it. The real spotlight SAR data …