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Time-frequency rate distribution (TFRD) indicates the characteristics of instantaneous frequency rate (IFR) of a signal. This paper proposed a method based on time-frequency rate distribution to estimate Doppler frequency rate by analyzing the linear frequency-modulated (LFM) characteristics of synthetic aperture radar (SAR) echo in the azimuth direction. This method can be applied to low signal-to-noise ratio (SNR) situation with high estimation precision. Simulation and practical results show the effectiveness of the method.