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For high-quality synthetic aperture radar (SAR) processing, Doppler centroid estimation is an essential procedure. An incorrect Doppler centroid would cause a loss of signal-to-noise ratio, an increase in the azimuth ambiguity level, and a shift in the location of the target. Based on the analysis of the range migration characteristic of the transmitter-fixed bistatic forward-looking SAR, a geometry-based Doppler centroid estimator is proposed in this letter. By searching for the range walk slope based on the minimum entropy, this method estimates the unambiguous Doppler centroid directly. Simulations validate the effectiveness of this method.