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To solve the parameter estimation problem of accelerating target in LFMCW (linear frequency-modulated continuous wave) radar while MTRC (migration through range cell) occurs, a direct phase differentiation method is proposed. By direct phase differentiation operation along the slow time dimension, the linear coupling of fast time and slow time is successfully removed, as well as the phase order reduction of the slow time dimension. Two dimensional FFT (fast Fourier transform) processing is carried out to the differentiated signal, and acceleration estimation can be achieved, along with the coarse estimation of the initial velocity. Then the up-sweep and down-sweep beat signals are multiplied by the compensation functions which are constructed based on the estimated parameters, respectively, and initial range and velocity can be accurately obtained through decoupling operation. Detail performances are analyzed, including the acceleration resolution, the maximum unambiguous acceleration and the SNR (signal-to-noise ratio) improvement factor. It shows that the proposed method has lower SNR threshold than secondary mixing combined DPT (discrete polynomial-phase transform) processing. Simulation results testify the efficiency of the method.