This paper considers the coherent integration problem for maneuvering target detection and motion parameters estimation, involving range migration (RM) and Doppler frequency migration (DFM) within the coherent pulse interval. A fast non-searching method based on adjacent cross correlation function (ACCF) and Lv's distribution (LVD) is proposed, where the adjacent correlation operation is first employed to remove the RM and reduce the order of DFM. After that, LVD is applied to realize the coherent integration, target detection and parameters estimation. In addition, at the cost of some performance loss, another fast method via ACCF iteratively is also introduced to further reduce the computational complexity and obtain the motion parameters estimation. The proposed two methods are fast in that they can be easily implemented by using complex multiplications, the fast Fourier transform (FFT) and inverse FFT (IFFT). Compared with the existing methods, the presented algorithms can obtain the motion parameters estimation without any searching procedure and can achieve a good balance between the computational cost and the detection ability as well as parameters estimation performance. Finally, several simulation experiments are provided to demonstrate the effectiveness.