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This paper considers the coherent integration problem for a maneuvering target with complex motions, where the velocity, acceleration, and jerk result in respectively the first-order range migration (FRM), second-order range migration (SRM), and third-order range migration (TRM) within the coherent pulse interval. A new coherent integration algorithm based on generalized keystone transform (KT) and second-order dechirp process is proposed, which employs the third-order KT, six-order KT, second-order KT, and fold factor searching to correct the TRM, SRM, and FRM, respectively. The range migration change during each step and computational complexity are also theoretically analyzed. Compared with the generalized Radon Fourier transform (GRFT) algorithm, the presented method can avoid the blind speed sidelobe (BSSL) and acquire close integration performance but with much lower computational cost. Simulations are provided to demonstrate the effectiveness. Finally, a generalized method, named generalized KT and generalized dechirp process (GKTGDP), is also introduced for the maneuvering target with arbitrary high-order range migration. [ABSTRACT FROM PUBLISHER]