Abstract: High-speed, low-observable, and maneuvering target detection is always the difficult problem for the early warning and detection of space target, ballistic target, and passive radar signal processing. The high-order motion information of maneuvering target is employed in this paper, such as acceleration and jerk, and two long-time coherent integration methods are proposed, i.e., Radon-fractional Fourier transform (RFRFT) and Radon fractional ambiguity function (RFRAF). The proposed methods can compensate the across range unit (ARU) and Doppler frequency migration (DFM) effects simultaneously during the long-time integration. The background clutter and noise can be well suppressed with higher integration gain. Experiment results using real radar data indicate that the coherent integration performance of the proposed methods is better than that of classical moving target detection (MTD), and ability of weak maneuvering target detection in strong clutter background.