Abstract: When detecting high-speed maneuvering targets with radar, their motion characteristics can result in distance walking and Doppler migration, which hinders the accumulation of phase reference. To address the effects of target motion, various motion parameters are searched typically in traditional algorithms which increases computational requirements. In this paper, a fast phase parameter accumulation algorithm for variable acceleration targets based on time reversing transform (TRT)-second-order keystone transform (SKT)-high-order ambiguity function (HAF) is introduced to address the above issues. The SKT and TRT are used to compensate for walking distance. Phase compensation function constructed by HAF estimation of the target acceleration is used to compensate for Doppler migration. The proposed method has a computational complexity that is three orders of magnitude lower than the generalized Radon-Fourier transform, and does not require any parameter search. The simulation results demonstrate that the proposed method reduces the detection threshold by 5 dB in comparison to the Radon-fractional ambiguity function and exhibits superior detection performance at low signal-to-noise ratios.