Dual-scale generalized Radon-Fourier transform family for long time coherent integration

Long time coherent integration (LTCI) is to accumulate target's energy through long time integration, which is an effective method for the detection of weak target. However, for a moving target, defocusing can occur due to the range migration (RM) and the Doppler frequency migration (DFM). To address this problem, RM and DFM corrections are required to in order to achieve a well-focused image for the subsequent detection. Due to the RM and DFM are caused by the same motion parameters, the generalized Radon-Fourier transform (GRFT), the optimal correction method, adopts the same searching space of motion parameters in order to eliminate both of these two effects simultaneously, leading to large redundant computation. To this end, this paper firstly proposes a dual-scaled decomposition of the target's motion parameter. Then utilizing this decomposition, the Range-Doppler joint GRFT are degraded into a GIFT process in Range domain and GFT processes in Doppler domain conditioned on the coarse motion parameter. With this appealing property, the joint correction of the RM and DFM effects is decoupled into a cascade procedure, firstly RM correction on the coarse searching space and then the DFM correction on the fine searching spaces, called Dual-Scaled GRFT (DS-GRFT). Compared with the standard GRFT, the proposed DS-GRFT can provide comparable performance while providing significant improvement on computational efficiency. Simulation experiments verify the effectiveness and the efficiency of the proposed method.