  Long Time Coherent Integration (LTCI) aims to accumulate target energy
through long time integration, which is an effective method for the detection
of a weak target. However, for a moving target, defocusing can occur due to
range migration (RM) and Doppler frequency migration (DFM). To address this
issue, RM and DFM corrections are required in order to achieve a well-focused
image for the subsequent detection. Since RM and DFM are induced by the same
motion parameters, existing approaches such as the generalized Radon-Fourier
transform (GRFT) or the keystone transform (KT)-matching filter process (MFP)
adopt the same search space for the motion parameters in order to eliminate
both effects, thus leading to large redundancy in computation. To this end,
this paper first proposes a dual-scale decomposition of the target motion
parameters, consisting of well designed coarse and fine motion parameters.
Then, utilizing this decomposition, the joint correction of the RM and DFM
effects is decoupled into a cascade procedure, first RM correction on the
coarse search space and then DFM correction on the fine search spaces. As such,
step size of the search space can be tailored to RM and DFM corrections,
respectively, thus avoiding large redundant computation effectively. The
resulting algorithms are called dual-scale GRFT (DS-GRFT) or dual-scale GRFT
(DS-KTMFP) which provide comparable performance while achieving significant
improvement in computational efficiency compared to standard GRFT (KT-MFP).
Simulation experiments verify their effectiveness and efficiency.
