Inverse Synthetic Aperture Radar (ISAR) imaging of maneuvering target has received much attention in recent years.In the paper

we first discuss translational motion compensation (TMC)

which is usually decomposed into two steps:envelope alignment and autofocus

and find that the existing envelope alignment algorithms are still effective for not too big maneuvering target whose migration through resolution cells (MTRC) does not take place

but the existing autofocus algorithms are not effective for maneuvering target in practice and in theory.According to coherent summation principle

we propose an iterative coherent summation autofocus (ICSA) algorithm

with PGA being a particular case of ICSA.Then we discuss maneuvering target imaging problem

in fact

which is an instantaneous spectrum estimation problem.Most existing algorithms are only effective when scatterers' echoes are linear frequency modulation (LFM) signals.For the situation when scatterers' time-frequency distribution is not linear

we put forward an adaptive chirplet decomposition method to estimate instantaneous frequency and instantaneous complex amplitude of multi-component polynomial phase signals

and propose a fast adaptive chirplet decomposition imaging (ACDI) algorithm by utilizing "Clean" technique.Real data processing proves that the proposed ICSA algorithm and ACDI algorithm are effective.