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For targets with complex motions, such as highly maneuvering airplanes and ships fluctuating with oceanic waves, the Doppler frequencies of scatterers are actually time-varying and azimuth echoes of a range cell have to be modeled as multicomponent cubic phase signals (CPSs) after the range alignment and the phase adjustment. In inverse synthetic aperture radar (ISAR) imaging based on the CPS model, the chirp rate and the quadratic chirp rate are identified as causes of the image defocus. In this paper, by employing a novel parametric symmetric self-correlation function and the keystone transform, an effective estimation algorithm, known as the modified Lv's distribution (MLVD), is presented for the CPS and applied to ISAR imaging of targets with complex motions. The MLVD is simple and can be easily implemented using the complex multiplication, the fast-Fourier transform (FFT), and the inverse FFT (IFFT …