A synthetic aperture radio/inverse synthetic aperture radar (SAR/ISAR) coherent system model and inversion to image a target moving with an unknown constant velocity in a stationary background are presented. The approach is based on a recently developed system modelling and inversion principle for SAR/ISAR imaging that utilizes the spatial Fourier decomposition of SAR data in the synthetic aperture domain to convert the SAR system model's nonlinear phase functions into linear phase functions suitable for a computationally manageable inversion. It is shown that SAR/ISAR imaging of a moving target can be converted into imaging the target in a stationary squint-mode SAR problem where the parameters of the squint-mode geometry depend on the target's velocity. A method for estimating the moving target's velocity that utilizes a spatial Doppler analysis of the SAR data within overlapping subapertures is presented. The spatial Doppler technique does not require the radar signal to be narrowband, so the reconstructed image's resolution is not sacrificed to improve the target's velocity estimator.