Impact of temporal Doppler on synthetic aperture sonar imagery

Synthetic Aperture Sonar (SAS) coherently processes the acoustic data acquired along a linear trajectory. The imaging process is in essence an inverse problem where the reflectivity of the seafloor has to be estimated. Several imaging algorithms have been proposed over the years including back-projection algorithms. One commonly assumed hypothesis, however, is that the antenna is motionless during transmission and reception. This hypothesis is known as the start-stop assumption. This paper questions the validity of this assumption, and proposes a full derivation of the SAS processing taking into account the vehicle motion by using the Lorentz transformation. The cell migration for the SAS system is computed and the validity limit of the stop-start assumption depending on the SAS system parameters is derived. Numerical examples of start-stop assumption violations are given and the Doppler cell migration correction on real SAS data are presented and discussed.