An autofocusing technique is proposed, based on the modelling of the instantaneous phase, induced by the relative radar/target motion, as a generic order polynomial and on the estimation of the polynomial coefficients by the so-called product high-order ambiguity function. The proposed estimation method is able to deal with multicomponent signals and is robust against model order mismatching, provided that the selected order is greater than the true order. The proposed method is compared with the phase gradient autofocusing method, and applications are presented of focusing of extended scenes and detection and imaging of moving targets