This paper addresses the non-iterative quality phase gradient autofocus (QPGA) technique which was originally proposed to remove one-dimensional phase errors in spotlight-mode synthetic aperture radar (SAR) imagery. By enriching the source pool, the method is modified in a way suitable for autofocus in stripmap-mode SAR system with the advantage of being independent of any priori assumptions. Unlike the QPGA the potential candidates, i.e., dominant scatterers located along azimuth in each specific range bin, are automatically selected by exploiting the one-dimensional RELAX algorithm. Furthermore, RELAX is capable of estimating the size of blur window which is, in fact, associated with the Doppler spread of signal spectrum. The corresponding model includes four parameters i.e., complex amplitude, delay, Doppler center and spectral width. The proposed method has been applied to data extracted by a ground-based rotating coherent Doppler radar operating in strip-mapping mode SAR, with the aim of high-resolution clutter detection.